丸吉 一暢

Abstract We propose a new dual description of four-dimensional $$ \mathcal{N} $$ = 1 SU(N) gauge theory with one adjoint (X) and N_f fundamental matters with a superpotential W = TrX^p+1. The dual theory consists of the $$ \mathcal{D} $$_p[SU(N)] Argyres-Douglas theory coupled to SU(N) gauge theory and N_f fundamentals with a superpotential deformation. We study renormalization group fixed points of the Argyres-Douglas dual theories with and without superpotential deformations, and identify the conditions for them to be dual to the fixed points of adjoint SQCD. We check our proposal via matching central charges, chiral operators and superconformal indices. We find that when N_f = 2N and p = 2, the dual theory flows to $$ \mathcal{N} $$ = 2 SU(N) superconformal QCD with 2N flavors upon suitable superpotential deformation, exhibiting supersymmetry enhancement.

Abstract When simulating the time evolution of quantum many-body systems on a digital quantum computer, one faces the challenges of quantum noise and of the Trotter error due to time discretization. For certain spin chains, it is possible to discretize the time evolution preserving integrability, so that an extensive set of conserved charges are exactly conserved after discretization. In this work we implement, on real quantum computers and on classical simulators, the integrable Trotterization of the spin-$1/2$ Heisenberg XXX spin chain. We study how quantum noise affects the time evolution of several conserved charges, and observe the decay of the expectation values. We in addition study the early time behaviors of time evolution, which can potentially be used to benchmark quantum devices and algorithms in the future. We also provide an efficient method to generate the conserved charges at higher orders.

<title>A<sc>bstract</sc> </title>We establish a correspondence between a class of Wilson-’t Hooft lines in four-dimensional <inline-formula><alternatives><tex-math>$$ \mathcal{N} $$</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math></alternatives></inline-formula> = 2 supersymmetric gauge theories described by circular quivers and transfer matrices constructed from dynamical L-operators for trigonometric quantum integrable systems. We compute the vacuum expectation values of the Wilson-’t Hooft lines in a twisted product space <italic>S</italic>¹ × _{<italic>ϵ</italic>} ℝ² × ℝ by supersymmetric localization and show that they are equal to the Wigner transforms of the transfer matrices. A variant of the AGT correspondence implies an identification of the transfer matrices with Verlinde operators in Toda theory, which we also verify. We explain how these field theory setups are related to four-dimensional Chern-Simons theory via embedding into string theory and dualities.

We explore the space of renormalization group flows that originate from<br /> $\mathcal{N}=1$ supersymmetric $SU(2)$ gauge theory with one adjoint and a pair<br /> of fundamental chiral multiplets. By considering all possible relevant<br /> deformations - including coupling to gauge-singlet chiral multiplets - we find<br /> 34 fixed points in this simple setup. We observe that theories in this class<br /> exhibit many novel phenomena: emergent symmetry, decoupling of operators, and<br /> narrow distribution of central charges $a/c$. This set of theories includes two<br /> of the $\mathcal{N}=2$ minimal Argyres-Douglas theories and their mass deformed<br /> versions. In addition, we find 36 candidate fixed point theories possessing<br /> unphysical fermionic operators -including one with central charges $(a,<br /> c)\simeq (0.20, 0.22)$ that are smaller than any known superconformal theory<br /> -that need further investigation.

We find an N= 1 gauge theory that flows to the rank-one N= 2 superconformal field theory with E7 flavor symmetry. We first obtain a Lagrangian description for the R0,N theory, which appears in the S-dual description of the SU(N) gauge theory with 2N fundamental hypermultiplets. This is a straightforward generalization of the proposed Lagrangian description for the E6 theory. The E7 theory is then obtained via partial Higgsing of the R0,4 theory. From this Lagrangian description, we compute the full superconformal index. We also consider twisted dimensional reduction on S2 to obtain N= (0 4) theory for the E7 one instanton string and compute its elliptic genus.

We study the quantization of Hitchin systems in terms of β-deformations of generalized matrix models related to conformal blocks of Liouville theory on punctured Riemann surfaces. We show that in a suitable limit, corresponding to the Nekrasov–Shatashvili one, the loop equations of the matrix model reproduce the Hamiltonians of the quantum Hitchin system on the sphere and the torus with marked points. The eigenvalues of these Hamiltonians are shown to be the ϵ1-deformation of the chiral observables of the corresponding N= 2 four dimensional gauge theory. Moreover, we find the exact wave-functions in terms of the matrix model representation of the conformal blocks with degenerate field insertions.

