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String Theory, Quantum Field Theory
Sungjay Lee is a theoretical physicist working mostly on Quantum Field Theory (QFT). This is a natural framework describing many different parts of physics, from particle physics, to condensed matter physics, and to statistical physics. To make fundamental theoretical advances in some of the most interesting problems in modern physics such as the strong nuclear force, strongly coupled systems of electrons, and quantum gravity, it is essential to understand QFT in the strongly coupled regime. Over the years, he has investigated new theoretical tools to understand the strong dynamics of supersymmetric field theory, conformal field theory, and string/Mtheory.



Publication at kias
NUMBER  P21028 
AUTHOR  Lee, Kimyeong,Duan, Zhihao,Sarkis, Matthieu,Lee, Sungjay 
TITLE  Bootstrapping fermionic rational CFTs with three characters 
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JOURNAL  JOURNAL OF HIGH ENERGY PHYSICS, 2022 
ABSTRACT  Recently, the modular linear differential equation (MLDE) for leveltwo congruence subgroups Gamma(theta), Gamma(0)(2) and Gamma(0)(2) of SL2(Z) was developed and used to classify the fermionic rational conformal field theories (RCFT). Two character solutions of the secondorder 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 thirdorder fermionic MLDE without poles. Especially, we focus on a class of the fermionic RCFTs whose NeveuSchwarz sector vacuum character has no freefermion currents and Ramond sector saturates the bound h(R) >= 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(tau), the character of the c = 12 fermionic CFT for Co0 sporadic group. 

Publication at kias
NUMBER  P20002 
AUTHOR  Lee, Kimyeong,Lee, Sungjay 
TITLE  Conformal Field Theories with Sporadic Group Symmetry 
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JOURNAL  COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2021 
ABSTRACT  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 = 1/2 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 GoddardKentOlive (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 E2(6)( 2) and F4( 2) of Lie type. Many of these examples are naturally associated to McKays (E) over cap (8) correspondence, and we use the structure of Nortons monstralizer pairs more generally to organize our presentation. 

Publication at kias
NUMBER  P21015 
AUTHOR  Lee, Sungjay 
TITLE  Emergent supersymmetry on the edges 
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JOURNAL  SCIPOST PHYSICS, 2021 
ABSTRACT  The WZW models describe the dynamics of the edge modes of ChernSimons theories in three dimensions. We explore the WZW models which can be mapped to supersymmetric theories via the generalized JordanWigner 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 ReadRezayi states at filling fraction nu = 1/2, 2/3 are able to support supersymmetry. 

Publication at kias
NUMBER  P20056 
AUTHOR  Lee, Kimyeong,Duan, Zhihao,Sarkis, Matthieu,Lee, Sungjay 
TITLE  Fermionic rational conformal field theories and modular linear differential equations 
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JOURNAL  PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS, 2021 
ABSTRACT  We define modular linear differential equations (MLDE) for the leveltwo congruence subgroups Gamma(theta), Gamma(0)(2) and Gamma(0)(2) of SL2(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 leveltwo congruence subgroups. We focus on the first and secondorder holomorphic MLDEs without poles and use them to find a large class of fermionic rational conformal field theories (fermionic RCFTs), which have nonnegative integer coefficients in the qseries 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. 

Publication at kias
NUMBER  
AUTHOR  Lee, Sungjay 
TITLE  Notes on superconformal representations in two dimensions 
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JOURNAL  NUCLEAR PHYSICS B, 2020 
ABSTRACT  We study global subalgebras of superconformal algebras in two dimensions and their unitary representations. Global superconformal multiplets are decomposed into conformal multiplets using RacahSpeiser algorithm, revealing many essential aspects of superconformal theories such as stressenergy 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 kforms under the Rsymmetry, which must be part of the super Virasoro algebra with N >= 3 supersymmetries. (C) 2020 The Author(s). Published by Elsevier B.V. 

