The elliptic genus of Calabi-Yau 3- and 4-folds, product formulae and generalized Kac-Moody algebras

1996/07/03 by C. D. D. Neumann, C.D.D. Neumann · 2 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Computation #Elliptic curve #Genus #Heterotic string theory #Product (mathematics) #String (physics) #hep-th

paper · pdf · doi:10.1016/s0393-0440(98)00015-1

published as J.Geom.Phys. 29 (1999) 5-12 · 10 pages, latex, no figures

arxiv created 1996/07/03 · openalex publication_date 1999/01/01 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In this paper the elliptic genus for a general Calabi-Yau fourfold is derived. The recent work of Kawai calculating N=2 heterotic string one-loop threshold corrections with a Wilson line turned on is extended to a similar computation where K3 is replaced by a general Calabi-Yau 3- or 4-fold. In all cases there seems to be a generalized Kac-Moody algebra involved, whose denominator formula appears in the result.

Citations

• Algebras, BPS states, and strings
• Moduli dependence of string loop corrections to gauge coupling constants
• Automorphic forms onO s +2,2(R) and infinite products
• Counting dyons in N = 4 string theory

Cited by

• Black hole entropy function, attractors and precision counting of microstates
• A twist in the dyon partition function