Vertex operator algebras and weak Jacobi forms

Matthew Krauel; Geoffrey Mason

doi:10.1142/S0129167X11007677

paper

Vertex operator algebras and weak Jacobi forms

arXiv:1103.0994 · doi:10.1142/S0129167X11007677

Abstract

Let $V$ be a strongly regular vertex operator algebra. For a state $h \in V_{1}$ satisfying appropriate integrality conditions, we prove that the space spanned by the trace functions Tr $_{M} q^{L (0) - c /24} ζ^{h (0)} ($ M $a$ V $- m o d u l e) i s a v ec t or - v a l u e d w e ak J a co bi f or m o f w e i g h t 0 an d a cer t ainin d e x$ <h, h >/2 $. W e d i sc u ssr e f in e m e n t s an d a ppl i c a t i o n so f t hi sr es u l tw h e n$ V $i s h o l o m or p hi c, in p a r t i c u l a r w e p r o v e t ha t i f$ g = e^{h(0)} $i s a f ini t eor d er a u t o m or p hi s m t h e n T r$ _V q^{L(0)-c/24}g $i s am o d u l a r f u n c t i o n o f w e i g h t 0 o na co n g r u e n ces u b g r o u p o f$ SL_2(Z)$.

Vertex operator algebras and weak Jacobi forms

Abstract

Cited by in corpus (6)