arXiv subjects

Jaewon Song

Publications and source records attributed to Jaewon Song.

At least 19 recordsLinked to original sources

arXiv2026

Dual N=1 Lagrangians for Argyres-Douglas theories

We find a new set of four-dimensional $\mathcal{N}=1$ Lagrangian gauge theories that flow in the infrared to $\mathcal{N}=2$ Argyres-Douglas theories of type $(A_1, A_{2n})$, $(A_1, A_{2n+1})$, $(A_1, D_{2n+1})$, and $(A_1, D_{2n+2})$. The new dual theories are given by $SU(2)^n$ quiver gauge theories with a number of gauge-singlet flip fields. This description provides dual theories for the previous $\mathcal{N}=1$ Lagrangian realizations given by $Sp(n)$ or $SU(n+1)$ gauge theories, exchanging the rank and the number of nodes in a quiver diagram.

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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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arXiv2026

Algebro-geometric bootstrapping from OPE decoupling

We conjecture that decoupling relations in the operator product expansion of a 4d $\mathcal{N}=2$ superconformal field theory (SCFT) are encoded by an algebro-geometric object: a bifiltered affine scheme. We demonstrate how this scheme reproduces the Macdonald index (thus the Schur index) as well as the Higgs branch. Although the associated scheme typically admits continuous deformations, we find that a geometric extremization principle uniquely fixes these moduli, thereby providing a possible geometric route toward a classification of 4d $\mathcal{N}=2$ SCFTs.

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arXiv2025

Macdonald index from 3d TQFT

We propose a new fermionic sum formula for the Macdonald index of a class of Argyres-Douglas theories. The formula arises naturally from a three-dimensional topological field theory obtained via a twisted dimensional reduction of the 4d theory. Such a reduction often gives rise to a 3d ${\mathcal N}=2$ abelian Chern-Simons matter theory, which is expected to flow to an ${\mathcal N}=4$ superconformal fixed point. After performing a topological twist, we obtain a 3d TFT admitting boundary conditions that support the vertex operator algebra associated with the original 4d theory. In this framework, the Macdonald index appears as a half-index of the 3d gauge theory, with the Macdonald grading determined by a distinguished $U(1)_A$ symmetry in the infrared ${\mathcal N}=4$ superconformal algebra. We present a general procedure to identify this $U(1)_A$ symmetry and, whenever possible, show that it reproduces the refined character of the associated vertex operator algebra, thereby recovering the Macdonald index. Our construction also gives a hint towards the IR formula for the Macdonald index in terms of 4d BPS particles on the Coulomb branch.

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arXiv2025

Large N Universality of 4d N=1 SCFTs with Simple Gauge Groups

We classify four-dimensional $\mathcal{N}=1$ supersymmetric gauge theories with a simple gauge group admitting a large $N$ limit that flow to non-trivial superconformal fixed points in the infrared. We focus on the cases where the large $N$ limit can be taken while keeping the flavor symmetry fixed so that the putative holographic dual has a fixed gauge group. We find that they can be classified into three types -- Type I, Type II, and Type III -- exhibiting universal behavior. Type I theories have $a \neq c$ in the large $N$ limit and scale linearly in $N$; the gap of scaling dimensions among BPS operators behaves as $1/N$. Type II theories have $a=c$ in the large $N$ limit, and satisfy $a \simeq c \simeq \frac{27}{128} \dim G$, and Type III theories have $a \simeq c \simeq \frac{1}{4} \dim G$. For Type II and Type III theories, the gap of scaling dimensions stays $O(1)$ in the large $N$ limit. We enumerate relevant and marginal operators of these theories and find that non-trivial conformal manifolds emerge upon relevant deformations. Moreover, we find that a modified version of the AdS Weak Gravity Conjecture, based on the supersymmetric Cardy formula, holds for all of these theories, even for finite $N$.

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arXiv2025

Index from a point

We propose an algebro-geometric interpretation of the Schur and Macdonald indices of four-dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs). We conjecture that there exists an affine scheme $X$, which reduces to the Higgs branch as a variety, such that the Hilbert series of the (appropriately-graded) arc space of its polynomial ring $J_\infty(\mathbb{C}[X])$ encodes the indices. Distinct local descriptions of a (singular) point correspond to distinct choices of $X$, giving rise to families of $\mathcal{N}=2$ SCFTs each without a Higgs branch. These local descriptions directly translate into nilpotency relations in the operator product expansions. We test our conjecture across a variety of (generalized) Argyres--Douglas theories.

