arXiv subjects

Sungjay Lee

Publications and source records attributed to Sungjay Lee.

At least 19 recordsLinked to original sources

arXiv2026

Resurgence of the Thermal Transition between Bounce and Sphaleron

We study the thermal transition between the bounce and the sphaleron in quantum mechanics with a metastable vacuum from the viewpoint of Borel resurgence. For two models representing a second-order and a first-order transition, we compute the perturbative expansion of the thermal free energy to high orders and extract the leading Borel singularity data $(A,b,S)$ as functions of temperature. The Borel singularity location $A$ reproduces the on-shell action of the dominant saddle on both sides of the transition, joining smoothly in the second-order case and developing a kink in the first-order case. The characteristic exponent $b$ jumps between $0$ and $1/2$ across the transition, counting the zero modes of the corresponding saddle. The Stokes constant $S$ matches the one-loop determinant around the saddle. The perturbative expansion around the false vacuum thus determines the transition temperature, the order of the transition, and the decay rate including the one-loop prefactor without relying on semiclassical inputs.

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arXiv2025

Fermionic Non-invertible Symmetry Behind Supersymmetric ADE Solitons

The non-perturbative constraints imposed by intrinsic fermionic non-invertible symmetries in 1+1 dimensional gapped systems remain largely unexplored. In this letter, we propose the superstrip algebra as a unified framework to catalog the categorical symmetry data in a massive fermionic model. The algebra and its representations explicitly encode the vacuum structure, soliton degeneracies, and their quantum numbers. As a demonstration, we apply this framework to the $\mathcal N=2$ minimal models with their least relevant deformation. We show that this specific deformation alone preserves a non-invertible superfusion category, a fermionic variant of $\text{SU}(2)_k$ known to underlie the $ADE$ classification of critical theories. Its superstrip algebra then accounts for the origin of the resulting $ADE$-type soliton spectrum and their fractional fermion number. Although our primary examples are supersymmetric and integrable, our framework itself relies on neither property, providing a new powerful tool for studying a broad class of strongly-coupled fermionic systems.

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arXiv2024

Web of 4D Dualities, Supersymmetric Partition functions and SymTFT

We study $\mathbb{Z}_N$ one-form center symmetries in four-dimensional gauge theories using the symmetry topological field theory (SymTFT). In this context, the associated TFT in the five-dimensional bulk is the BF model. We revisit its canonical quantization and construct topological boundary states on several important classes of four manifolds that are spin, non-spin and torsional. We highlight a web of four-dimensional dualities, which can be naturally interpreted within the SymTFT framework. We also point out an intriguing class of four-dimensional gauge theories that exhibit mixed 't Hooft anomaly between one-form symmetries. In the second part of this work, we extend the SymTFT to account for various quantities protected by supersymmetry (SUSY) in SUSY gauge theories. We proposed that their behaviour under various symmetry operations are entirely captured by the topological boundary of the SymTFT, resulting in strong constraints. Concrete examples are considered, including the Witten index, the lens space index and the Donaldson-Witten and Vafa-Witten partition functions.

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arXiv2023

A non-unitary bulk-boundary correspondence: Non-unitary Haagerup RCFTs from S-fold SCFTs

We introduce a novel class of two-dimensional non-unitary rational conformal field theories (RCFTs) whose modular data are identical to the generalized Haagerup-Izumi modular data. Via the bulk-boundary correspondence, they are related to the three-dimensional non-unitary Haagerup topological field theories, recently constructed by a topological twisting of three-dimensional ${\cal N}=4$ rank-zero superconformal field theories (SCFTs), called S-fold SCFTs. We propose that, up to the overall factors, the half-indices of the rank-zero SCFTs give the explicit Nahm representation of four conformal characters of the RCFTs including the vacuum character. Using the theory of Bantay-Gannon, we can successfully complete them into the full admissible conformal characters of the RCFTs.

