arXiv subjects

Chiung Hwang

Publications and source records attributed to Chiung Hwang.

At least 19 recordsLinked to original sources

arXiv2026

Algorithmic Dualization of Unitary Circular Quivers

We introduce a field-theoretic algorithm to find the $SL(2,\mathbb{Z})$ duality web of 3d $\mathcal{N}=4$ circular quiver theories with unitary gauge groups, extending the algorithm for linear quivers. Although circular and linear quivers share the same local structure, the circular topology requires additional ingredients, which we formulate in terms of topological and baryonic QFT blocks, together with new $SL(2,\mathbb{Z})$ duality moves acting on them. For good circular quivers, this provides a field-theoretic derivation of mirror symmetry and extends it to the full $SL(2,\mathbb{Z})$ duality web. We then study bad circular quivers, distinguishing between local badness, associated with under-balanced gauge nodes, and global badness, arising from the circular topology itself. In particular, we analyze the magnetic and electric dual frames of globally bad circular quivers and provide additional evidence for the proposed duality by matching the Higgs branch index with the dual Coulomb branch index. The latter exhibits a structure reminiscent of permutation-group gauging and reveals a refined relation to the ADHM quiver, flowing to the $\mathcal{N}=8$ infrared fixed point.

hep-th↗

arXiv2025

M2-brane indices on Higgs vacua and black holes

As an exact count of protected states, the superconformal index provides a powerful probe into holography and quantum aspects of gravity, reproducing the Bekenstein--Hawking entropy of supersymmetric AdS black holes in the large-$N$ limit. As a step toward understanding quantum black hole microstates, we study the finite-$N$ index of the 3d ADHM quiver gauge theory, a UV description of the 3d $\mathcal N=8$ SCFT dual to M-theory on AdS$_4 \times S^7$. In this note, we analyze both microcanonical and canonical features of the superconformal index. By computing the index to sufficiently high orders using the factorization formula, we identify signatures of quantum black hole states in the finite-$N$ spectrum of the ADHM quiver, which align with the leading large-$N$ contribution reflecting the holographic dual black hole entropy. Furthermore, we introduce the complex-$\beta$ phase diagram of the index, which exhibits distinct peaks potentially associated with different gravitational saddles. We also examine the Hilbert series limit of the factorized index. Our results demonstrate that the finite-$N$ index encodes rich information about black hole microstates and their quantum gravitational interpretation.

hep-th↗

arXiv2024

S-confinement of 3d Argyres-Douglas theories and the Seiberg-like duality with an adjoint matter

We propose an $\mathcal{N}=2$ preserving deformation that leads to the confining phase of the 3d reduction of the $D_p[SU(N)]$ Argyres-Douglas theories, referred to as $\mathbb{D}_p[SU(N)]$. This deformation incorporates monopole superpotential terms, which have recently played interesting roles in exploring possible RG fixed points of 3d supersymmetric gauge theories. Employing this confining phenomenon in 3d $\mathbb{D}_p[SU(N)]$ theories, we also propose a deconfined version of the Kim-Park duality, an IR duality for 3d $\mathcal{N}=2$ adjoint SQCDs, where an adjoint matter field is replaced by a linear quiver tail of $\mathbb{D}_p[SU(N)]$. Surprisingly, both the confinement of deformed $\mathbb{D}_p[SU(N)]$ and the deconfined Kim-Park duality can be proven only assuming some basic 3d $\mathcal{N}=2$ IR dualities. Finally, we propose a variant of the Kim-Park duality deformed by a single monopole superpotential term, which can also be derived using the same method.

hep-th↗

arXiv2024

Probing bad theories with the dualization algorithm I

Recently an algorithm to build $SL(2,\mathbb{Z})$ duals, including mirror duals, of 3d $\mathcal{N}=4$ quiver theories and their 4d $\mathcal{N}=1$ uplift has been introduced. In this work we use this new tool to study the so-called bad theories. Our approach allows us to determine exactly indices/partition functions for generic values of fugacities/real mass and FI parameters revealing their surprising feature: the 4d index/3d partition function of a bad theory behaves as a sum of distributions rather than an ordinary function of the deformation parameters. We focus on the bad SQCD, with $U(N_c)$ gauge group in 3d and $USp(2N_c)$ in 4d, while in an upcoming paper we will consider linear quivers which, in the 3d case, have both unitary and special unitary bad nodes.

