arXiv subjects

Kazunobu Maruyoshi

Publications and source records attributed to Kazunobu Maruyoshi.

At least 19 recordsLinked to original sources

arXiv2026

Non-invertible symmetry and vertex operator algebra outer-automorphism

We argue that the non-invertible symmetry of $\mathcal{N}=4$ super Yang-Mills theory, obtained by combining S-duality, half-space gauging, and R-symmetry twist, is realized as an outer-automorphism of the associated vertex operator algebra. Hence, the Schur and Macdonald index of $\mathcal{N}=4$ super Yang-Mills theory with non-invertible symmetry twist corresponds to the (refined) vacuum character of the associated vertex operator algebra with the outer-automorphism twist. We provide a few checks of our proposal from the large-$N$ limit and by matching the fusion rules, which involve charge conjugation on local operators. The `charged' Schur index indeed matches the outer-automorphism-twisted vacuum character.

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arXiv2024

Large Landscape of 4d Superconformal Field Theories from Small Gauge Theories

We systematically explore the space of renormalization group flows of four-dimensional $\mathcal{N}=1$ superconformal field theories (SCFTs) triggered by relevant deformations, as well as by coupling to free chiral multiplets with relevant operators. In this way, we classify all possible fixed point SCFTs that can be obtained from certain rank 1 and 2 supersymmetric gauge theories with small amount of matter multiplets, identifying 7,346 inequivalent fixed points which pass a series of non-trivial consistency checks. This set of fixed points exhibits interesting statistical behaviors, including a narrow distribution of central charges $(a, c)$, a correlation between the number of relevant operators and the ratio $a/c$, and trends in the lightest operator dimension versus $a/c$. The ratio $a/c$ of this set is distributed between $0.7228$ and $1.2100$, where the upper bound is larger than that of previously known interacting SCFTs. Moreover, we find a plethora of highly non-perturbative phenomena, such as (super)symmetry enhancements, operator decoupling, non-commuting renormalization group flows, and dualities. We especially identify amongst these fixed points a new SCFT that has smaller central charges $(a, c) = (\frac{633}{2000},\frac{683}{2000})$ than that of the deformed minimal Argyres-Douglas theory, as well as novel Lagrangian duals for certain $\mathcal{N}=1$ deformed Argyres-Douglas theories. We provide a website https://qft.kaist.ac.kr/landscape to navigate through our set of fixed points.

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arXiv2023

Dualities of Adjoint SQCD and Supersymmetry Enhancement

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 $W = \text{Tr}\, X^{p+1}$. 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.

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arXiv2023

Conserved charges in the quantum simulation of integrable spin chains

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. The Trotter error in integrable spin chains can be under control if the discrete time evolution preserves integrability. In this work we implement, on a real quantum computer 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 the 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.

quant-ph↗

arXiv2021

Wilson-'t Hooft lines as transfer matrices

We establish a correspondence between a class of Wilson-'t Hooft lines in four-dimensional $\mathcal{N} = 2$ 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 $S^1 \times_ε\mathbb{R}^2 \times \mathbb{R}$ 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.

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arXiv2019

Landscape of Simple Superconformal Field Theories in 4d

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

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arXiv2018

A "Lagrangian" for the E7 Superconformal Theory

We find an N=1 gauge theory that flows to the rank-one N=2 superconformal field theory with $E_7$ flavor symmetry. We first obtain a Lagrangian description for the $R_{0, N}$ 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 $E_6$ theory. The $E_7$ theory is then obtained via partial Higgsing of the $R_{0, 4}$ theory. From this Lagrangian description, we compute the full superconformal index. We also consider twisted dimensional reduction on $S^2$ to obtain N=(0, 4) theory for the $E_7$ one instanton string and compute its elliptic genus.

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arXiv2018

4d N=1 from 6d N=(1,0) on a torus with fluxes

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

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arXiv2017

Enhancement of Supersymmetry via Renormalization Group Flow and the Superconformal Index

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.

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arXiv2017

N=1 Deformations and RG Flows of N=2 SCFTs

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 N=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 $R_{0,N}$ theories of class $\mathcal{S}$ and some of rank-one SCFTs, where the deformation gives genuine N=1 fixed points.

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arXiv2016

On Painlevé/gauge theory correspondence

We elucidate the relation between Painlevé equations and four-dimensional rank one ${\cal N= 2}$ theories by identifying the connection associated to Painlevé isomonodromic problems with the oper limit of the flat connection of the Hitchin system associated to gauge theories and by studying the corresponding renormalisation group flow. Based on this correspondence we provide long-distance expansions at various canonical rays for all Painlevé functions in terms of magnetic and dyonic Nekrasov partition functions for ${\cal N= 2}$ SQCD and Argyres-Douglas theories at self-dual Omega background $ε_1+ε_2= 0$, or equivalently in terms of $c= 1$ irregular conformal blocks.

hep-th↗

arXiv2016

Surface defects as transfer matrices

The supersymmetric index of the 4d $\mathcal{N} = 1$ 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 $\mathrm{SU}(2)$ 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-$\mathcal{S}$ and -$\mathcal{S}_k$ theories in the presence of the surface defects.

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arXiv2016

N=1 Deformations and RG Flows of N=2 SCFTs, Part II: Non-principal deformations

We continue to investigate the $\mathcal{N}=1$ deformations of four-dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) labeled by a nilpotent element of the flavor symmetry. This triggers a renormalization group (RG) flow to an $\mathcal{N}=1$ SCFT. We systematically analyze all possible deformations of this type for certain classes of $\mathcal{N}=2$ 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 $\mathcal{N}=2$ 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 $(A_1, D_{2N-1})$ 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 $\mathcal{N}=1$ theories where the fixed point is described by an $\mathcal{N}=2$ 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.

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arXiv2015

Chiral theories of class S

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.

hep-th↗

arXiv2015

$β$-deformed matrix models and the 2d/4d correspondence

This is the fourth article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J.Teschner. It describes a very useful mathematical representation of the results of the localisation computations of instanton partition functions as integrals having a form familiar from the study of matrix models. Techniques from the study of matrix models can be employed to extract important information on the instanton partition functions in various limits and special cases.

hep-th↗

arXiv2015

Quiver Tails and N=1 SCFTs from M5-branes

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 UV descriptions of four-dimensional 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.

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arXiv2013

BPS spectrum of Argyres-Douglas theory via spectral network

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

hep-th↗

arXiv2013

N=1 dynamics with T_N theory

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.

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