We elucidate the relation between Painlev\&#039;e equations and four-dimensional<br /> rank one ${\cal N= 2}$ theories by identifying the connection associated to<br /> Painlev\&#039;e isomonodromic problems with the oper limit of the flat connection of<br /> the Hitchin system associated to gauge theories and by studying the<br /> corresponding renormalisation group flow. Based on this correspondence we<br /> provide long-distance expansions at various canonical rays for all Painlev\&#039;e<br /> functions in terms of magnetic and dyonic Nekrasov partition functions for<br /> ${\cal N= 2}$ SQCD and Argyres-Douglas theories at self-dual Omega background<br /> $\epsilon_1+\epsilon_2= 0$, or equivalently in terms of $c= 1$ irregular<br /> conformal blocks.

Compactifying N=(1,0) theories on a torus, with additional fluxes for global<br /> symmetries, we obtain N=1 supersymmetric theories in four dimensions. It is<br /> shown that for many choices of flux these models are toric quiver gauge<br /> theories with singlet fields. In particular we compare the anomalies deduced<br /> from the description of the six-dimensional theory and the anomalies of the<br /> quiver gauge theories. We also give predictions for anomalies of<br /> four-dimensional theories corresponding to general compactifications of<br /> M5-branes probing C_2/Z_k singularities.

We find a four-dimensional N = 1 gauge theory which flows to the minimal interacting N = 2 superconformal field theory, the Argyres-Douglas theory, in the infrared up to the extra free chiral multiplets. The gauge theory is obtained from a certain N = 1 preserving deformation of the N = 2 SU(2) gauge theory with four fundamental hypermultiplets. From this description, we compute the full superconformal index and find agreements with the known results in special limits.

We study certain N = 1 preserving deformations of four-dimensional N = 2 superconformal field theories (SCFTs) with non-abelian flavor symmetry. The deformation is described by adding an A = 1 chiral multiplet transforming in the adjoint representation of the flavor symmetry with a superpotential coupling, and giving a nilpotent vacuum expectation value to the chiral multiplet which breaks the flavor symmetry. This triggers a renormalization group flow to an infrared SCFT. Remarkably, we find classes of theories flow to enhanced N = 2 supersymmetric fixed points in the infrared under the deformation. They include generalized Argyres-Douglas theories and rank-one SCFTs with non-abelian flavor symmetries. Most notably, we find renormalization group flows from the deformed conformal SQCDs to the (A(1), A(n)) Argyres-Douglas theories. From these "Lagrangian descriptions," we compute the full superconformal indices of the (A(1), A(n)) theories and find agreements with the previous results. Furthermore, we study the cases, including the T-N and RON theories of class S and some of rank-one SCFTs, where the deformation gives genuine N = 1 fixed points.

We continue to investigate the N = 1 deformations of four-dimensional N = 2 superconformal field theories (SCFTs) labeled by a nilpotent element of the flavor symmetry [1]. This triggers a renormalization group (RG) flow to an N = 1 SCFT. We systematically analyze all possible deformations of this type for certain classes of N = 2 SCFTs: conformal SQCDs, generalized Argyres-Douglas theories and the E-6 SCFT. We find a number of examples where the amount of supersymmetry gets enhanced to N = 2 at the end point of the RG flow. Most notably, we find that the SU(N) and Sp(N) conformal SQCDs can be deformed to flow to the Argyres-Douglas (AD) theories of type (A(1), D2N-1) and (A(1), D-2N) respectively. This RG flow therefore allows us to compute the full superconformal index of the (A(1), D-N) class of AD theories. Moreover, we find an infrared duality between N = 1 theories where the fixed point is described by an N = 2 AD theory. We observe that the classes of examples that exhibit supersymmetry enhancement saturate certain bounds for the central charges implied by the associated two-dimensional chiral algebra.

The supersymmetric index of the 4D N = 1 theory realized by a brane tiling coincides with the partition function of an integrable 2D lattice model. We argue that a class of half-BPS surface defects in brane tiling models are represented on the lattice model side by transfer matrices constructed from L-operators. For the simplest surface defects in theories with SU(2) flavor groups, we identify the relevant L-operator as that discovered by Sklyanin in the context of the eight-vertex model. We verify this identification by computing the indices of class-S and -Sk theories in the presence of the surface defects.

We study a class of four-dimensional N = 1 superconformal field theories obtained from the six-dimensional (1, 0) theory, on M5-branes on C-2/Z(k) orbifold singularity, compactified on a Riemann surface. This produces various quiver gauge theories whose matter contents are chiral. We classify the building blocks associated to pairs-of-pants, and study the gauging of them as the gluing of punctures. The Riemann surface picture makes the duality invariance of the resulting quiver theories manifest: the theories associated to the same Riemann surface flow to the same nontrivial infrared fixed point. We explicitly check this from the 't Hooft anomalies of the global symmetries and central charges.

We study a class of four-dimensional N = 1 superconformal field theories obtained by wrapping M5-branes on a Riemann surface with punctures. We identify four-dimensional UV descriptions of the SCFTs corresponding to curves with a class of punctures. The quiver tails appearing in these UV descriptions differ significantly from their N = 2 counterpart. We find a new type of object that we call the 'Fan'. We show how to construct new N = 1 superconformal theories using the Fan. Various dual descriptions for these SCFTs can be identified with different colored pair-of-pants decompositions. For example, we find an N = 1 analog of Argyres-Seiberg duality for the SU(N ) SQCD with 2N flavors. We also compute anomaly coefficients and superconformal indices for these theories and show that they are invariant under dualities.

We demonstrate that the supersymmetry can be dynamically broken even in theories without a Lagrangian. The example we study is the four-dimensional SU(N) gauge theory coupled to a strongly coupled superconformal theory, called TN, which does not have a Lagrangian description at present. Such a theory without Lagrangians can be analyzed due to the supersymmetry and duality. The model is a direct generalization of the model of supersymmetry breaking on deformed moduli space in supersymmetric QCD with an SU(2) gauge group. © 2013 American Physical Society.

We study the dynamics of N = 1 supersymmetric systems consisting of the strongly-coupled superconformal theory T-N, SU(N) gauge groups, and fundamental chiral multiplets. We demonstrate that such systems exhibit familiar phenomena such as deformation of the vacuum moduli space, appearance of the dynamical superpotential, and Coulomb branches with N = 1 Seiberg-Witten curves. The analysis requires a rather detailed knowledge of the chiral ring of the T-N theory, which will also be discussed at length.

We provide an M-theory geometric set-up to describe four-dimensional N = 1 gauge theories. This is realized by a generalization of Hitchin's equation. This framework encompasses a rich class of theories including superconformal and confining ones. We show how the spectral data of the generalized Hitchin's system encode the infrared properties of the gauge theory in terms of N = 1 curves. For N = 1 deformations of N = 2 theories in class S, we show how the superpotential is encoded in an appropriate choice of boundary conditions at the marked points in different S-duality frames. We elucidate our approach in a number of cases - including Argyres-Douglas points, confining phases and gaugings of T-N theories - and display new results for linear and generalized quivers.

We study the BPS spectrum of four-dimensional $\mathcal{N}=2$ superconformal<br /> field theory of Argyres-Douglas type, obtained via twisted compactification of<br /> six-dimensional $A_{N-1}$ $(2,0)$ theory on a sphere with an irregular<br /> puncture, by using spectral networks. We give strong evidence of the<br /> equivalence of $\mathcal{N}=2$ superconformal field theories from<br /> six-dimensional theories of different ranks by systematically comparing the<br /> chamber structure and wall-crossing phenomena.

We show that the N=1 supersymmetric SU(N) gauge theory with 2N flavors without superpotential has not only the standard Seiberg dual description but also another dual description involving two copies of the so-called T-N theory. This is a natural generalization to N &gt; 2 of a dual description of SU(2) gauge theory with 4 flavors found by Csaki, Schmaltz, Skiba and Terning. We also study dualities of other N=1 SCFTs involving copies of T-N theories. Our duality is the basic operation from which a recently-found web of N=1 dualities obtained by compactifying M5-branes on Riemann surfaces can be derived field-theoretically.

There have been two distinct schemes studied in the literature for instanton counting in A(p-1) asymptotically locally Euclidean (ALE) spaces. We point out that the two schemes - namely the counting of orbifolded instantons and instanton counting in the resolved space - lead in general to different results for partition functions. We illustrate this observation in the case of N = 2 U(N) gauge theory with 2N flavors on the A(p-1) ALE space. We propose simple relations between the instanton partition functions given by the two schemes and test them by explicit calculations.

We explore the proposal that the six-dimensional (2, 0) theory on the Riemann surface with irregular punctures leads to a four-dimensional gauge theory coupled to the isolated N = 2 superconformal theories of Argyres-Douglas type, and to two-dimensional conformal field theory with irregular states. Following the approach of Gaiotto-Teschner for the Virasoro case, we construct W-3 irregular states by colliding a single SU(3) puncture with several regular punctures of simple type. If n simple punctures are colliding with the SU(3) puncture, the resulting irregular state is a simultaneous eigenvector of the positive modes L-n, ... , L-2n and W-2n, ... , W-3n of the W-3 algebra. We find the corresponding isolated SCFT with an SU(3) flavor symmetry as a nontrivial IR fixed point on the Coulomb branch of the SU(3) linear quiver gauge theories, by confirming that its Seiberg-Witten curve correctly predicts the conditions for the W-3 irregular states. We also compare these SCFT's with the ones obtained from the BPS quiver method.

We compute the Nekrasov partition function of gauge theories on the (resolved) toric singularities C-2/F in terms of blow-up formulae. We discuss the expansion of the partition function in the epsilon(1), epsilon(2) -&gt; 0 limit along with its modular properties and how to derive them from the M-theory perspective. On the two-dimensional conformal field theory side, our results can be interpreted in terms of representations of the direct sum of Heisenberg plus W-N-algebrae with suitable central charges, which can be computed from the fan of the resolved toric variety. We provide a check of this correspondence by computing the central charge of the two-dimensional theory from the anomaly polynomial of M5-brane theory. Upon using the AGT correspondence our results provide a candidate for the conformal blocks and three-point functions of a class of the two-dimensional CFTs which includes parafermionic theories.

We study the Higgs branches of the superconformal points of four-dimensional N=2 super Yang-Mills (SYM) which appear due to the occurrence of mutually local monopoles having appropriate charges. We show, for example, that the maximal superconformal point of SU(2n) SYM has a Higgs branch of the form C-2/Z(n). These Higgs branches are intrinsic to the superconformal field theory (SCFT) at the superconformal point, but do not appear in the SYM theory in which it is embedded. This is because the embedding is a UV extension of the SCFT in which some global symmetry acting on the Higgs branch is gauged irrelevantly. Higgs branches deduced from earlier direct studies of these isolated SCFTs using BPS wall-crossing or 3-d mirror symmetry agree with the ones we find here using just the Seiberg-Witten data for the SYM theories.

We present a relation between quiver gauge theories on the ALE space and correlators of super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for the full Nekrasov partition function and show that, up to a U(1) factor, the instanton partition function is given by the product of the character of times the super Virasoro conformal block on the torus with one puncture. Moreover, we match the perturbative gauge theory contribution with super Liouville three-point functions.

We study N = 2 supersymmetric SU(2) gauge theories coupled to non-Lagrangian superconformal field theories induced by compactifying the six dimensional A(1) (2,0) theory on Riemann surfaces with irregular punctures. These are naturally associated to Hitchin systems with wild ramification whose spectral curves provide the relevant Seiberg-Witten geometries. We propose that the prepotential of these gauge theories on the Omega-background can be obtained from the corresponding irregular conformal blocks on the Riemann surfaces via a generalization of the coherent state construction to the case of higher order singularities.

We provide evidence that the conformal blocks of N = 1 super Liouville conformal field theory are described in terms of the SU(2) Nekrasov partition function on the ALE space O-P1(-2).

We study generalized matrix models corresponding to n-point Virasoro conformal blocks on Riemann surfaces with arbitrary genus g. Upon ACT correspondence, these describe four dimensional N = 2 SU(2)(n+3g-3) gauge theories with generalized quiver diagrams. We obtain the generalized matrix models from the perturbative evaluation of the Liouville correlation functions and verify the consistency of the description with respect to degenerations of the Riemann surface. Moreover, we derive the Seiberg-Witten curve for the N = 2 gauge theory as the spectral curve of the generalized matrix model, thus providing a check of ACT correspondence at all genera.

We study the generalized matrix model which corresponds to the n-point toric Virasoro conformal block. This describes four-dimensional N = 2 SU(2)(n) gauge theory with circular quiver diagram by the AGT relation. We first verify that the generalized matrix model is obtained from the perturbative calculation of the Liouville correlation function. We then derive the Seiberg-Witten curve for N = 2 gauge theory as a spectral curve of the generalized matrix model.

We study the dual descriptions recently discovered for the Seiberg-Witten theory in the presence of surface operators. The Nekrasov partition function for a four-dimensional N = 2 gauge theory with a surface operator is believed equal to the wave-function of the corresponding integrable system, or the Hitchin system, and is identified with the conformal block with a degenerate field via the AGT relation. We verify the conjecture by showing that the null state condition leads to the Schrodinger equations of the integrable systems. Furthermore, we show that the deformed prepotential emerging from the period integrals of the principal function corresponds to monodromy operation of the conformal block. We also give the instanton partition functions for the asymptotically free SU(2) gauge theories in the presence of the surface operator via the AGT relation. We find that these partition functions involve the counting of two- and four-dimensional instantons. (C) 2010 Elsevier B.V. All rights reserved.

We discuss the Penner-type matrix model which has been proposed to explain the AGT relation between the 2-dimensional Liouville theory and 4-dimensional N = 2 superconformal gauge theories. In our previous communication we have obtained the spectral curve of the matrix model and showed that it agrees with that derived from M-theory. We have also discussed the decoupling limit of massive flavors and proposed new matrix models which describe Seiberg-Witten theory with flavors N-f = 2, 3. In this article we explicitly evaluate the free energy of these matrix models and show that they in fact reproduce the amplitudes of Seiberg-Witten theory.

We review the quiver matrix model (the ITEP model) in the light of the recent progress on 2d-4d connection of conformal field theories, in particular, on the relation between Toda field theories and a class of quiver superconformal gauge theories. On the basis of the CFT representation of the β deformation of the model, a quantum spectral curve is introduced as «det(x - igs∂φ(z))» = 0 at finite JV and for β ≠ 1. The planar loop equation in the large N limit follows with the aid of W n constraints. Residue analysis is provided both for the curve of the matrix model with the "multi-log" potential and for the Seiberg-Witten curve in the case of SU(n) with In flavors, leading to the matching of the mass parameters. The isomorphism of the two curves is made manifest.

We consider low energy processes described by the N = 2 supercurrent on its partially (to N = 1) and spontaneously broken vacuum and the attendant Nambu-Goldstone ferdmion (NGF), which the presence of the electric and magnetic Fayet-Iliopoulos (FI) terms is responsible for. We show suppressions of amplitudes decaying into the NGF as its momentum becomes small. In the Lagrangian realization (namely, the model of aiXiv:hep-th/0409060) of the conserved supercurrent, the NGF resides in the overall U(1), which is nonetheless not decoupled, and interacts with the SU(N) sector through non-derivative as well as derivative couplings. The low energy suppression is instead accomplished by a cancellation between the annihilation diagram from the Yukawa couplings and the contact four-Fermi terms. We give a complete form of the supercurrent and the model is recast in more transparent notation. (C) 2009 Elsevier B.V. All rights reserved.

We discuss the Penner type matrix model recently proposed by Dijkgraaf and Vafa for a possible explanation of the relation between four-dimensional gauge theory and Liouville theory by making use of the connection of the matrix model to two-dimensional CFT. We first consider the relation of gauge couplings defined in UV and IR regimes of N-f = 4, N = 2 supersymmetric gauge theory being related as q(UV) = upsilon(2)(q(IR))(4)/upsilon(3)(q(IR))(4). We then use this relation to discuss the action of modular transformation on the matrix model and determine its spectral curve. We also discuss the decoupling of massive flavors from the N-f = 4 matrix model and derive matrix models describing asymptotically free N = 2 gauge theories. We find that the Penner type matrix theory reproduces correctly the standard results of N = 2 supersymmetric gauge theories.

We construct N = 1 A-D-E quiver gauge theory with the gauge kinetic term which depends on the adjoint chiral superfields, as a low energy effective theory on D5-branes wrapped on 2-cycles of Calabi-Yau 3-fold in IIB string theory. The field-dependent gauge kinetic term can be engineered by introducing B-field which holomorphically varies on the base space (complex plane) of Calabi-Yau. We consider Weyl reflection on A-D-E node, which acts non-trivially on the gauge kinetic term. It is known that Weyl reflection is related to N = 1 electric-magnetic duality. Therefore, the non-trivial action implies an extension of the electric-magnetic duality to the case with the field-dependent gauge kinetic term. We show that this extended duality is consistent from the field theoretical point of view. We also consider the duality map of the operators.