hep-th↗

arXiv2024

Probing bad theories with the dualization algorithm II

We continue our analysis of bad theories, focusing on quiver theories with bad unitary and special unitary gauge groups in three dimensions. By extending the dualization algorithm we prove that the partition function of bad linear quivers can be written as a distribution, given by a sum of terms involving a product of delta functions times the partition function of a good quiver theory. We describe in detail the good quiver theories appearing in the partition function of the bad theory and discuss the brane interpretation of our result. We also discuss in detail the lift of these theories to 4d quivers with symplectic gauge groups, in which our results can be recovered by studying the Higgsing triggered by the expectation value for certain chiral operators. The paper is accompanied by a Mathematica file which implements the algorithm for an arbitrary unitary bad linear quiver.

hep-th↗

arXiv2023

The $SL(2,\mathbb{Z})$ dualization algorithm at work

Recently an algorithm to dualize a theory into its mirror dual has been proposed, both for $3d$ $\mathcal{N}=4$ linear quivers and for their $4d$ $\mathcal{N}=1$ uplift. This mimics the manipulations done at the level of the Type IIB brane setup that engineers the $3d$ theories, where mirror symmetry is realized as $S$-duality, but it is enirely field-theoretic and based on the application of genuine infra-red dualities that implement the local action of $S$-duality on the quiver. In this paper, we generalize the algorithm to the full duality group, which is $SL(2,\mathbb{Z})$ in $3d$ and $PSL(2,\mathbb{Z})$ in $4d$. This also produces dualities for $3d$ $\mathcal{N}=3$ theories with Chern--Simons couplings, some of which have enhanced $\mathcal{N}=4$ supersymmetry, and their new $4d$ $\mathcal{N}=1$ counterpart. In addition, we propose three ways to study the RG flows triggered by possible VEVs appearing at the last step of the algorithm, one of which uses a new duality that implements the Hanany--Witten move in field theory.

hep-th↗

arXiv2022

Dualities from dualities: the sequential deconfinement technique

It is an interesting question whether a given infra-red duality between quantum field theories can be explained in terms of other more elementary dualities. For example recently it has been shown that mirror dualities can be obtained by iterative applications of Seiberg-like dualities. In this paper we continue this line of investigation focusing on theories with tensor matter. In such cases one can apply the idea of deconfinement, which consists of trading the tensor matter for extra gauge nodes by means of a suitable elementary duality. This gives an auxiliary dual frame which can then be manipulated with further dualizations, in an iterative procedure eventually yielding an interesting dual description of the original theory. The sequential deconfinement technique has avatars in different areas of mathematical physics, such as the study of hypergeometric and elliptic hypergeometric integral identities or of $2d$ free field correlators. We discuss various examples in the context $4d$ $\mathcal{N}=1$ supersymmetric theories, which are related to elliptic hypergeometric integrals. These include a new self-duality involving a quiver theory which exhibits a non-trivial global symmetry enhancement to $E_6$.

hep-th↗

arXiv2022

Rethinking mirror symmetry as a local duality on fields

We introduce an algorithm to piecewise dualise linear quivers into their mirror dual. The algorithm uses two basic duality moves and the properties of the $S$-wall which can all be derived by iterative applications of Seiberg-like dualities.

