The Giant Graviton Expansion from Bubbling Geometry

2024/02/29 by Deddo, Evan, Liu, James T., Zayas, Leopoldo A. Pando +1
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2402.19452

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_∞(q) ∑_m=0^∞ q^mN\mathcal I_m(q), where m is the number of giant gravitons. We derive this expansion directly in supergravity from the class of half-BPS solutions due to Lin, Lunin, and Maldacena in type IIB supergravity. The moduli space of these configurations can be quantized using covariant quantization methods. We review how this quantization leads to the graviton index, \cal I_∞(q), and present a modification that leads to the precise expression for the expansion in terms of giant gravitons. Our proposal provides a derivation of the giant graviton expansion directly in terms of supergravity degrees of freedom. We also comment on how to derive the expansion in terms of the effective Fermi droplet picture.

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