Superconformal Partition Functions and Non-perturbative Topological Strings

Abstract

We propose a non-perturbative definition for refined topological strings. This can be used to compute the partition function of superconformal theories in 5 dimensions on squashed S^5 and the superconformal index of a large number of 6 dimensional (2,0) and (1,0) theories, including that of N coincident M5 branes. The result can be expressed as an integral over the product of three combinations of topological string amplitudes. SL(3,Z) modular transformations acting by inverting the coupling constants of the refined topological string play a key role.

51 pages, 5 figures; added clarification of the relation between topological strings and a generalization of the triple sine function

References in corpus (29)

• Solutions Of Four-Dimensional Field Theories Via M Theory
• An Index for 4 dimensional Super Conformal Theories
• Phase Transitions In M-Theory And F-Theory
• SUSY Gauge Theories on Squashed Three-Spheres
• Extremal Transitions and Five-Dimensional Supersymmetric Field Theories
• QKZ equation with |q|=1 and correlation functions of the XXZ model in the gapless regime
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• Quantum Foam and Topological Strings
• Comments on Chern-Simons Contact Terms in Three Dimensions
• R-Twisting and 4d/2d Correspondences
• The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere
• N=2 supersymmetric theories on squashed three-sphere
• BPS States of Exceptional Non-Critical Strings
• Classifying bases for 6D F-theory models
• From 4d superconformal indices to 3d partition functions
• Toric bases for 6D F-theory models
• Relation between the 4d superconformal index and the S^3 partition function
• $N^3$-behavior from 5D Yang-Mills theory
• Instantons on the 5-sphere and M5-branes
• BPS Degeneracies and Superconformal Index in Diverse Dimensions
• On the instantons and the hypermultiplet mass of N=2* super Yang-Mills on S^4
• Perturbative partition function for a squashed S^5
• Braids, Walls, and Mirrors
• M-theory and a Topological String Duality
• Non-Abelian Tensor Towers and (2,0) Superconformal Theories
• Open BPS Wall Crossing and M-theory
• Five-dimensional gauge theory and compactification on a torus
• Exact results for five-dimensional superconformal field theories with gravity duals
• Supersymmetric Partition Functions and a String Theory in 4 Dimensions

Cited by in corpus (41)

• Non-perturbative effects and the refined topological string
• The $(2,0)$ superconformal bootstrap
• M-Strings
• Cardy Formulae for SUSY Theories in d=4 and d=6
• On orbifolds of M-Strings
• Ding-Iohara-Miki symmetry of network matrix models
• Instantons on the 5-sphere and M5-branes
• Perturbative partition function for a squashed S^5
• Elliptic Genus of E-strings
• 3d & 5d gauge theory partition functions as q-deformed CFT correlators
• 5D partition functions, q-Virasoro systems and integrable spin-chains
• Exact results on ABJ theory and the refined topological string
• 5d Partition Functions with A Twist
• Supersymmetric Casimir Energy and the Anomaly Polynomial
• ABJM Wilson Loops in Arbitrary Representations
• E + E $\to$ H
• Supersymmetric Rényi Entropy in Five Dimensions
• Borel summability of perturbative series in 4d N=2 and 5d N=1 theories
• Instanton effects and quantum spectral curves
• Towards Classification of 5d SCFTs: Single Gauge Node
• Little strings and T-duality
• Holomorphic blocks and the 5d AGT correspondence
• Instanton Effects in Orientifold ABJM Theory
• 6d strings from new chiral gauge theories
• Quantum vortices, M2-branes and black holes
• (q,t)-KZ equation for Ding-Iohara-Miki algebra
• Instanton Effects in Rank Deformed Superconformal Chern-Simons Theories from Topological Strings
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• Localisation on Sasaki-Einstein manifolds from holomophic functions on the cone
• General instanton counting and 5d SCFT
• Supersymmetric Renyi Entropy and Weyl Anomalies in Six-Dimensional (2,0) Theories
• 7D supersymmetric Yang-Mills on curved manifolds
• Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index
• BPS spectrum, wall crossing and quantum dilogarithm identity
• Bootstrapping the $S^5$ partition function
• Asymptotic M5-brane entropy from S-duality
• Factorization of the 3d superconformal index
• Multiple sine, multiple elliptic gamma functions and rational cones
• One-loop Chern-Simons terms in five dimensions
• Euclidean quantum M5 brane theory on $S^1\times S^5$
• The geometric Langlands twist in five and six dimensions