Monster anatomy
Title 
: Monster anatomy 
Journal 
: JOURNAL OF HIGH ENERGY PHYSICS, 2019 
Publication at kias
NUMBER  P18107 
AUTHOR  Lee, Kimyeong,Bae, JinBeom,Lee, Sungjay 
TITLE  Monster anatomy 
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JOURNAL  JOURNAL OF HIGH ENERGY PHYSICS, 2019 
ABSTRACT  We investigate the two dimensional conformal fi eld theories ( CFTs) of c = 47 2, c = 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 B, the triple covering of the largest Fischer group, 3 Fi 0 24 and multiple covering of the second largest Conway group, 2 2 1+22 Co 2. Various twined characters are shown to satisfy generalized bilinear relations involving Mckay Thompson series. We also rediscover that the ` self dual twodimensional bosonic conformal fi eld theory of c = 12 has the Conway group Co 0 2 Co 1 as an automorphism group. 

Publication at kias
NUMBER  P18102 
AUTHOR  Lee, Sungjay,Song, Jaewon 
TITLE  Vanishing OPE coefficients in 4d N=2 SCFTs 
ARCHIVE  arXiv:1812.04743 
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JOURNAL  JOURNAL OF HIGH ENERGY PHYSICS, 2019 
ABSTRACT  We discuss the local (gauged) Weyl symmetry and its spontaneous breaking and apply it to model building beyond the standard model (SM) and inflation. In models with nonminimal couplings of the scalar fields to the Ricci scalar that are conformal invariant, the spontaneous generation by a scalar field(s) vacuum expectation value of a positive Newton constant demands a negative kinetic term for the scalar field or vice versa. This is naturally avoided in models with additional Weyl gauge symmetry. The Weyl gauge field omega(mu) couples to the scalar sector but not to the fermionic sector of a SMlike Lagrangian. The field omega(mu) undergoes a Stueckelberg mechanism and becomes massive after eating the (radial mode) wouldbe Goldstone field (dilaton rho) in the scalar sector. Before the decoupling of omega(mu), the dilaton can act as an UV regulator and maintain the Weyl symmetry at the quantum level, with relevance for solving the hierarchy problem. After the decoupling of omega(mu), the scalar potential depends only on the remaining (angular variables) scalar fields, which can be the Higgs field, inflaton, etc. We show that a successful inflation is then possible with one of these scalar fields identified as the inflaton. While our approach is derived in the Riemannian geometry with omega(mu) introduced to avoid ghosts, the natural framework is that of Weyl geometry, which for the same matter spectrum is shown to generate the same Lagrangian, up to a total derivative. 

Publication at kias
NUMBER  P18096 
AUTHOR  Lee, Sungjay,Bae, JinBeom,Song, Jaewon 
TITLE  Modular constraints on superconformal field theories 
ARCHIVE  arXiv:1811.00976 
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JOURNAL  JOURNAL OF HIGH ENERGY PHYSICS, 2019 
ABSTRACT  We constrain the spectrum of N = (1, 1) and N = (2, 2) superconformal field theories in twodimensions by requiring the NSNS sector partition function to be invariant under the congruence subgroup of the full modular group SL(2, Z). We employ semidefinite 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 noncurrent 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 . Some of the candidate theories have been discussed by Hohn in the context of selfdual 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). 

Publication at kias
NUMBER  P18087 
AUTHOR  Lee, Sungjay,Bae, JinBeom 
TITLE  Recent Developments in Modular Bootstrap 
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JOURNAL  JOURNAL OF THE KOREAN PHYSICAL SOCIETY, 2018 
ABSTRACT  We give a short review over recent works on modular constraints on the twodimensional (supersymmetric) CFTs and their implications to the threedimensional quantum gravity in anti de Sitter space via the holographic principle. 

Publication at kias
NUMBER  P18005 
AUTHOR  Yi, Piljin,Lee, Sungjay,Hwang, Chiung 
TITLE  Holonomy saddles and supersymmetry 
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JOURNAL  PHYSICAL REVIEW D, 2018 
ABSTRACT  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 Hsaddles. The phenomenon occurs regardless of the spacetime dimensions, and here we explore such Hsaddles for d = 4 N = 1 theories on T2 fibered over Sigma(g), in the limits of elongated T2. This naturally generates novel relationships between 4d and 3d partition functions, including ones between 4d and 3d Witten indices, and also leads us to reexamine recent studies of the Cardy exponents and the Casimir energies and of their purported connections to the 4d anomalies. 

