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.
Localization in Supergravity and Quantum $AdS_4/CFT_3$ Holography
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abstract
We compute the quantum gravity partition function of M-theory on $AdS_4 \times X_7 $ by using localization techniques in four-dimensional gauged supergravity obtained by a consistent truncation on the Sasaki-Einstein manifold $X_{7}$. The supergravity path integral reduces to a finite dimensional integral over two collective coordinates that parametrize the localizing instanton solutions. The renormalized action of the off-shell instanton solutions depends linearly and holomorphically on the "square root" prepotential evaluated at the center of $AdS_{4}$. The partition function resembles the Laplace transform of the wave function of a topological string and with an assumption about the measure for the localization integral yields an Airy function in precise agreement with the computation from the boundary ABJM theory on a 3-sphere. Our bulk quantum gravity computation is nonperturbatively exact in four-dimensional Planck length but ignores corrections due to brane-instantons.
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hep-th 2representative citing papers
Defines an N=2 supersymmetric and gauge-invariant path integral measure for N=2 SQCD using N=1 superfields and derives the N=2 chiral anomaly while preserving supersymmetry.
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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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Supersymmetric and Gauge-Invariant Path Integral Measure in $\mathcal N=2$ SQCD
Defines an N=2 supersymmetric and gauge-invariant path integral measure for N=2 SQCD using N=1 superfields and derives the N=2 chiral anomaly while preserving supersymmetry.