Squashing, Mass, and Holography for 3d Sphere Free Energy

Abstract

We consider the sphere free energy $F(b;m_I)$ in $\mathcal{N}=6$ ABJ(M) theory deformed by both three real masses $m_I$ and the squashing parameter $b$, which has been computed in terms of an $N$ dimensional matrix model integral using supersymmetric localization. We show that setting $m_3=i\frac{b-b^{-1}}{2}$ relates $F(b;m_I)$ to the round sphere free energy, which implies infinite relations between $m_I$ and $b$ derivatives of $F(b;m_I)$ evaluated at $m_I=0$ and $b=1$. For $\mathcal{N}=8$ ABJ(M) theory, these relations fix all fourth order and some fifth order derivatives in terms of derivatives of $m_1,m_2$, which were previously computed to all orders in $1/N$ using the Fermi gas method. This allows us to compute ${\partial }_b^{4}F{|}_{b=1}$ and ${\partial }_b^{5}F{|}_{b=1}$ to all orders in $1/N$, which we precisely match to a recent prediction to sub-leading order in $1/N$ from the holographically dual $Ad{S}_4$ bulk theory.

23 pages

References in corpus (8)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Writing CFT correlation functions as AdS scattering amplitudes
• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• The Unreasonable Effectiveness of Higher-Derivative Supergravity in AdS${}_4$ Holography
• Exact results on ABJ theory and the refined topological string
• Conformal field theories on deformed spheres, anomalies, and supersymmetry

Cited by in corpus (15)

• Large $N$ Partition Functions of the ABJM Theory
• ABJM at Strong Coupling from M-theory, Localization, and Lorentzian Inversion
• ABJM at finite $N$ via 4d supergravity
• 4d N=2 supergravity observables from Nekrasov-like partition functions
• Squashing and supersymmetry enhancement in three dimensions
• One-Dimensional Sectors From the Squashed Three-Sphere
• The type IIA Virasoro-Shapiro amplitude in AdS${}_4$ $\times$ CP${}^3$ from ABJM theory
• Maximally symmetric nuts in 4d $\mathcal{N}=2$ higher derivative supergravity
• Higher-Derivative Supergravity, AdS${}_4$ Holography, and Black Holes
• 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
• Dualities and loops on squashed $S^3$
• $S^1$ Reduction of 4D $\mathcal{N}=3$ SCFTs and Squashing Independence of ABJM Theories
• Flavor deformations and supersymmetry enhancement in $4d$ $\mathcal{N}=2$ theories
• The Holographic Contributions to the Sphere Free Energy