Publication at kias
NUMBER  P17005 
AUTHOR  Lee, Sungjay 
TITLE  Supersymmetric vortex defects in two dimensions 
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JOURNAL  JOURNAL OF HIGH ENERGY PHYSICS, 2018 
ABSTRACT  We study codimensiontwo BPS defects in 2d N = (2, 2) supersymmetric gauge theories, focusing especially on those characterized by vortexlike singularities in the dynamical or nondynamical gauge field. We classify possible SUSYpreserving 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 0d2d coupled systems. Our defect correlators are shown to be consistent with the mirror symmetry duality between Abelian gauged linear sigma models and LandauGinzburg models, as well as that between the minimal model and its orbifold. We also study the vortex defects inserted at conical singularities. 

Publication at kias
NUMBER  P17089 
AUTHOR  Lee, Sungjay,Bae, JinBeom,Song, Jaewon 
TITLE  Modular constraints on conformal field theories with currents 
ARCHIVE  1708.08815 
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JOURNAL  JOURNAL OF HIGH ENERGY PHYSICS, 2017 
ABSTRACT  We study constraints coming from the modular invariance of the partition function of twodimensional conformal field theories. We constrain the spectrum of CFTs in the presence of holomorphic and antiholomorphic currents using the semidefinite programming. In particular, we find the bounds on the twist gap for the noncurrent 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 WessZuminoWitten models for the Delignes exceptional series, the Monster CFT and the Baby Monster CFT. We also study modular constraints imposed by Walgebras of various type and observe that the bounds on the gap depend on the choice of Walgebra in the small central charge region. 

Publication at kias
NUMBER  P10025 
AUTHOR  Lee, Sungjay 
TITLE  AGT on the Sduality wall 
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JOURNAL  JOURNAL OF HIGH ENERGY PHYSICS, 2010 
ABSTRACT  Threedimensional gauge theory T[G] arises on a domain wall between fourdimensional N = 4 SYM theories with the gauge groups G and its Sdual G(L). We argue that the N = 2* mass deformation of the bulk theory induces a massdeformation of the theory T[G] on the wall. The partition functions of the theory T[SU(2)] and its massdeformation on the threesphere are shown to coincide with the transformation coefficient of Liouville onepoint conformal block on torus under the Sduality. 

Publication at kias
NUMBER  P10018 
AUTHOR  Lee, KiMyeong,Lee, Sungjay 
TITLE  1/2BPS Wilson loops and vortices in ABJM model 
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JOURNAL  JOURNAL OF HIGH ENERGY PHYSICS, 2010 
ABSTRACT  We explore the lowenergy dynamics of 1/2BPS heavy particles coupled to the ABJM model via the Higgsing of M2branes, with focus on physical understanding of the recently discovered 1/2BPS Wilson loop operators. The lowenergy theory of 1/2BPS heavy particles turns out to have the U(N vertical bar N) supergauge symmetry, which explains the novel structure of the 1/2BPS Wilson loop operator as a holonomy of a U(N vertical bar N) superconnection. We show that the supersymmetric transformation of the Wilson loop operator can be identified as a fermionic supergauge transformation, which leads to their invariance under half of the supersymmetry. We also argue that 1/2BPS Wilson loop operators appear as 1/2BPS vortices with vorticity 1/k. Such a vortex can be naturally interpreted as a membrane wrapping the Z(k) cycle once, or type IIA fundamental string. 

