ABJM on ellipsoid and topological strings

Abstract

It is known that the large N expansion of the partition function in ABJM theory on a three-sphere is completely determined by the topological string on local Hirzebruch surface F_0. In this note, we investigate the ABJM partition function on an ellipsoid, which has a conventional deformation parameter b. Using 3d mirror symmetry, we find a remarkable relation between the ellipsoid partition function for b^2=3 (or b^2=1/3) in ABJM theory at k=1 and a matrix model for the topological string on another Calabi-Yau threefold, known as local P^2. As in the case of b=1, we can compute the full large N expansion of the partition function in this case. This is the first example of the complete large N solution in ABJM theory on the squashed sphere. Using the obtained results, we also analyze the supersymmetric Renyi entropy.

29 pages

References in corpus (15)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Notes on SUSY Gauge Theories on Three-Sphere
• Summing Up All Genus Free Energy of ABJM Matrix Model
• Probing non-perturbative effects in M-theory
• Exact results on ABJ theory and the refined topological string
• Exact ABJM Partition Function from TBA
• Topological Strings and Quantum Spectral Problems
• M-theoretic matrix models
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings
• Supersymmetric Rényi Entropy in Five Dimensions
• Super-Rényi Entropy & Wilson Loops for N=4 SYM and their Gravity Duals
• The holographic supersymmetric Renyi entropy in five dimensions
• TBA-like integral equations from quantized mirror curves

Cited by in corpus (20)

• The Unreasonable Effectiveness of Higher-Derivative Supergravity in AdS${}_4$ Holography
• Large $N$ Partition Functions of the ABJM Theory
• 3d $\mathcal{N}=4$ OPE Coefficients from Fermi Gas
• Squashing, Mass, and Holography for 3d Sphere Free Energy
• Factorization of log-corrections in AdS${}_4$/CFT${}_3$ from supergravity localization
• ABJM at finite $N$ via 4d supergravity
• 4d N=2 supergravity observables from Nekrasov-like partition functions
• $q$-Virasoro modular double and 3d partition functions
• BPS relations from spectral problems and blowup equations
• Entanglement Entropy of ABJM Theory and Entropy of Topological Black Hole
• Exact results for ABJ Wilson loops and open-closed duality
• Maximally symmetric nuts in 4d $\mathcal{N}=2$ higher derivative supergravity
• Geometric transition in Non-perturbative Topological string
• Higher-Derivative Supergravity, AdS${}_4$ Holography, and Black Holes
• Supersymmetry Breaking Phase in Three Dimensional Large N Gauge Theories
• Constant maps in equivariant topological strings and geometric modeling of fluxes
• Exact large $N$ expansion of $\mathcal{N}=4$ circular quiver Chern-Simons theories and squashing
• 3d dualities with decoupled sectors and brane transitions
• Dualities and loops on squashed $S^3$
• Painlevé Kernels and Surface Defects at Strong Coupling