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.

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 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 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

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