p-adic vertex operator algebras

2022/07/15 by Franc, Cameron, Mason, Geoffrey
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Number Theory (math.NT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2207.07455

Abstract

We postulate axioms for a chiral half of a nonarchimedean 2-dimensional bosonic conformal field theory, that is, a vertex operator algebra in which a p-adic Banach space replaces the traditional Hilbert space. We study some consequences of our axioms leading to the construction of various examples, including p-adic commutative Banach rings and p-adic versions of the Virasoro, Heisenberg, and the Moonshine module vertex operator algebras. Serre p-adic modular forms occur naturally in some of these examples as limits of classical 1-point functions.

Related

• Invitation to p-adic vertex algebras
• Conformal field theories associated to regular chiral vertex operator algebras I: theories over the projective line
• Classical and quantum conformal field theories
• 2D conformal field theory and vertex operator algebras
• Characters in p-adic Heisenberg and Lattice Vertex Operator Algebras