Large $N$ twisted partition functions in 3d-3d correspondence and Holography

Abstract

We study the large $N$ limit of twisted partition functions on ${\mathcal{M}}_{g,p}$, the $S^1$ bundle of degree $p$ over a Riemann surface of genus $g$, for 3D $\mathcal{N}=2$ superconformal field theories arising as low-energy limit of wrapped $N$ M5-branes on hyperbolic 3-manifold $M$. We study contributions from two Bethe vacua which correspond to two canonical irreducible $SL(N,\mathbb{C})$ flat connections on $M$ via 3D-3D correspondence. Using mathematical results on perturbtaive Chern-Simons invariants around the flat connections, we find universal expressions for the large $N$ twisted partition functions contributed from the two Bethe vacua in term of the hyperbolic volume of $M$. The two large $N$ partition functions perfectly match the on-shell actions for two Bolt-type solutions in the holographic dual $Ad{S}_4$ gravity respectively.

7 pages. v2: references added

References in corpus (11)

• Wrapped M5-branes, consistent truncations and AdS/CMT
• Seifert fibering operators in 3d $\mathcal{N}=2$ theories
• Holographic microstate counting for AdS${}_4$ black holes in massive IIA supergravity
• Universal RG Flows Across Dimensions and Holography
• Bethe/Gauge correspondence on curved spaces
• SL(2,C) Chern-Simons theory and the asymptotic behavior of the colored Jones polynomial
• Symmetry enhancement and closing of knots in 3d/3d correspondence
• Partition functions on 3d circle bundles and their gravity duals
• Holography of 3d-3d correspondence at Large N
• Teichmuller TQFT vs Chern-Simons Theory
• Smallest 3d hyperbolic manifolds via simple 3d theories

Cited by in corpus (23)

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• Three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories and partition functions on Seifert manifolds: A review
• Universal Spinning Black Holes and Theories of Class $\mathcal{R}$
• Geometry of $\mathcal{I}$-extremization and black holes microstates
• A slow review of the AGT correspondence
• M-theoretic Genesis of Topological Phases
• Precision Microstate Counting for the Entropy of Wrapped M5-branes
• Factorization of log-corrections in AdS${}_4$/CFT${}_3$ from supergravity localization
• Differential Cohomotopy implies intersecting brane observables via configuration spaces and chord diagrams
• Higher-Derivative Supergravity, Wrapped M5-branes, and Theories of Class $\mathcal{R}$
• Universal Logarithmic Behavior in Microstate Counting and the Dual One-loop Entropy of AdS${}_4$ Black Holes
• Aspects of AdS${}_2$ classification in M-theory: Solutions with mesonic and baryonic charges
• The Topologically Twisted Index in the 't Hooft Limit and the Dual AdS${}_4$ Black Hole Entropy
• Wrapped Brane Solutions in Romans $F(4)$ Gauged Supergravity
• Adjoint Reidemeister torsions from wrapped M5-branes
• Black holes and Large $N$ complex saddles in 3D-3D correspondence
• New supersymmetric AdS${}_6$ black holes from matter-coupled F(4) gauged supergravity
• Non-hyperbolic 3-manifolds and 3D field theories for 2D Virasoro minimal models
• 3D-3D Correspondence from Seifert Fibering Operators
• Wrapped $M5$-branes and complex saddle points
• Supersymmetric AdS${}_6$ black holes from ISO(3)xU(1) F(4) gauged supergravity