We propose a number of new Seiberg dualities of N = 1 quiver gauge theories. The new Seiberg dualities originate in new S-dualities of N = 2 superconformal field theories recently proposed by Gaiotto. N = 2 S-dual theories deformed by suitable mass terms flow to our N = 1 Seiberg dual theories. We show that the number of exactly marginal operators is universal for these Seiberg dual theories and the 't Hooft anomaly matching holds for these theories. These provide strong evidence for the new Seiberg dualities. Furthermore, we study in detail the Klebanov-Witten type theory and its dual as a concrete example. We show that chiral operators and their non-linear relations match between these theories. These arguments also give non-trivial consistency checks for our proposal.

We study the vacuum structure of the U(N) gauge model with partially broken N = 2 supersymmetry. From the analysis of the classical vacua of this model, we point out that in addition to the ordinary N = 1 supersymmetric vacua. there are vacua with negative gauge coupling constants, which preserve another N = 1 supersymmetry. These latter vacua can be analyzed by using SUSY/non-SUSY duality which is recently proposed by Aganagic, Beem, Seo and Vafa. A dual description of these in UV is U(N) gauge theory where the supersymmetry is broken by spurion superfields. Following them, we see that there are supersymmetry preserving vacua as well as supersymmetry breaking vacua of low energy effective theory. (C) 2008 Elsevier B.V. All rights reserved.

We consider the matter induced part of the effective superpotential of N = 2, U(N) gauge model in which N = 2 supersymmetry is spontaneously broken to N = 1, by using the properties of the chiral ring and the generalized Konishi anomaly equations derived in our previous paper [H. Itoyama, K. Maruyoshi, Phys. Lett. B 650 (2007) 298, arXiv: 0704.1060 [hep-th]]. It is shown that the effective superpotential is related to the planar free energy of the matrix model by a formula which consists of two parts-the well-known part due to Dijkgraaf-Vafa and the part that acts as a deformation of the couplings. These couplings are those of the original bare prepotential in the action and at the same time matrix model couplings. (c) 2007 Elsevier B.V. All rights reserved.

We review the matter induced part of the effective superpotential of N = 2, U(N) gauge model in which N = 2 supersymmetry is spontaneously broken to N = 1. We derive this by the diagrammatical computation and by using the properties of the chiral ring and the generalized Konishi anomaly equations.

We construct an action of N = 2 affine An quiver gauge model having non-canonical kinetic terms and equipped with electric and magnetic FI terms. N = 2 supersymmetry is shown to be broken to N = 1 spontaneously and N = 1 multiplets realized on the vacua are given. We also mention the models with different gauge groups. It is argued that the affine A1 quiver gauge model provides a dynamical realization to approach the Klebanov-Witten N = 1 fixed point. © 2007 Elsevier B.V. All rights reserved.

We consider the effective superpotential of N=2, U(N) gauge model where N=2 supersymmetry is spontaneously broken to N=1. By the computation of loop diagrams, we obtain a formula for the effective superpotential which is deformed from the well-known form of the effective superpotential of N=1, U(N) gauge model with a tree level

It is known that the fermionic shift symmetry of the)V = 1, U(N) gauge model with a superpotential of an adjoint chiral superfield is replaced by the second (spontaneously broken) supersymmetry in the N = 2, U(N) gauge model with a prepotential and Fayet-Iliopoulos parameters. Based on a diagrammatic analysis, we demonstrate how the well-known form of the effective superpotential in the former model is modified in the latter. A set of two equations on the one-point functions stating the Konishi anomaly is modified accordingly. (c) 2007 Elsevier B.V. All rights reserved.

We study a U(N) gauged script N = 2 supergravity model with one hypermultiplet parametrizing SO(4,1)/SO(4) quaternionic manifold. Local script N = 2 supersymmetry is known to be spontaneously broken to script N = 1 in the Higgs pha.se of U(1)graviphoton x U(1). Several properties are obtained of this model in the vacuum of unbroken SU(N) gauge group. In particular, we derive mass spectrum analogous to the rigid counterpart and put the entire resulting potential on this vacuum in the standard superpotential form of script N = 1 supergravity. © World Scientific Publishing Company.

We review the general gauged N=2 supergravity coupled to an arbitrary number of vector multiplets and hypermultiplets. We consider two different models where N=2 supersymmetry is broken to N=1 spontaneously, one has a U(1) vector multiplet and the other has a U(N) vector multiplet. In both cases, partial breaking of N=2 supersymmetry is accomplished by the Higgs and the super-Higgs mechanisms. The mass spectrum can be evaluated and we conclude that the resulting models have N=1 supersymmetry. This is based on master thesis submitted to Graduate School of Science, Osaka City University, in March