Counting Giant Gravitons in AdS_3

TL;DR

This paper quantizes BPS brane solutions in AdS_3 and analyzes their role in the spectrum of string theory, revealing protected states, spectrum matches, and insights into elliptic genus computations.

Contribution

It provides a detailed quantization of BPS brane probes in AdS_3, connecting them to boundary states and clarifying the structure of BPS sectors in string theory.

Findings

Discrete SL(2,R) representations for BPS states

Protection of 1/2 BPS states due to geodesic nature

Agreement with known 1/2 BPS spectrum and elliptic genus insights

Abstract

We quantize the set of all quarter BPS brane probe solutions in global AdS_3 \times S^3 \times T^4/K3 found in arxiv:0709.1168 [hep-th]. We show that, generically, these solutions give rise to states in discrete representations of the SL(2,R) WZW model on AdS_3. Our procedure provides us with a detailed description of the low energy 1/4 and 1/2 BPS sectors of string theory on this background. The 1/4 BPS partition function jumps as we move off the point in moduli space where the bulk theta angle and NS-NS fields vanish. We show that generic 1/2 BPS states are protected because they correspond to geodesics rather than puffed up branes. By exactly quantizing the simplest of the probes above, we verify our description of 1/4 BPS states and find agreement with the known spectrum of 1/2 BPS states of the boundary theory. We also consider the contribution of these probes to the elliptic genus and discuss puzzles, and their possible resolutions, in reproducing the elliptic genus of the symmetric product.