Duality and Combinatorics of Long Strings in ADS3

TL;DR

This paper explores the counting of long strings in ADS3 within Type IIB string theory, revealing the action of duality groups and their relation to non-perturbative phenomena and instanton moduli space structures.

Contribution

It demonstrates the role of duality groups in the non-perturbative spectrum of long strings in ADS3 and connects these symmetries to instanton moduli space compactifications.

Findings

Duality group $O(5,5;Z)$ acts on long string states.

Counting functions relate to Fock space states.

Symmetry groups appear in instanton moduli space structures.

Abstract

The counting of long strings in ADS3, in the context of Type IIB string theory on $ADS_3 \times S^3 \times T^4$, is used to exhibit the action of the duality group $O(5,5;Z)$, and in particular its Weyl Subgroup $S_5 \bowtie Z_2$, in the non-perturbative phenomena associated with continuous spectra of states in these backgrounds. The counting functions are related to states in Fock spaces. The symmetry groups also appear in the structure of compactifications of instanton moduli spaces on $T^4$.