Conformal Field Theories with Sporadic Group Symmetry

Bae, Jin-Beom; Harvey, Jeffrey A.; Lee, Kimyeong; Lee, Sungjay; Rayhaun, Brandon C.

doi:10.1007/s00220-021-04207-7

Cited by 15 publications

(20 citation statements)

References 94 publications

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“…For instance, the characters of the Ising model and babymonster CFT are combined to produce J(τ ) [9]. The bilinear relation has been utilized to analyze the monstralizing commutant pair in [24]. It turns out that the solutions of the fermionic MLDE also exhibit bilinear relations for some cases.…”

Section: Jhep01(2022)089mentioning

confidence: 99%

“…Here we present the Fourier coefficients of the vector-valued modular form by exploiting Rademacher's idea. An application of the Rademacher expansion to the vector-valued modular form has been discussed in the literature, e.g., [24,33].…”

Section: Rademacher Expansionmentioning

confidence: 99%

“…It has been known that the process of the above decomposition can be formulated by using the mathematical notion of the commutant subalgebra of Monster VOA. The explicit examples of Monster deconstruction have been discussed in [24,41] with choosing t 1 (z) as the stress-energy tensor of the minimal models or Z k parafermion model. As a consequence, the Monster deconstruction leads us to specific RCFTs which exhibit sporadic groups in their modular invariant partition function.…”

Section: Bilinear Relations Of Fermionic Rcftmentioning

confidence: 99%

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Bootstrapping fermionic rational CFTs with three characters

Bae

Duan

Lee

et al. 2022

J. High Energ. Phys.

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Recently, the modular linear differential equation (MLDE) for level-two congruence subgroups Γθ, Γ0(2) and Γ0(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 hR ≥ $$ \frac{C}{24} $$ 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 Co0 sporadic group.

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Section: Jhep01(2022)089mentioning

confidence: 99%

Section: Rademacher Expansionmentioning

confidence: 99%

Section: Bilinear Relations Of Fermionic Rcftmentioning

confidence: 99%

See 1 more Smart Citation

Bootstrapping fermionic rational CFTs with three characters

Bae

Duan

Lee

et al. 2022

J. High Energ. Phys.

Self Cite

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“…Including cases with only a single vacuum interpretation, we see that there are in total ten possible cases with no Kac-Moody. Among them, the (c, n J ) = 116 5 , 0 case matches with the theory denoted V F 24 in [47,48]. This theory is associated with the 3.F i 24 subgroup of the monster group, and the inner product of the three-state Potts and V F 24 characters gives the Monster CFT.…”

Section: Four Charactersmentioning

confidence: 55%

Holomorphic modular bootstrap revisited

Kaidi

Lin

Parra-Martinez

2021

J. High Energ. Phys.

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In this work we revisit the “holomorphic modular bootstrap”, i.e. the classification of rational conformal field theories via an analysis of the modular differential equations satisfied by their characters. By making use of the representation theory of PSL(2, ℤn), we describe a method to classify allowed central charges and weights (c, hi) for theories with any number of characters d. This allows us to avoid various bottlenecks encountered previously in the literature, and leads to a classification of consistent characters up to d = 5 whose modular differential equations are uniquely fixed in terms of (c, hi). In the process, we identify the full set of constraints on the allowed values of the Wronskian index for fixed d ≤ 5.

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“…For example, the Z 2 symmetry of the c = 1/2 Ising model acts as an element of the 2A conjugacy class of the Monster, an obervation due to Miyamoto. Many generalizations of this idea have been worked out, see [53,5] for further examples and constructions. A similar phenomenon for the Conway CFT is explored in [24].…”

Section: Connections To Cft/voamentioning

confidence: 99%

Snowmass White Paper: Moonshine

Harrison¹,

Harvey²,

Paquette³

2022

Preprint

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We present a brief overview of Moonshine with an emphasis on connections to physics. Moonshine collectively refers to a set of phenomena connecting group theory, analytic number theory, and vertex operator algebras or conformal field theories. Modern incarnations of Moonshine arise in various BPS observables in string theory and, via dualities, invariants in enumerative geometry. We survey old and new developments, and highlight some of the many open questions that remain.

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Conformal Field Theories with Sporadic Group Symmetry

Cited by 15 publications

References 94 publications

Bootstrapping fermionic rational CFTs with three characters

Bootstrapping fermionic rational CFTs with three characters

Holomorphic modular bootstrap revisited

Snowmass White Paper: Moonshine

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