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Ensembles in M-theory and Holography
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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 $N$.
Forward citations
Cited by 6 Pith papers
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Holographic Tests of the $\mu$ Ensemble
Fixed-μ ensemble computations in 11d supergravity reproduce ABJM partition functions (squashed S³, SCI, TTI) as Airy functions via a Laplace transform whose measure is fixed by bulk zero-mode counting.
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Indices of M5 and M2 branes at finite $N$ from equivariant volumes, and a new duality
Finite-N indices for M5- and M2-branes are expressed via the same equivariant characteristic classes, generalizing M2/M5 duality through geometry exchange.
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Bootstrapping ABJM theory
A bootstrap approach applied to ABJM theory yields analytic derivations of instanton corrections to the free energy and to 1/2 and 1/6 BPS Wilson loops, confirming relations previously known only conjecturally.
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Towards OSV in AdS
Derives Z_{S^1×S^2} ∼ |Z_{S^3_b}|^2 for 3d N=2 SCFTs and links it holographically to supersymmetric AdS4 black hole partition functions, akin to OSV.
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Membrane instantons and non-perturbative effects in $\mathrm{AdS}_{4}/\mathrm{CFT}_{3}$
Establishes equivalence of BPS conditions for M2-branes to associativity in G2-structures and computes one-loop partition functions via transversely elliptic complexes for invariant cycles in Sasaki-Einstein manifolds...
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Membrane instantons and non-perturbative effects in $\mathrm{AdS}_{4}/\mathrm{CFT}_{3}$
BPS conditions for M2-branes wrapping cycles in weak G2 manifolds are equivalent to associativity, with one-loop effects for invariant cycles in Sasaki-Einstein orbifolds expressed via equivariant indices and recoveri...
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