Publication at kias
NUMBER  P09052 
AUTHOR  Yi, Piljin,Lee, Sungjay 
TITLE  A study of WallCrossing: flavored kinks in D=2 QED 
ARCHIVE  arXiv:0902.4515 
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JOURNAL  JOURNAL OF HIGH ENERGY PHYSICS, 2010 
ABSTRACT  We study spectrum of D = 2 N = (2, 2) QED with N + 1 massive charged chiral multiplets, with care given to precise supermultiplet countings. In the infrared the theory flows to CPN model with twisted masses, where we construct generic flavored kink solitons for the large mass regime, and study their quantum degeneracies. These kinks are qualitatively different and far more numerous than those of small mass regime, with features reminiscent of multipronged (p, q) string web, complete with the wallcrossing behavior. It has been also conjectured that spectrum of this theory is equivalent to the hypermultiplet spectrum of a certain D = 4 SeibergWitten theory. We find that the correspondence actually extends beyond hypermultiplets in D = 4, and that many of the relevant indices match. However, a D = 2 BPS state is typically mapped to several different kind of dyons whose individual supermultiplets are rather complicated; the match of index comes about only after summing over indices of these different dyons. We note general wallcrossing behavior of flavored BPS kink states, and compare it to those of D = 4 dyons. 

Publication at kias
NUMBER  P09037 
AUTHOR  Lee, Sungjay,Lee, Sangmin 
TITLE  Topological ChernSimons sigma model 
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JOURNAL  JOURNAL OF HIGH ENERGY PHYSICS, 2009 
ABSTRACT  We consider topological twisting of recently constructed ChernSimonsmatter theories in three dimensions with N = 4 or higher supersymmetry. We enumerate physically inequivalent twistings for each N, and find two different twistings for N = 4, one for N = 5, 6, and four for N = 8. We construct the two types of N = 4 topological theories, which we call A/Bmodels, in full detail. The Amodel has been recently studied by Kapustin and Saulina. The Bmodel is new and it consists solely of a ChernSimons term of a complex gauge field up to BRSTexact terms. We also compare the new theories with topological YangMills theories and find some interesting connections. In particular, the Amodel seems to off er a new perspective on Casson invariant and its relation to RozanskyWitten theory. 

Publication at kias
NUMBER  P09009 
AUTHOR  Lee, KiMyeong,Lee, Sungjay 
TITLE  Nonrelativistic superconformal M2brane theory 
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JOURNAL  JOURNAL OF HIGH ENERGY PHYSICS, 2009 
ABSTRACT  We investigate the low energy physics of particles in the symmetric phase of the N = 6 massdeformed ABJM theory in terms of the superconformal nonrelativistic field theory with 14 supercharges. They describe a certain kind of excitations on M2 branes in the background of external fourform flux. We study the nonrelativistic superconformal algebra and their representations by using the operatorstate correspondence with the related harmonic oscillator Hamiltonian. We find the unitarity bounds on the scaling dimension and particle number of any local operator, and comment on subtleties in computing the superconformal Witten index that counts the chiral operators. 

Publication at kias
NUMBER  P08062 
AUTHOR  Yi, Piljin,Lee, Sungjay,Lee, KiMyeong 
TITLE  A nonperturbative test of M2brane theory 
ARCHIVE  0809.1771 
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JOURNAL  JOURNAL OF HIGH ENERGY PHYSICS, 2008 
ABSTRACT  We discuss nonperturbative effects in the ABJM model due to monopole instantons. We begin by constructing the instanton solutions in the U(2) x U(2) model, explicitly, and computing the Euclidean action. The Wickrotated Lagrangian is complex and its BPS monopole instantons are found to be a delicate version of the usual t HooftPolyakov monopole solutions. They are generically 1/3 BPS but become 1/2 BPS at special locus in the moduli space of two M2branes, yet each instanton carries eight fermionic zero modes, regardless of the vacuum choice. The low energy effective action induced by monopole instantons are quartic order in derivatives. The resulting vertices are nonperturbative in 1/k, as expected, but are rational functions of the vacuum moduli. We also analyze the system of two M2branes in the supergravity framework and compute the higher order interactions via 11dimensional supergraviton exchange. The comparison of the two shows that the instanton vertices are precisely reproduced by this M2brane picture, supporting the proposal that the ABJM model describes multiple M2branes. 