hep-th↗

arXiv2022

4d $S$-duality wall and $SL(2,\mathbb{Z})$ relations

In this paper we present various $4d$ $\mathcal{N}=1$ dualities involving theories obtained by gluing two $E[USp(2N)]$ blocks via the gauging of a common $USp(2N)$ symmetry with the addition of $2L$ fundamental matter chiral fields. For $L=0$ in particular the theory has a quantum deformed moduli space with chiral symmetry breaking and its index takes the form of a delta-function. We interpret it as the Identity wall which identifies the two surviving $USp(2N)$ of each $E[USp(2N)]$ block. All the dualities are derived from iterative applications of the Intriligator--Pouliot duality. This plays for us the role of the fundamental duality, from which we derive all others. We then focus on the $3d$ version of our $4d$ dualities, which now involve the $\mathcal{N}=4$ $T[SU(N)]$ quiver theory that is known to correspond to the $3d$ $S$-wall. We show how these $3d$ dualities correspond to the relations $S^2=-1$, $S^{-1}S=1$ and $T^{-1} S T=S^{-1} T S$ for the $S$ and $T$ generators of $SL(2,\mathbb{Z})$. These observations lead us to conjecture that $E[USp(2N)]$ can also be interpreted as a $4d$ $S$-wall.

hep-th↗

arXiv2022

Monopole deformations of 3d Seiberg-like dualities with adjoint matters

We propose new 3d $\mathcal{N}=2$ Seiberg-like dualities by considering various monopole superpotential deformations on 3d $\mathcal{N}=2$ $U(N_c)$ SQCDs with fundamental and adjoint matter fields. We provide nontrivial evidence of these new dualities by comparing the superconformal indices, from which we analyze the change of the moduli space due to the monopole deformation. In addition, we perform the $F$-maximization to check the relevance of the monopole deformation for some examples, one of which is found to exhibit nontrivial symmetry enhancement in the IR. We prove such enhancement of the global symmetry using the superconformal index.

hep-th↗

arXiv2021

Rank $Q$ E-String on Spheres with Flux

We consider compactifications of rank $Q$ E-string theory on a genus zero surface with no punctures but with flux for various subgroups of the $\text{E}_8\times \text{SU}(2)$ global symmetry group of the six dimensional theory. We first construct a simple Wess-Zumino model in four dimensions corresponding to the compactification on a sphere with one puncture and a particular value of flux, the cap model. Using this theory and theories corresponding to two punctured spheres with flux, one can obtain a large number of models corresponding to spheres with a variety of fluxes. These models exhibit interesting IR enhancements of global symmetry as well as duality properties. As an example we will show that constructing sphere models associated to specific fluxes related by an action of the Weyl group of $\text{E}_8$ leads to the S-confinement duality of the $\text{USp}(2Q)$ gauge theory with six fundamentals and a traceless antisymmetric field. Finally, we show that the theories we discuss possess an $\text{SU}(2)_{\text{ISO}}$ symmetry in four dimensions that can be naturally identified with the isometry of the two-sphere. We give evidence in favor of this identification by computing the `t Hooft anomalies of the $\text{SU}(2)_{\text{ISO}}$ in 4d and comparing them with the predicted anomalies from 6d.

hep-th↗

arXiv2021

Flips, dualities and symmetry enhancements

We present various 4d $\mathcal{N}=1$ theories enjoying IR global symmetry enhancement. The models we consider have the $USp(2n)$ gauge group, 8 fundamental, one antisymmetric chirals and various numbers of gauge singlets. By suitably turning on superpotential deformations involving the singlets which break part of the UV symmetry we flow to SCFTs with $E_6$, $SO(10)$, $SO(9)$, $SO(8)$ and $F_4$ IR global symmetry. We explain these patterns of symmetry enhancement following two arguments due to Razamat, Sela and Zafrir. The first one involves the study of the relations satisfied by marginal operators, while the second one relies on the existence of self-duality frames.

hep-th↗

arXiv2020

4d mirror-like dualities

We construct a family of $4d$ $\mathcal{N}=1$ theories that we call $E^σ_ρ[USp(2N)]$ which exhibit a novel type of $4d$ IR duality very reminiscent of the mirror duality enjoyed by the $3d$ $\mathcal{N}=4$ $T^σ_ρ[SU(N)]$ theories. We obtain the $E^σ_ρ[USp(2N)]$ theories from the recently introduced $E[USp(2N)]$ theory, by following the RG flow initiated by vevs labelled by partitions $ρ$ and $σ$ for two operators transforming in the antisymmetric representations of the $USp(2N) \times USp(2N)$ IR symmetries of the $E[USp(2N)]$ theory. These vevs are the $4d$ uplift of the ones we turn on for the moment maps of $T[SU(N)]$ to trigger the flow to $T^σ_ρ[SU(N)]$. Indeed the $E[USp(2N)]$ theory, upon dimensional reduction and suitable real mass deformations, reduces to the $T[SU(N)]$ theory. In order to study the RG flows triggered by the vevs we develop a new strategy based on the duality webs of the $T[SU(N)]$ and $E[USp(2N)]$ theories.

