Supersymmetric States in M5/M2 CFTs

TL;DR

This paper derives an exact finite N partition function for BPS states in M5 and M2 brane conformal field theories, connecting field theory and supergravity descriptions, and revealing deviations at high energies.

Contribution

It provides a novel exact formula for BPS state partition functions in M-brane CFTs, bridging Coulomb branch quantization and supergravity giant graviton analysis.

Findings

Partition function matches supergravity at low energies.

Deviations from supergravity appear at high energies scaling with N.

Connects Coulomb branch quantization with holographic duals.

Abstract

We propose an exact, finite $N$ formula for the partition function over $1/4^{th}$ BPS states in the conformal field theory on the world volume of $N$ coincident M5 branes and $1/8^{th}$ BPS states in the theory of $N$ coincident M2 branes. We obtain our partition function by performing the radial quantization of the Coulomb Branches of these theories, and rederive the same formula from the quantization of supersymmetric giant and dual giant gravitons in $AdS_7 \times S^4$ and $AdS_4 \times S^7$. Our partition function is qualitatively similar to the analogous quantity in ${\cal N}=4$ Yang Mills. It reduces to the sum over supersymmetric multi gravitons at low energies, but deviates from this supergravity formula at energies that scale like a positive power of $N$.