Holomorphic CFTs and Topological Modular Forms

Article Mathematics

Dimension formulae and generalised deep holes of the Leech lattice vertex operator algebra

Sven Moeller et al.

Summary: The paper proves a dimension formula and introduces the concept of generalized deep holes in Aut(V). It also demonstrates a bijective relationship between the generalized deep holes and strongly rational, holo-morphic vertex operator algebras with non-vanishing weight-1 space. This has significant implications for the construction of these vertex operator algebras.

ANNALS OF MATHEMATICS (2023)

添加到收藏夹

Article Physics, Multidisciplinary

Topological modular forms and the absence of a heterotic global anomaly

Yuji Tachikawa

Summary: This paper discusses a possible Z(24)-valued pure gravitational anomaly in heterotic compactifications and shows that it can be proven to vanish using the theory of topological modular forms, assuming the validity of the Stolz-Teichner conjecture.

PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS (2022)

添加到收藏夹

Article Mathematics

Systematic orbifold constructions of Schellekens' vertex operator algebras from Niemeier lattices

Gerald Hohn et al.

Summary: We present a systematic and rigorous construction of all 70 strongly rational, holomorphic vertex operator algebras V of central charge 24 with non-zero weight-one space V1 as cyclic orbifold constructions associated with the 24 Niemeier lattice vertex operator algebras VN and certain 226 short automorphisms in Aut(VN). We show that these automorphisms are exactly the generalised deep holes introduced in Moller and Scheithauer (Ann. of Math.) of the Niemeier lattice vertex operator algebras, with the additional property that their orders are equal to those of the corresponding outer automorphisms. Together with previous constructions, this provides three different uniform constructions of these vertex operator algebras, which are related through 11 algebraic conjugacy classes in Co0. Finally, we prove that each strongly rational, holomorphic vertex operator algebra V of central charge 24 with a non-zero weight-one space V1 is uniquely determined by the Lie algebra structure of V1.

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES (2022)

添加到收藏夹

Article Mathematics

Non-abelian orbifolds of lattice vertex operator algebras

Thomas Gemunden et al.

Summary: This paper investigates orbifolds of holomorphic lattice vertex operator algebras for non-abelian finite automorphism groups G, constructing twisted modules and projective representations to extract irreducible modules of fixed-point VOAs, and ultimately constructing new holomorphic VOAs of central charge 48 and 72.

JOURNAL OF ALGEBRA (2021)

添加到收藏夹

Article Mathematics

Schellekens' list and the very strange formula

Jethro van Ekeren et al.

Summary: In this paper, a fundamentally different and simpler proof of Schellekens' list of 71 Lie algebras is presented. Utilizing the dimension formula and Kac's formula, it is shown how a strongly rational, holomorphic vertex operator algebra with central charge 24 can be constructed from the Leech lattice vertex operator algebra. This method allows for the classification of these vertex operator algebras by studying properties of the Leech lattice, demonstrating the construction for 43 of the 70 non-zero Lie algebras on Schellekens' list, with computationally expensive cases omitted.

ADVANCES IN MATHEMATICS (2021)

添加到收藏夹

Article Physics, Particles & Fields

4-manifolds and topological modular forms

Sergei Gukov et al.

Summary: By compactifying the topologically twisted 6d (1, 0) theories on 4-manifolds with flavor symmetry backgrounds, a connection between the topology of smooth 4-manifolds and the theory of topological modular forms has been established. The study reveals that the equivariant topological Witten genus of the 2d theory can generate a new invariant, and provides a better understanding of the relationship between 2d (0, 1) theories and TMF spectra.

JOURNAL OF HIGH ENERGY PHYSICS (2021)

添加到收藏夹

Article Mathematics