Ensembles in M-theory and Holography

TL;DR

This paper explores how the choice of ensembles in M-theory affects the calculation of partition functions and their holographic duals, highlighting the significance of ensemble selection in matching gravitational and field theory observables.

Contribution

It introduces the M2-ensemble in M-theory, analyzing its implications for holography and clarifying its role in relating gravitational and field theory observables.

Findings

M2-ensemble fixes the M-theory three-form potential.

In AdS4, the M2-ensemble corresponds to a grand canonical ensemble.

Partition functions in this ensemble suggest one-loop exactness.

Abstract

We discuss that the string/M-theory partition function requires a choice of ensembles, depending on which background fields are held fixed. The background fields correspond to worldvolume couplings in the effective action approach to the superstring, which we extrapolate to the M2-brane. One natural ensemble in this context, which we call the M2-ensemble, corresponds to fixing the value of the M-theory three-form potential. In holographic setups the choice of ensemble is important when comparing to observables in the dual field theory. Indeed, in AdS$_4$ holography the M2-ensemble does not map gravitational observables directly to field theory observables at a fixed rank $N$, but rather to observables in the grand canonical ensemble. We remark that many M2-brane partition functions take a simple form in this ensemble hinting at one-loop exactness. We also discuss how in AdS$_7$ holography, the M2-ensemble does correspond to the canonical ensemble in the field theory, i.e. the (2,0) theory at fixed rank $N$.