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arXiv2023

$\mathbb{Z}_N$ Duality and Parafermions Revisited

Given a two-dimensional bosonic theory with a non-anomalous $\mathbb{Z}_2$ symmetry, the orbifolding and fermionization can be understood holographically using three-dimensional BF theory with level $2$. From a Hamiltonian perspective, the information of dualities is encoded in a topological boundary state which is defined as an eigenstate of certain Wilson loop operators (anyons) in the bulk. We generalize this story to two-dimensional theories with non-anomalous $\mathbb{Z}_N$ symmetry, focusing on parafermionization. We find the generic operators defining different topological boundary states including orbifolding and parafermionization with $\mathbb{Z}_N$ or subgroups of $\mathbb{Z}_N$, and discuss their algebraic properties as well as the $\mathbb{Z}_N$ duality web.

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arXiv2022

On Classification of Fermionic Rational Conformal Field Theories

We systematically study how the integrality of the conformal characters shapes the space of fermionic rational conformal field theories in two dimensions. The integrality suggests that conformal characters on torus with a given choice of spin structures should be invariant under a principal congruence subgroup of $\mathrm{PSL}(2,\mathbb{Z})$. The invariance strongly constrains the possible values of the central charge as well as the conformal weights in both Neveu-Schwarz and Ramond sectors, which improves the conventional holomorphic modular bootstrap method in a significant manner. This allows us to make much progress on the classification of fermionic rational conformal field theories with the number of independent characters less than five.

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arXiv2021

Can the energy bound $E \geq 0$ imply supersymmetry?

We utilize the integrality conjecture to show that the torus partition function of a fermionic rational conformal theory in the Ramond-Ramond sector becomes a constant when the bound $h^R \ge \frac{c}{24}$ is satisfied, where $h^R$ denote the conformal weights of Ramond states and $c$ is the central charge. The constant-valued Ramond-Ramond partition function strongly suggests the presence of supersymmetry unless a given theory has free fermions. The lower bound $h^R \ge \frac{c}{24}$ can then be identified with the unitarity bound of $\mathcal{N}=1$ supersymmetry. We thus propose that, for rational CFTs without free fermions, $(h^R-c/24) \geq 0$ can imply supersymmetry.

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arXiv2021

Emergent Supersymmetry on the Edges

The WZW models describe the dynamics of the edge modes of Chern-Simons theories in three dimensions. We explore the WZW models which can be mapped to supersymmetric theories via the generalized Jordan-Wigner transformation. Some of such models have supersymmetric Ramond vacua, but the others break the supersymmetry spontaneously. We also make a comment on recent proposals that the Read-Rezayi states at filling fraction $ν=1/2,~2/3$ are able to support supersymmetry.

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arXiv2021

Bootstrapping Fermionic Rational CFTs with Three Characters

Recently, the modular linear differential equation (MLDE) for level-two congruence subgroups $Γ_θ, Γ^{0}(2)$ and $Γ_0(2)$ of $\text{SL}_2(\mathbb{Z})$ was developed and used to classify the fermionic rational conformal field theories (RCFT). Two character solutions of the second-order fermionic MLDE without poles were found and their corresponding CFTs are identified. Here we extend this analysis to explore the landscape of three character fermionic RCFTs obtained from the third-order fermionic MLDE without poles. Especially, we focus on a class of the fermionic RCFTs whose Neveu-Schwarz sector vacuum character has no free-fermion currents and Ramond sector saturates the bound $h^{\text{R}} \ge \frac{c}{24}$, which is the unitarity bound for the supersymmetric case. Most of the solutions can be mapped to characters of the fermionized WZW models. We find the pairs of fermionic CFTs whose characters can be combined to produce $K(τ)$, the character of the $c=12$ fermionic CFT for $\text{Co}_0$ sporadic group.

