Topic:The Giant Graviton Expansion of Partition Functions and Gravitational Degrees of Freedom

Speaker: Prof. Leopoldo A. Pando Zayas

Coordinates: PCFT C1124, 16:00, Friday, August 1

Abstract: The superconformal index of half-BPS states in  \({\cal N}=4\) supersymmetric Yang-Mills with gauge group \(U(N)\) admits an expansion in terms of giant gravitons,  \({\cal I}_N(q)={\cal I}_\infty(q) \sum\limits_{m=0}^\infty q^{mN}\hat{\mathcal I}_m(q)\), where \(m\) is the number of giant gravitons and \({\cal I}_\infty(q)\) is the graviton index. The expansion can be viewed as the implementation of trace relations for finite \(N\). We derive this expansion directly in supergravity from the class of half-BPS solutions due to Lin, Lunin, and Maldacena in type IIB supergravity. We also consider giant gravitons in the probe approximation when they are described by classical brane configurations in AdS\(_p\times S^q\) wrapping a particular cycle, and spinning in \(S^q\). We quantize the full set of fluctuations of these configurations and show that they are sufficient to capture all the supersymmetric single-letter partition functions of the dual field theory. We explicitly discuss the cases of D3, M2 and M5 and reproduce the single-letter partition functions for all fractions of supersymmetry.