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arXiv2024

A Family of Vertex Algebras from Argyres-Douglas Theory

We find that multiple vertex algebras can arise from a single 4d $\mathcal{N}=2$ superconformal field theory (SCFT). The connection is given by the BPS monodromy operator $M$, which is a wall-crossing invariant quantity that captures the BPS spectrum on the Coulomb branch. For a class of low-rank Argyres-Douglas theories, we find that the trace of the multiple powers of the monodromy operator $\mathrm{Tr} M^N$ yield modular functions that can be identified with the vacuum characters of certain vertex algebra for each $N$. In particular, we realize unitary VOAs of the Deligne-Cvitanovi\'c exceptional series type $(A_2)_1$, $(G_2)_1$, $(D_4)_1$, $(F_4)_1$, $(E_6)_1$ from Argyres-Douglas theories. We also find the modular invariant characters of the `intermediate vertex algebras' $(E_{7\frac{1}{2}})_1$ and $(X_1)_1$. Our analysis allows us to construct 3d $\mathcal{N}=2$ gauge theories that flow to $\mathcal{N}=4$ SCFTs in the IR, whose specialized half-index can be identified with these modular invariant characters.

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arXiv2024

A landscape of 4d N=1 SCFTs with a=c

We study a landscape of four-dimensional $\mathcal{N}=1$ superconformal field theories (SCFTs) with identical central charges. These theories are obtained by renormalization group flows triggered by supersymmetry-preserving superpotential deformations of the $\mathcal{N}=1$ gauging of the flavor symmetry of a collection of $\mathcal{N}=2$ $\mathcal{D}_p(G)$ Argyres--Douglas SCFTs. In this work, we focus on the fixed points in the landscape of the $SU(3)$ gauging of three copies of the $\mathcal{D}_2(SU(3)) = H_2$ theory together with an adjoint-valued chiral multiplet. We catalogue the network of $a = c$ fixed points, and, along the way, we find a variety of dualities and instances of supersymmetry enhancement.

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arXiv2024

Generalized symmetry constraints on deformed 4d (S)CFTs

We explore the consequence of generalized symmetries in four-dimensional $\mathcal{N}=1$ superconformal field theories. First, we classify all possible supersymmetric gauge theories with a simple gauge group that have a nontrivial one-form symmetry and flows to a superconformal field theory. Upon identifying unbroken discrete zero-form symmetries from the ABJ anomaly, we find that many of these theories have mixed zero-form/one-form 't Hooft anomalies. Then we classify the relevant deformations of these SCFTs that preserve the anomaly. From this mixed anomaly together with the anomalies of the discrete zero-form symmetries, we find obstructions for the relevant deformations of these SCFTs to flow to a trivially gapped phase. We also study non-Lagrangian SCFTs formed by gauging copies of Argyres-Douglas theories and constrain their deformations. In particular, we explore a new duality between the diagonal gauging of two $\mathcal{D}_3(SU(N))$ theories and $SU(N)$ gauge theory with two adjoints. We also repeat our analysis for a host of non-supersymmetric gauge theories having nontrivial one-form symmetry including examples that appear to flow to Bank-Zaks type CFTs.

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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

Large $N$ Universality of 4d $\mathcal{N}=1$ Superconformal Index and AdS Black Holes

We study the large $N$ limit of the matrix models associated with the superconformal indices of four-dimensional $\mathcal{N}=1$ superconformal field theories. We find that for a large class of $\mathcal{N}=1$ superconformal gauge theories, the superconformal indices in the large $N$ limit of such theories are dominated by the 'parallelogram' saddle, providing $O(N^2)$ free energy for the generic value of chemical potentials. This saddle corresponds to BPS black holes in AdS$_5$ whenever a holographic dual description is available. Our saddle applies to a large class of gauge theories, including ADE quiver gauge theories, and the theories with rank-2 tensor matters. Our analysis works for most $\mathcal{N}=1$ superconformal gauge theories that admit a suitable large $N$ limit while keeping the flavor symmetry fixed. We also find 'multi-cut' saddle points, which correspond to the orbifolded Euclidean black holes in AdS$_5$.

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arXiv2023

Supersymmetric Cardy Formula and the Weak Gravity Conjecture in AdS/CFT

The Weak Gravity Conjecture (WGC) in anti-de Sitter spacetime (AdS) asserts the existence of an operator in the boundary conformal field theory (CFT) whose scaling dimension-to-charge ratio satisfies a certain upper bound. This bound is specified by the ratio of the conformal central charge $c$ and the flavor central charge $k_F$. We propose a modified bound in AdS5/CFT4, determined by a combination of two central charges $3c-2a$ instead of $c$. This combination arises in the Cardy-like limit of the 4d superconformal index, which captures the Bekenstein-Hawking entropy of large BPS black holes in AdS5. Using the new bound, we find that certain superconformal field theories (SCFTs) that are previously thought to violate the AdS WGC, including SQCDs in the conformal window, do satisfy the WGC. We check this version of the WGC against all possible superconformal gauge theories with SU(N) gauge group admitting a large N limit when the superpotential is absent. We conjecture the modified version of the WGC is a generic property of any 4d SCFT, regardless of the existence of a weakly coupled gravity dual or a large N limit.