Publication at kias
NUMBER  P08046 
AUTHOR  Lee, KiMyeong,Hosomichi, Kazuo,Lee, Sungjay 
TITLE  N=5, 6 superconformal ChernSimons theories and M2branes on orbifolds 
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JOURNAL  JOURNAL OF HIGH ENERGY PHYSICS, 2008 
ABSTRACT  We explore further our recent generalization of the N = 4 superconformal ChernSimons theories of Gaiotto and Witten. We find and construct explicitly theories of enhanced N = 5 or 6 supersymmetry, especially N = 5, Sp(2M) x O(N) and N = 6, Sp(2M) x O(2) theories. The U(M) x U(N) theory coincides with the N = 6 theory of Aharony, Bergman, Jafferis and Maldacena (ABJM). We argue that the N = 5 theory with Sp(2N) x O(2N) gauge group can be understood as an orientifolding of the ABJM model with U(2N) x U(2N) gauge group. We briefly discuss the Type IIB brane construction of the N = 5 theory and the geometry of the Mtheory orbifold. 

Publication at kias
NUMBER  
AUTHOR  Lee, KiMyeong,Hosomichi, Kazuo,Lee, Sungjay 
TITLE  Massdeformed BaggerLambert theory and its BPS objects 
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JOURNAL  PHYSICAL REVIEW D, 2008 
ABSTRACT  We find a 16supersymmetric massdeformed BaggerLambert theory with SO(4) x SO(4) global R symmetry. The R charge plays the role of the noncentral term in the superalgebra. This theory has one symmetric vacuum and two inequivalent broken sectors of vacua. Each sector of the broken symmetry has SO(4) geometry. We find the 1/2 BPS domain walls connecting the symmetric phase and any broken phase, and 1/4 BPS supertubelike objects, which may appear as anyonic qballs in the symmetric phase or vortices in the broken phase. We also discuss mass deformations, which reduce the number of supersymmetries. 

Publication at kias
NUMBER  P08028 
AUTHOR  Lee, KiMyeong,Lee, Sungjay 
TITLE  Dyonic instantons in 5dim YangMills ChernSimons theories 
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JOURNAL  JOURNAL OF HIGH ENERGY PHYSICS, 2008 
ABSTRACT  We consider the BPS dyonic instantons in the 5dim supersymmetric YangMills ChernSimons theories. Its field theoretic structures and the moduli space dynamics in term of the ADHM data have been explored in detail. We find that the field theoretic ChernSimons term leads to an effective magnetic field on instanton moduli space. 

Publication at kias
NUMBER  P08039 
AUTHOR  Lee, KiMyeong,Hosomichi, Kazuo,Leea, Sungjay 
TITLE  N=4 superconformal ChernSimons theories with hyper and twisted hyper multiplets 
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JOURNAL  JOURNAL OF HIGH ENERGY PHYSICS, 2008 
ABSTRACT  We extend the N = 4 superconformal ChernSimons theories of Gaiotto and Witten to those with additional twisted hypermultiplets. The new theories are generically linear quiver gauge theories with the two types of hypermultiplets alternating between gauge groups. Our construction includes the BaggerLambert model of SO(4) gauge group. A family of abelian theories are identified with those proposed earlier in the context of the Mcrystal model for M2branes probing (C2/Z(n))(2) orbifolds. Possible extension with nonabelian BF couplings and string/Mtheory realization are briefly discussed. 
 2015Present: Professor, Korea Institute for Advanced Study
 20132015: Enrico Fermi Fellow, The University of Chicago
 20122015: STFC Ernest Rutherford Fellow, University of Cambridge
 20102012: Research Associate, University of Cambridge
 20102010: Assistant Professor, Korea Institute for Advanced Study
 20082010: Research Fellow, Korea Institute for Advanced Study
 20022008: Ph.D., Seoul National University
 2017: Baekcheon Physics Prize, Korean Physical Society, Korea
 2016: Young Scientist Award (Presidential), Korean Academy of Science and Technology, Korea
 2016: Junior Fellowship, Fondation Science Mathématique de Paris, France
 2012: Enrico Fermi Fellowship, The University of Chicago, USA
 2012: Ernest Rutherford Fellowship, Science and Technology Facilities Council, UK
 2009: Haksool Research Prize, Korea Institute for Advanced Study, Korea
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