The Giant Graviton Expansion from Bubbling Geometry
arxiv(2024)
摘要
The superconformal index of half-BPS states in N=4 supersymmetric
Yang-Mills with gauge group U(N) admits an expansion in terms of giant
gravitons, I_N(q)= I_∞(q) ∑_m=0^∞
q^mNℐ̂_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, 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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