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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

Emergent N=4 supersymmetry from N=1

We discover a four-dimensional $\mathcal{N}=1$ supersymmetric field theory that is dual to the $\mathcal{N}=4$ super Yang-Mills theory with gauge group $SU(2n+1)$ for each $n$. The dual theory is constructed through the diagonal gauging of the $SU(2n+1)$ flavor symmetry of three copies of a strongly-coupled superconformal field theory (SCFT) of Argyres-Douglas type. We find that this theory flows in the infrared to a strongly-coupled $\mathcal{N}=1$ SCFT that lies on the same conformal manifold as $\mathcal{N}=4$ super Yang-Mills with gauge group $SU(2n+1)$. Our construction provides a hint on why certain $\mathcal{N}=1,2$ SCFTs have identical central charges ($a=c$).

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arXiv2022

Operator spectroscopy for 4d SCFTs with a=c

We study a rich set of four-dimensional superconformal field theories (SCFTs) with both central charges identical: $a = c$. These are constructed via the diagonal $\mathcal{N}=2$ or $\mathcal{N}=1$ gauging of the flavor symmetry $G$ of a collection of $\mathcal{N}=2$ Argyres-Douglas theories of type $\mathcal{D}_p(G)$, with or without adjoint chiral multiplets, in arXiv:2106.12579 and arXiv:2111.12092. We compute superconformal indices of some theories where the rank of $G$ is low, performing a refined test for unitarity, and further determine the relevant and marginal operator content in detail. We find that most of these theories flow to interacting SCFTs with $a=c$ in the infrared.

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arXiv2022

Higgs, Coulomb, and Hall-Littlewood

The Higgs branch of 4d $\mathcal{N}=2$ SCFTs can be analyzed via the Hilbert series of the Higgs branch or, in special cases, by computing the Hall-Littlewood index. For any class $\mathcal{S}$ theory corresponding to a genus-zero Riemann surface, they are conjectured to be identical. We present several families of counterexamples. We find that for any class $\mathcal{S}$ theory with four or more $\mathbb{Z}_2$-twisted punctures, they do not match. We construct 3d mirrors for such theories and analyze their Coulomb branch Hilbert series to compute the Higgs branch Hilbert series of the 4d theory. We further construct $a=c$ theories in class $\mathcal{S}$ using the twisted punctures, and these theories, which includes the $\hat{D}_4(SU(2n+1))$ theories, have Hall--Littlewood index different from the Hilbert series of the Higgs branch. We conjecture that this is the case for all $a=c$ theories with non-empty Higgs branch, including $\mathcal{N}\ge 3$ SCFTs.

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arXiv2022

Supersymmetric Spectral Form Factor and Euclidean Black Holes

The late-time behavior of spectral form factor (SFF) encodes the inherent discreteness of a quantum system, which should be generically non-vanishing. We study an index analog of the microcanonical spectrum form factor in four-dimensional $\mathcal{N}=4$ super Yang-Mills theory. In the large $N$ limit and at large enough energy, the most dominant saddle corresponds to the black hole in the AdS bulk. This gives rise to the slope that decreases exponentially for a small imaginary chemical potential, which is a natural analog of an early time. We find that the `late-time' behavior is governed by the multi-cut saddles that arise in the index matrix model, which are non-perturbatively sub-dominant at early times. These saddles become dominant at late times, preventing the SFF from decaying. These multi-cut saddles correspond to the orbifolded Euclidean black holes in the AdS bulk, therefore giving the geometrical interpretation of the `ramp.' Our analysis is done in the standard AdS/CFT setting without ensemble average or wormholes.

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arXiv2021

Infinitely many 4d N=1 SCFTs with a=c

We study a rich set of four-dimensional $\mathcal{N}=1$ superconformal field theories (SCFTs) with both central charges identical: $a = c$. We construct them via the diagonal $\mathcal{N}=1$ gauging of the flavor symmetry $G$ of a collection of $\mathcal{N}=2$ Argyres--Douglas theories of type $\mathcal{D}_p(G)$, with or without additional adjoint chiral multiplets. In this way, we construct infinitely-many theories that flow to interacting SCFTs with $a = c$ in the infrared. Finally, we briefly highlight the features of the SCFTs without $a = c$ that arise from generalizing this construction.

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