Borcherds Algebras and N=4 Topological Amplitudes

TL;DR

This paper demonstrates that the BPS-state spectrum in heterotic string theory compactified on T^2 forms a Borcherds algebra, which governs threshold corrections in N=4 topological string amplitudes, providing an algebraic framework for BPS states.

Contribution

The paper explicitly constructs a Borcherds algebra from heterotic BPS-states and links its denominator formula to N=4 topological string amplitudes, realizing the algebra of BPS-states controlling threshold corrections.

Findings

BPS-states form a Borcherds algebra G.

Denominator formula of an extended algebra G_{ext} appears in one-loop amplitude.

Constructs an explicit algebraic structure controlling heterotic string threshold corrections.

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.