Holomorphic CFTs and topological modular forms

Abstract

We use the theory of topological modular forms to constrain bosonic holomorphic CFTs, which can be viewed as $(0,1)$ SCFTs with trivial right-moving supersymmetric sector. A conjecture by Segal, Stolz and Teichner requires the constant term of the partition function to be divisible by specific integers determined by the central charge. We verify this constraint in large classes of physical examples, and rule out the existence of an infinite set of extremal CFTs, including those with central charges $c=48,72,96$ and $120$.

arXiv comment7 pages; v2: references added

References in corpus (7)

• Meromorphic c=24 Conformal Field Theories
• Construction and Classification of Holomorphic Vertex Operator Algebras
• Holomorphic SCFTs with small index
• Genus Two Partition Functions of Extremal Conformal Field Theories
• Dimension Formulae and Generalised Deep Holes of the Leech Lattice Vertex Operator Algebra
• Schellekens' List and the Very Strange Formula
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Cited by in corpus (4)

• Bosonic Rational Conformal Field Theories in Small Genera, Chiral Fermionization, and Symmetry/Subalgebra Duality
• Hecke Relations, Cosets and the Classification of 2d RCFTs
• On a ${\mathbb{Z}}_3$-valued discrete topological term in 10d heterotic string theories
• A T-Duality of Non-Supersymmetric Heterotic Strings and an implication for Topological Modular Forms