Subleading analysis for S<SUP>3</SUP> partition functions of N=2 holographic SCFTs

초록

We investigate the 3-sphere partition functions of various 3d N = 2 holographic SCFTs arising from the N stack of M2-branes in the 't Hooft limit both analytically and numerically. We first employ a saddle point approximation to evaluate the free energy F = - log Z at the planar level, tracking the first subleading corrections in the large 't Hooft coupling lambda expansion. Subsequently, we improve these results by determining the planar free energy to all orders in the large lambda expansion via numerical analysis. Remarkably, the resulting planar free energies turn out to take a universal form, supporting a prediction that these S-3 partition functions are all given in terms of an Airy function even beyond the special cases where the Airy formulae were derived analytically in the literature; in this context we also present new Airy conjectures in several examples. The subleading behaviors we captured encode a part of quantum corrections to the M-theory path integrals around dual asymptotically Euclidean AdS(4) backgrounds with the corresponding internal manifolds through holographic duality.

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