Borcherds Algebras and N=4 Topological Amplitudes

Abstract

The perturbative spectrum of BPS-states in the E_8 x E_8 heterotic string theory compactified on T^2 is analysed. We show that the space of BPS-states forms a representation of a certain Borcherds algebra G which we construct explicitly using an auxiliary conformal field theory. The denominator formula of an extension G_{ext} \supset G of this algebra is then found to appear in a certain heterotic one-loop N=4 topological string amplitude. Our construction thus gives an N=4 realisation of the idea envisioned by Harvey and Moore, namely that the `algebra of BPS-states' controls the threshold corrections in the heterotic string.

39 pages

References in corpus (13)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Wall-Crossing from Boltzmann Black Hole Halos
• Walls of Marginal Stability and Dyon Spectrum in N=4 Supersymmetric String Theories
• Product Representation of Dyon Partition Function in CHL Models
• D-instantons and twistors
• Dyon Spectrum in Generic N=4 Supersymmetric Z_N Orbifolds
• Duality Orbits, Dyon Spectrum and Gauge Theory Limit of Heterotic String Theory on T^6
• N=4 Topological Amplitudes and String Effective Action
• Generalized Kac-Moody Algebras from CHL dyons
• Geometric Configurations, Regular Subalgebras of E10 and M-Theory Cosmology
• Harmonicity in N=4 supersymmetry and its quantum anomaly
• Topological Amplitudes and Physical Couplings in String Theory
• The Spectra of Supersymmetric States in String Theory