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Title | : Bootstrapping fermionic rational CFTs with three characters |
Journal | : JOURNAL OF HIGH ENERGY PHYSICS, 2022 |
NUMBER | P21028 |
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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 level-two 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 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(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 Co-0 sporadic group. |
Title | : Conformal Field Theories with Sporadic Group Symmetry |
Journal | : COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2021 |
NUMBER | P20002 |
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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 Goddard-KentOlive (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 E-2(6)( 2) and F-4( 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. |
Title | : Emergent supersymmetry on the edges |
Journal | : SCIPOST PHYSICS, 2021 |
NUMBER | P21015 |
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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 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 nu = 1/2, 2/3 are able to support supersymmetry. |
Title | : Fermionic rational conformal field theories and modular linear differential equations |
Journal | : PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS, 2021 |
NUMBER | P20056 |
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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 level-two 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 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 (fermionic RCFTs), 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. |
Title | : Notes on superconformal representations in two dimensions |
Journal | : NUCLEAR PHYSICS B, 2020 |
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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 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 N >= 3 supersymmetries. (C) 2020 The Author(s). Published by Elsevier B.V. |
Title | : Monster anatomy |
Journal | : JOURNAL OF HIGH ENERGY PHYSICS, 2019 |
NUMBER | P18107 |
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AUTHOR | Lee, Kimyeong,Bae, Jin-Beom,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. |
Title | : Vanishing OPE coefficients in 4d N=2 SCFTs |
Journal | : JOURNAL OF HIGH ENERGY PHYSICS, 2019 |
NUMBER | P18102 |
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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 SM-like Lagrangian. The field omega(mu) undergoes a Stueckelberg mechanism and becomes massive after eating the (radial mode) would-be 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. |
Title | : Modular constraints on superconformal field theories |
Journal | : JOURNAL OF HIGH ENERGY PHYSICS, 2019 |
NUMBER | P18096 |
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AUTHOR | Lee, Sungjay,Bae, Jin-Beom,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 two-dimensions by requiring the NS-NS sector partition function to be invariant under the congruence subgroup of the full modular group SL(2, 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 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 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). |
Title | : Recent Developments in Modular Bootstrap |
Journal | : JOURNAL OF THE KOREAN PHYSICAL SOCIETY, 2018 |
NUMBER | P18087 |
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AUTHOR | Lee, Sungjay,Bae, Jin-Beom |
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 two-dimensional (supersymmetric) CFTs and their implications to the three-dimensional quantum gravity in anti de Sitter space via the holographic principle. |
Title | : Holonomy saddles and supersymmetry |
Journal | : PHYSICAL REVIEW D, 2018 |
NUMBER | P18005 |
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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 H-saddles. The phenomenon occurs regardless of the spacetime dimensions, and here we explore such H-saddles for d = 4 N = 1 theories on T-2 fibered over Sigma(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 reexamine recent studies of the Cardy exponents and the Casimir energies and of their purported connections to the 4d anomalies. |
Title | : Supersymmetric vortex defects in two dimensions |
Journal | : JOURNAL OF HIGH ENERGY PHYSICS, 2018 |
NUMBER | P17005 |
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AUTHOR | Lee, Sungjay |
TITLE | Supersymmetric vortex defects in two dimensions |
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JOURNAL | JOURNAL OF HIGH ENERGY PHYSICS, 2018 |
ABSTRACT | 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. |
Title | : Modular constraints on conformal field theories with currents |
Journal | : JOURNAL OF HIGH ENERGY PHYSICS, 2017 |
NUMBER | P17089 |
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AUTHOR | Lee, Sungjay,Bae, Jin-Beom,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 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 Delignes exceptional series, the Monster CFT and the Baby Monster CFT. We also study modular constraints imposed by W-algebras of various type and observe that the bounds on the gap depend on the choice of W-algebra in the small central charge region. |
Title | : AGT on the S-duality wall |
Journal | : JOURNAL OF HIGH ENERGY PHYSICS, 2010 |
NUMBER | P10025 |
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AUTHOR | Lee, Sungjay |
TITLE | AGT on the S-duality wall |
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JOURNAL | JOURNAL OF HIGH ENERGY PHYSICS, 2010 |
ABSTRACT | Three-dimensional gauge theory T[G] arises on a domain wall between four-dimensional N = 4 SYM theories with the gauge groups G and its S-dual G(L). We argue that the N = 2* mass deformation of the bulk theory induces a mass-deformation of the theory T[G] on the wall. The partition functions of the theory T[SU(2)] and its mass-deformation on the three-sphere are shown to coincide with the transformation coefficient of Liouville one-point conformal block on torus under the S-duality. |
Title | : 1/2-BPS Wilson loops and vortices in ABJM model |
Journal | : JOURNAL OF HIGH ENERGY PHYSICS, 2010 |
NUMBER | P10018 |
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AUTHOR | Lee, Ki-Myeong,Lee, Sungjay |
TITLE | 1/2-BPS Wilson loops and vortices in ABJM model |
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JOURNAL | JOURNAL OF HIGH ENERGY PHYSICS, 2010 |