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arXiv2021

Fermionic Rational Conformal Field Theories and Modular Linear Differential Equations

We define Modular Linear Differential Equations (MLDE) for the level-two congruence subgroups $Γ_\vartheta$, $Γ^0(2)$ and $Γ_0(2)$ of $\text{SL}_2(\mathbb Z)$. Each subgroup corresponds to one of the spin structures on the torus. The pole structures of the fermionic MLDEs are investigated by exploiting the valence formula for the level-two congruence subgroups. We focus on the first and second order holomorphic MLDEs without poles and use them to find a large class of `Fermionic Rational Conformal Field Theories', which have non-negative integer coefficients in the $q$-series expansion of their characters. We study the detailed properties of these fermionic RCFTs, some of which are supersymmetric. This work also provides a starting point for the classification of the fermionic Modular Tensor Category.

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arXiv2020

Notes on Superconformal Representations in Two Dimensions

We study global subalgebras of superconformal algebras in two dimensions and their unitary representations. Global superconformal multiplets are decomposed into conformal multiplets using Racah-Speiser algorithm, revealing many essential aspects of superconformal theories such as stress-energy tensor, conserved current, supersymmetric deformation and supersymmetry enhancement. Character formulae for the representations are presented. We further find a collection of conserved charges that are $k$-forms under the R-symmetry, which must be part of the super Virasoro algebra with $\mathcal{N} \geq 3$ supersymmetries.

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arXiv2020

Conformal Field Theories with Sporadic Group Symmetry

The monster sporadic group is the automorphism group of a central charge $c=24$ vertex operator algebra (VOA) or meromorphic conformal field theory (CFT). In addition to its $c=24$ stress tensor $T(z)$, this theory contains many other conformal vectors of smaller central charge; for example, it admits $48$ commuting $c=\frac12$ conformal vectors whose sum is $T(z)$. Such decompositions of the stress tensor allow one to construct new CFTs from the monster CFT in a manner analogous to the Goddard-Kent-Olive (GKO) coset method for affine Lie algebras. We use this procedure to produce evidence for the existence of a number of CFTs with sporadic symmetry groups and employ a variety of techniques, including Hecke operators, modular linear differential equations, and Rademacher sums, to compute the characters of these CFTs. Our examples include (extensions of) nine of the sporadic groups appearing as subquotients of the monster, as well as the simple groups ${}^2{E}_6(2)$ and ${F}_4(2)$ of Lie type. Many of these examples are naturally associated to McKay's $\widehat{E_8}$ correspondence, and we use the structure of Norton's monstralizer pairs more generally to organize our presentation.

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arXiv2019

Vanishing OPE Coefficients in 4d N=2 SCFTs

We compute the superconformal characters of various short multiplets in 4d N=2 superconformal algebra, from which selection rules for operator products are obtained. Combining with the superconformal index, we show that a particular short multiplet appearing in the n-fold product of stress-tensor multiplet is absent in the $(A_1, A_{2n})$ Argyres-Douglas (AD) theory. This implies that the operator product expansion (OPE) coefficients involving this multiplet vanish whenever the central charge $c$ is identical to that of the AD theory. Similarly, by considering the n-th power of the current multiplet, we show that a particular short multiplet and OPE coefficients vanish for a class of AD theories with ADE flavor symmetry. We also consider the generalized AD theory of type $(A_{k-1}, A_{n-1})$ for coprime k, n and compute its Macdonald index using the associated W-algebra under a mild assumption. This allows us to show that a number of short multiplets and OPE coefficients vanish in this theory. We also provide a Mathematica file along with this paper, where we implement the algorithm by Cordova-Dumitrescu-Intriligator to compute the spectrum of 4d N=2 superconformal multiplets as well as their superconformal character.

