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Article
Physics, Particles & Fields
Zhihao Duan et al.
Summary: We study how the integrality of conformal characters affects the space of fermionic rational conformal field theories in two dimensions. The integrality implies that conformal characters on a Torus with a given spin structure should be invariant under a principal congruence subgroup of PSL(2,Z). This invariance strongly constrains the possible values of the central charge and conformal weights in the Neveu-Schwarz and Ramond sectors, leading to significant improvements in the conventional holomorphic modular bootstrap method. As a result, we make significant progress in classifying fermionic rational conformal field theories with fewer than five independent characters.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Article
Physics, Multidisciplinary
Jan Albert et al.
Summary: This article verifies the theory of topological modular forms (TMF) that the elliptic genera of physical theories satisfy a certain divisibility property determined by the theory's gravitational anomaly. The author verifies this prediction in Duncan's supermoonshine module, as well as in tensor products and orbifolds. The author also develops machinery for computing the elliptic genera of general alternating orbifolds and discusses the relation to the elusive periodicity class of TMF.
PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS
(2023)
Article
Materials Science, Multidisciplinary
Gil Young Cho et al.
Summary: This paper presents a systematic method for classifying fermionic topological orders by explicitly building their modular data, which encodes the statistics between anyons. The authors classify the orders up to rank 10 and obtain both unitary and nonunitary modular data, including two new classes. They also determine the chiral central charges using a novel method that does not require explicit computations of modular extensions.
Article
Materials Science, Multidisciplinary
Gil Young Cho et al.
Summary: This research provides a method for classifying fermionic topological orders and successfully determines the modular data up to rank 10, including both unitary and nonunitary modular data. This contributes to a better understanding and application in topological quantum computers.
Article
Physics, Particles & Fields
Jin-Beom Bae et al.
Summary: This study extends the analysis to three-character fermionic RCFTs and focuses on a specific class of fermionic RCFTs that can be mapped to characters of fermionized WZW models.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Zhihao Duan et al.
Summary: In this article, we systematically study the Hecke relations and coset relations among 2D rational conformal field theories (RCFTs), and propose that the characters of any 2D RCFT can be realized as a Hecke image or the coset of a Hecke image with respect to a c = 8k theory. We check this proposal for all admissible theories with up to five characters and discover new Hecke relations. This study provides interesting examples of vector-valued modular functions up to rank seven.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Mathematical
Jin-Beom Bae et al.
Summary: The monster sporadic group is the automorphism group of a central charge c = 24 vertex operator algebra (VOA) or meromorphic conformal field theory (CFT). By decomposing the stress tensor, new CFTs with sporadic symmetry groups can be constructed, and evidence for their existence has been produced using various techniques to compute their characters. Examples include sporadic groups appearing as subquotients of the monster, as well as simple Lie groups such as E-2(6)(2) and F-4(2).
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2021)
Article
Physics, Particles & Fields
Justin Kulp
Summary: In this short note, the authors discuss the existence of two additional fermionic unitary minimal models not covered in recent work. These models are obtained by fermionizing the Z(2) symmetry of the m = 11 and m = 12 exceptional unitary minimal models. The explanation provided clarifies why these are the only missing cases.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Sarah M. Harrison et al.
Summary: This study examines the Lie superalgebras of a chiral superstring compactified on F-24, demonstrating their Borcherds-Kac-Moody superalgebra structure. The models are dependent on the choice of an N = 1 supercurrent, with admissible choices labeled by semisimple Lie algebras of dimension 24. Additionally, the process of obtaining F-24 via orbifolding from another holomorphic SCFT is discussed.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Multidisciplinary
Jin-Beom Bae et al.
Summary: This work explores modular linear differential equations for different subgroups of SL2(Z), investigates the pole structures of the fermionic MLDEs, and identifies a class of fermionic RCFTs with non-negative integer coefficients in their q-series expansion. Some of these fermionic RCFTs are found to be supersymmetric, laying the groundwork for further classification of the fermionic modular tensor category.
PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS
(2021)
Article
Physics, Multidisciplinary
Jin-Beom Bae et al.
Summary: The study investigates WZW models that can be mapped to supersymmetric theories via the generalized Jordan-Wigner transformation, finding that some have supersymmetric Ramond vacua while others spontaneously break supersymmetry. Additionally, comments are made on recent proposals suggesting that Read-Rezayi states at filling fractions nu = 1/2, 2/3 may support supersymmetry.
Article
Physics, Multidisciplinary
Chang-Tse Hsieh et al.
Summary: We demonstrated the existence of a fermionic minimal model for each c = 1-6/m(m + 1), m >= 3, containing half-integral spin operators in its spectrum. This generalization extends to the Majorana fermion for c = 1/2, m = 3 and the smallest N = 1 supersymmetric minimal model for c = 7/10, m = 4. We also provided explicit Hamiltonians on Majorana chains to realize these fermionic minimal models.
PHYSICAL REVIEW LETTERS
(2021)
Article
Mathematics
Theo Johnson-Freyd
Summary: The study classifies N=1 SVOAs and finds two infinite families and nine exceptional examples, all related to the Leech lattice. The research also clarifies fermionic versions of various VOA operations.
TUNISIAN JOURNAL OF MATHEMATICS
(2021)
Article
Physics, Multidisciplinary
Jeffrey A. Harvey et al.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2020)
Article
Physics, Particles & Fields
Ingo Runkel et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2020)
Article
Physics, Mathematical
Sarah M. Harrison et al.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2019)
Article
Physics, Particles & Fields
Jin-Beom Bae et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2019)
Article
Physics, Multidisciplinary
Andreas Karch et al.
Article
Physics, Multidisciplinary
Thomas Creutzig et al.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2018)
Article
Physics, Particles & Fields
Jeffrey A. Harvey et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2018)
Article
Physics, Mathematical
Paul Bruillard et al.
JOURNAL OF MATHEMATICAL PHYSICS
(2017)
Article
Materials Science, Multidisciplinary
Tian Lan et al.
Article
Physics, Particles & Fields
T Gannon
Article
Physics, Mathematical
P Bantay
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2003)