hep-th↗

arXiv2020

Universal 3d Cardy Block and Black Hole Entropy

We discuss the Cardy limit of 3d supersymmetric partition functions which allow the factorization into the hemisphere indices: the generalized superconformal index, the refined topologically twisted index and the squashed sphere partition function. In the Cardy limit, the hemisphere index can be evaluated by the saddle point approximation where there exists a dominant saddle point contribution, which we call the Cardy block. The Cardy block turns out to be a simple but powerful object as it is a building block of other partition functions in the Cardy limit. The factorization to the Cardy block allows us to find universal relations among the partition functions, which we formulate as index theorems. Furthermore, if we consider a holographic 3d SCFT and its large $N$ limit, those partition functions relate to various entropic quantities of the dual gravity theory in AdS$_4$. As a result, our result provides the microscopic derivation of the universal relations among those entropic quantities of the gravity theory. We also discuss explicit examples, which confirm our general index theorems.

hep-th↗

arXiv2020

Generalized Euler Index, Holonomy Saddles, and Wall-Crossing

We formulate Witten index problems for theories with two supercharges in a Majorana doublet, as in $d=3$ $\mathcal N=1$ theories and dimensional reduction thereof. Regardless of spacetime dimensions, the wall-crossing occurs generically, in the parameter space of the real superpotential $W$. With scalar multiplets only, the path integral reduces to a Gaussian one in terms of $dW$, with a winding number interpretation, and allows an in-depth study of the wall-crossing. After discussing the connection to well-known mathematical approaches such as the Morse theory, we move on to Abelian gauge theories. Even though the index theorem for the latter is a little more involved, we again reduce it to winding number countings of the neutral part of $dW$. The holonomy saddle plays key roles for both dimensions and also in relating indices across dimensions.

hep-th↗

arXiv2020

Entropy functions of BPS black holes in AdS$_4$ and AdS$_6$

We find the entropy functions of supersymmetric black holes in AdS$_4$ and AdS$_6$ with electric charges and angular momenta. Extremizing these functions, one obtains the entropies and the chemical potentials of known analytic black hole solutions.

hep-th↗

arXiv2019

Quantum vortices, M2-branes and black holes

We study the partition functions of BPS vortices and magnetic monopole operators, in gauge theories describing $N$ M2-branes. In particular, we explore two closely related methods to study the Cardy limit of the index on $S^2\times\mathbb{R}$. The first method uses the factorization of this index to vortex partition functions, while the second one uses a continuum approximation for the monopole charge sums. Monopole condensation confines most of the $N^2$ degrees of freedom except $N^{\frac{3}{2}}$ of them, even in the high temperature deconfined phase. The resulting large $N$ free energy statistically accounts for the Bekenstein-Hawking entropy of large BPS black holes in $AdS_4\times S^7$. Our Cardy free energy also suggests a finite $N$ version of the $N^{\frac{3}{2}}$ degrees of freedom.

hep-th↗

arXiv2018

On 3d Seiberg-like Dualities with Two Adjoints

We study $N = 2$ 3-d theories with two adjoints and fundamental flavors along with D-type superpotential. For superpotential $W_{D_{n+2}} = \mathrm{Tr} \left(X^{n+1}+X Y^2\right)$ with $n$ odd, we propose the 3d dualities, which we motivate from the dimensional reduction of the related 4-d theory. We consider the factorization of the superconformal index and match precisely the vortex partition function of the dual pairs. In the language of the Higgs branch localization, the nonzero contribution of the vortex partition function comes from the discrete Higgs vacua of the massively deformed theory, which precisely matches with that of the dual theory. We also clarify the monopole operators parametrizing the Coulomb branch of such theories. Existence of independent monopole operators of charge 2 is crucial to describe the Coulomb branch.

hep-th↗