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arXiv2019

Monster Anatomy

We investigate the two-dimensional conformal field theories (CFTs) of $c=\frac{47}{2}$, $c=\frac{116}{5}$ and $c=23$ `dual' to the critical Ising model, the three state Potts model and the tensor product of two Ising models, respectively. We argue that these CFTs exhibit moonshines for the double covering of the baby Monster group, $2\cdot \mathbb{B}$, the triple covering of the largest Fischer group, $3\cdot \text{Fi}_{24}'$ and multiple-covering of the second largest Conway group, $2\cdot 2^{1+22} \cdot \text{Co}_2$. Various twined characters are shown to satisfy generalized bilinear relations involving Mckay-Thompson series. We also rediscover that the `self-dual' two-dimensional bosonic conformal field theory of $c=12$ has the Conway group $\text{Co}_{0}\simeq2\cdot\text{Co}_1$ as an automorphism group.

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arXiv2018

Modular Constraints on Superconformal Field Theories

We constrain the spectrum of $\mathcal{N}=(1, 1)$ and $\mathcal{N}=(2, 2)$ superconformal field theories in two-dimensions by requiring the NS-NS sector partition function to be invariant under the $Γ_θ$ congruence subgroup of the full modular group $SL(2, \mathbb{Z})$. We employ semi-definite programming to find constraints on the allowed spectrum of operators with or without $U(1)$ charges. Especially, the upper bounds on the twist gap for the non-current primaries exhibit interesting peaks, kinks, and plateau. We identify a number of candidate rational (S)CFTs realized at the numerical boundaries and find that they are realized as the solutions to modular differential equations associated to $Γ_θ$. Some of the candidate theories have been discussed by Höhn in the context of self-dual extremal vertex operator (super)algebra. We also obtain bounds for the charged operators and study their implications to the weak gravity conjecture in AdS$_3$.

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arXiv2018

Modular Constraints on Conformal Field Theories with Currents

We study constraints coming from the modular invariance of the partition function of two-dimensional conformal field theories. We constrain the spectrum of CFTs in the presence of holomorphic and anti-holomorphic currents using the semi-definite programming. In particular, we find the bounds on the twist gap for the non-current primaries depend dramatically on the presence of holomorphic currents, showing numerous kinks and peaks. Various rational CFTs are realized at the numerical boundary of the twist gap, saturating the upper limits on the degeneracies. Such theories include Wess-Zumino-Witten models for the Deligne's exceptional series, the Monster CFT and the Baby Monster CFT. We also study modular constraints imposed by $\mathcal{W}$-algebras of various type and observe that the bounds on the gap depend on the choice of $\mathcal{W}$-algebra in the small central charge region.

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arXiv2018

Holonomy Saddles and Supersymmetry

In gauge theories on a spacetime equipped with a circle, the holonomy variables, living in the Cartan torus, play special roles. With their periodic nature properly taken into account, we find that a supersymmetric gauge theory in $d$ dimensions tends to reduce in the small radius limit to a disjoint sum of multiple $(d-1)$ dimensional theories at distinct holonomies, called $H$-saddles. The phenomenon occurs regardless of the spacetime dimensions, and here we explore such $H$-saddles for $d=4$ $\cal N=1$ theories on $T^2$ fibred over $Σ_g$, in the limits of elongated $T^2$. This naturally generates novel relationships between 4d and 3d partition functions, including ones between 4d and 3d Witten indices, and also leads us to re-examine recent studies of the Cardy exponents and the Casimir energies and of their purported connections to the 4d anomalies.

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arXiv2018

Supersymmetric vortex defects in two dimensions

We study codimension-two BPS defects in 2d N=(2,2) supersymmetric gauge theories, focusing especially on those characterized by vortex-like singularities in the dynamical or non-dynamical gauge field. We classify possible SUSY-preserving boundary conditions on charged matter fields around the vortex defects, and derive a formula for defect correlators on the squashed sphere. We also prove an equivalence relation between vortex defects and 0d-2d coupled systems. Our defect correlators are shown to be consistent with the mirror symmetry duality between Abelian gauged linear sigma models and Landau-Ginzburg models, as well as that between the minimal model and its orbifold. We also study the vortex defects inserted at conical singularities.

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