Large $N$ Partition Functions of the ABJM Theory

Abstract

We study the large $N$ limit of some supersymmetric partition functions of the $\mathrm{U}(N{)}_k\times \mathrm{U}(N{)}_{-k}$ ABJM theory computed by supersymmetric localization. We conjecture an explicit expression, valid to all orders in the large $N$ limit, for the partition function on the $\mathrm{U}(1)\times \mathrm{U}(1)$ invariant squashed sphere in the presence of real masses in terms of an Airy function. Several non-trivial tests of this conjecture are presented. In addition, we derive an explicit compact expression for the topologically twisted index of the ABJM theory valid at fixed $k$ to all orders in the $1/N$ expansion. We use these results to derive the topologically twisted index and the sphere partition function in the 't Hooft limit which correspond to genus $\mathtt{g}$ type IIA string theory free energies to all orders in the ${\alpha }^{\prime }$ expansion. We discuss the implications of our results for holography and the physics of AdS${}_4$ black holes.

v1: 56 pages, 4 figures; v2: corrected typos in equations (2.5) and (4.69), updated references; v3: added footnote 11, minor revisions in Subsection 4.4; v4: minor typos corrected

References in corpus (57)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• Black Hole Attractors and the Topological String
• Towards the F-Theorem: N=2 Field Theories on the Three-Sphere
• The Exact Superconformal R-Symmetry Extremizes Z
• From weak to strong coupling in ABJM theory
• Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory
• Black hole microstates in AdS${}_4$ from supersymmetric localization
• Topological Amplitudes in String Theory
• A topologically twisted index for three-dimensional supersymmetric theories
• Supersymmetric Field Theories on Three-Manifolds
• Supersymmetric AdS_4 black holes and attractors
• Summing Up All Genus Free Energy of ABJM Matrix Model
• Consistent Kaluza-Klein Reductions for General Supersymmetric AdS Solutions
• Comments on twisted indices in 3d supersymmetric gauge theories
• Instanton Effects in ABJM Theory from Fermi Gas Approach
• Exact microstate counting for dyonic black holes in AdS4
• Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant
• The gravity dual of supersymmetric gauge theories on a squashed three-sphere
• Nonperturbative black hole entropy and Kloosterman sums
• The Holography of F-maximization
• A Universal Counting of Black Hole Microstates in AdS${}_4$
• Quantum black holes, localization and the topological string
• Supersymmetric Index from Black Hole Entropy
• D-brane Charges in Gravitational Duals of 2+1 Dimensional Gauge Theories and Duality Cascades
• Anomalous radius shift in AdS(4)/CFT(3)
• Large $N$ matrix models for 3d $\mathcal{N}=2$ theories: twisted index, free energy and black holes
• Supersymmetric partition functions and the three-dimensional A-twist
• Supersymmetry of topological Kerr-Newmann-Taub-NUT-aDS spacetimes
• Holomorphic Anomaly in Gauge Theories and Matrix Models
• The Unreasonable Effectiveness of Higher-Derivative Supergravity in AdS${}_4$ Holography
• M-Fivebranes Wrapped on Supersymmetric Cycles II
• Probing non-perturbative effects in M-theory
• Localization in Supergravity and Quantum $Ad{S}_4/CF{T}_3$ Holography
• A One-loop Test of Quantum Black Holes in Anti de Sitter Space
• Solving M-theory with the Conformal Bootstrap
• The M-Theory S-Matrix From ABJM: Beyond 11D Supergravity
• Euclidean Black Saddles and AdS${}_4$ Black Holes
• Instanton effects in ABJM theory with general R-charge assignments
• Localization of the action in AdS/CFT
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• Localization on three-dimensional manifolds
• The M-theory Archipelago
• Three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories and partition functions on Seifert manifolds: A review
• On the quantum entropy function in 4d gauged supergravity
• ABJM on ellipsoid and topological strings
• 3d $\mathcal{N}=4$ OPE Coefficients from Fermi Gas
• Squashing, Mass, and Holography for 3d Sphere Free Energy
• Large N duality beyond the genus expansion
• ABJM at finite $N$ via 4d supergravity
• 4d N=2 supergravity observables from Nekrasov-like partition functions
• Higher-Derivative Supergravity, Wrapped M5-branes, and Theories of Class $\mathcal{R}$
• One-loop determinants for black holes in 4d gauged supergravity
• The Topologically Twisted Index in the 't Hooft Limit and the Dual AdS${}_4$ Black Hole Entropy
• Squashing and supersymmetry enhancement in three dimensions
• Spin Structures and AdS${}_4$ Holography

Cited by in corpus (11)

• Boundary terms and conserved charges in higher-derivative gauged supergravity
• Comments on ABJM free energy on $S^3$ at large $N$ and perturbative expansions in M-theory and string theory
• Matrix Models and Holography: Mass Deformations of Long Quiver Theories in 5d and 3d
• Toric gravitational instantons in gauged supergravity
• Conformal bounds in three dimensions from entanglement entropy
• The thermal bootstrap for the critical O(N) model
• Microscopics of de Sitter Entropy from Precision Holography
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• Exact large $N$ expansion of $\mathcal{N}=4$ circular quiver Chern-Simons theories and squashing
• Dualities and loops on squashed $S^3$
• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview