TBA for non-perturbative moduli spaces

Abstract

Recently, an exact description of instanton corrections to the moduli spaces of 4d N=2 supersymmetric gauge theories compactified on a circle and Calabi-Yau compactifications of Type II superstring theories was found. The equations determining the instanton contributions turn out to have the form of Thermodynamic Bethe Ansatz. We explore further this relation and, in particular, we identify the contact potential of quaternionic string moduli space with the free energy of the integrable system and the Kahler potential of the gauge theory moduli space with the Yang-Yang functional. We also show that the corresponding S-matrix satisfies all usual constraints of 2d integrable models, including crossing and bootstrap, and derive the associated Y-system. Surprisingly, in the simplest case the Y-system is described by the MacMahon function relevant for crystal melting and topological strings.

25 pages, 1 figure

References in corpus (8)

• Gluon scattering amplitudes at strong coupling
• String loop corrected hypermultiplet moduli spaces
• Nonperturbative corrections to 4D string theory effective actions from SL(2,Z) duality and supersymmetry
• D-instantons and twistors
• Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3
• Quantum mirror symmetry and twistors
• Linear perturbations of Hyperkahler metrics
• Large D-instanton effects in string theory

Cited by in corpus (15)

• An Operator Product Expansion for Polygonal null Wilson Loops
• Twistor Approach to String Compactifications: a Review
• D3-instantons, Mock Theta Series and Twistors
• Fivebrane instantons, topological wave functions and hypermultiplet moduli spaces
• A slow review of the AGT correspondence
• $R^3$ index for four-dimensional $N=2$ field theories
• S-duality in Twistor Space
• S-duality and refined BPS indices
• Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
• Quiver gauge theories and integrable lattice models
• Hypermultiplet metric and D-instantons
• Fivebrane instantons in Calabi-Yau compactifications
• Heavenly metrics, BPS indices and twistors
• c-map as c=1 string
• Quantum TBA for refined BPS indices