ABSTRACT | We explore the low-energy dynamics of 1/2-BPS heavy particles coupled to the ABJM model via the Higgsing of M2-branes, with focus on physical understanding of the recently discovered 1/2-BPS Wilson loop operators. The low-energy theory of 1/2-BPS heavy particles turns out to have the U(N vertical bar N) supergauge symmetry, which explains the novel structure of the 1/2-BPS 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 1/2-BPS Wilson loop operators appear as 1/2-BPS 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. |
Title | : A study of Wall-Crossing: flavored kinks in D=2 QED |
Journal | : JOURNAL OF HIGH ENERGY PHYSICS, 2010 |
NUMBER | P09052 |
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AUTHOR | Yi, Piljin,Lee, Sungjay |
TITLE | A study of Wall-Crossing: 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 multi-pronged (p, q) string web, complete with the wall-crossing behavior. It has been also conjectured that spectrum of this theory is equivalent to the hypermultiplet spectrum of a certain D = 4 Seiberg-Witten 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 wall-crossing behavior of flavored BPS kink states, and compare it to those of D = 4 dyons. |
Title | : Topological Chern-Simons sigma model |
Journal | : JOURNAL OF HIGH ENERGY PHYSICS, 2009 |
NUMBER | P09037 |
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AUTHOR | Lee, Sungjay,Lee, Sangmin |
TITLE | Topological Chern-Simons sigma model |
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JOURNAL | JOURNAL OF HIGH ENERGY PHYSICS, 2009 |
ABSTRACT | We consider topological twisting of recently constructed Chern-Simons-matter 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/B-models, in full detail. The A-model has been recently studied by Kapustin and Saulina. The B-model is new and it consists solely of a Chern-Simons term of a complex gauge field up to BRST-exact terms. We also compare the new theories with topological Yang-Mills theories and find some interesting connections. In particular, the A-model seems to off er a new perspective on Casson invariant and its relation to Rozansky-Witten theory. |
Title | : Nonrelativistic superconformal M2-brane theory |
Journal | : JOURNAL OF HIGH ENERGY PHYSICS, 2009 |
NUMBER | P09009 |
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AUTHOR | Lee, Ki-Myeong,Lee, Sungjay |
TITLE | Nonrelativistic superconformal M2-brane 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 mass-deformed 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 four-form flux. We study the nonrelativistic superconformal algebra and their representations by using the operator-state 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. |
Title | : A nonperturbative test of M2-brane theory |
Journal | : JOURNAL OF HIGH ENERGY PHYSICS, 2008 |
NUMBER | P08062 |
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AUTHOR | Yi, Piljin,Lee, Sungjay,Lee, Ki-Myeong |
TITLE | A nonperturbative test of M2-brane theory |
ARCHIVE | 0809.1771 |
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JOURNAL | JOURNAL OF HIGH ENERGY PHYSICS, 2008 |
ABSTRACT | We discuss non-perturbative 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 Wick-rotated Lagrangian is complex and its BPS monopole instantons are found to be a delicate version of the usual t Hooft-Polyakov monopole solutions. They are generically 1/3 BPS but become 1/2 BPS at special locus in the moduli space of two M2-branes, 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 M2-branes in the supergravity framework and compute the higher order interactions via 11-dimensional supergraviton exchange. The comparison of the two shows that the instanton vertices are precisely reproduced by this M2-brane picture, supporting the proposal that the ABJM model describes multiple M2-branes. |
Title | : N=5, 6 superconformal Chern-Simons theories and M2-branes on orbifolds |
Journal | : JOURNAL OF HIGH ENERGY PHYSICS, 2008 |
NUMBER | P08046 |
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AUTHOR | Lee, Ki-Myeong,Hosomichi, Kazuo,Lee, Sungjay |
TITLE | N=5, 6 superconformal Chern-Simons theories and M2-branes 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 Chern-Simons 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 M-theory orbifold. |
Title | : Mass-deformed Bagger-Lambert theory and its BPS objects |
Journal | : PHYSICAL REVIEW D, 2008 |
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AUTHOR | Lee, Ki-Myeong,Hosomichi, Kazuo,Lee, Sungjay |
TITLE | Mass-deformed Bagger-Lambert theory and its BPS objects |
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JOURNAL | PHYSICAL REVIEW D, 2008 |
ABSTRACT | We find a 16-supersymmetric mass-deformed Bagger-Lambert 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 q-balls in the symmetric phase or vortices in the broken phase. We also discuss mass deformations, which reduce the number of supersymmetries. |
Title | : Dyonic instantons in 5-dim Yang-Mills Chern-Simons theories |
Journal | : JOURNAL OF HIGH ENERGY PHYSICS, 2008 |
NUMBER | P08028 |
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AUTHOR | Lee, Ki-Myeong,Lee, Sungjay |
TITLE | Dyonic instantons in 5-dim Yang-Mills Chern-Simons theories |
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JOURNAL | JOURNAL OF HIGH ENERGY PHYSICS, 2008 |
ABSTRACT | We consider the BPS dyonic instantons in the 5-dim supersymmetric Yang-Mills Chern-Simons 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 Chern-Simons term leads to an effective magnetic field on instanton moduli space. |
Title | : N=4 superconformal Chern-Simons theories with hyper and twisted hyper multiplets |
Journal | : JOURNAL OF HIGH ENERGY PHYSICS, 2008 |
NUMBER | P08039 |
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AUTHOR | Lee, Ki-Myeong,Hosomichi, Kazuo,Leea, Sungjay |
TITLE | N=4 superconformal Chern-Simons 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 Chern-Simons theories of Gaiotto and Witten to those with additional twisted hyper-multiplets. The new theories are generically linear quiver gauge theories with the two types of hyper-multiplets alternating between gauge groups. Our construction includes the Bagger-Lambert model of SO(4) gauge group. A family of abelian theories are identified with those proposed earlier in the context of the M-crystal model for M2-branes probing (C-2/Z(n))(2) orbifolds. Possible extension with non-abelian BF couplings and string/M-theory realization are briefly discussed. |