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.