Counting giant gravitons inAdS3

Abstract

We quantize the set of all quarter Bogomol'nyi-Prasad-Sommerfield (BPS) brane probe solutions in global ${\mathrm{AdS}}_{3}\ifmmode\times\else\texttimes\fi{}{S}^{3}\ifmmode\times\else\texttimes\fi{}{T}^{4}/K3$ found in G. Mandal, S. Raju, and M. Smedback, preceding article, Phys. Rev. D 77, 046011 (2008).. We show that, generically, these solutions give rise to states in discrete representations of the $SL(2,R)$ Wess-Zumino-Witten model on ${\mathrm{AdS}}_{3}$. Our procedure provides us with a detailed description of the low energy $\frac{1}{4}$ and $\frac{1}{2}$ BPS sectors of string theory on this background. The $\frac{1}{4}$ BPS partition function jumps as we move off the point in moduli space where the bulk theta angle and Neveu-Schwarz fields vanish. We show that generic $\frac{1}{2}$ 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 $\frac{1}{4}$ BPS states and find agreement with the known spectrum of $\frac{1}{2}$ 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.