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Title:
A gravity interpretation for the Bethe ansatz expansion ofthe N=4 SYM index
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Abstract:
This talk is based on work in progress with FrancescoBenini, Ohad Mamroud and Paolo Milan. We review the form of the Bethe ansatzexpansion for the N=4 SU(N) SYM index in the large N limit, including the knownsolutions to the Bethe ansatz equations, and including both perturbative andnon-perturbative terms in 1/N. The index is related to the partition functionof N=4 SYM on S^3xS^1, and in the large N limit it should be described bysumming over Euclidean gravity solutions with appropriate asymptotic behavior.We show that (for the case of equal chemical potentials for the two angular momenta)each Bethe ansatz contribution arises from a specific supersymmetric (complex)black hole solution, which reproduces both its perturbative and itsnon-perturbative behavior. A priori there are many more gravitational solutionsthan Bethe ansatz contributions, but we show that by considering thenon-perturbative effects, the extra solutions are ruled out, leading to aprecise match between the solutions on both sides.
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