Transformations of Spherical Blocks

Abstract

We further explore the correspondence between N=2 supersymmetric SU(2) gauge theory with four flavors on epsilon-deformed backgrounds and conformal field theory, with an emphasis on the epsilon-expansion of the partition function natural from a topological string theory point of view. Solving an appropriate null vector decoupling equation in the semi-classical limit allows us to express the instanton partition function as a series in quasi-modular forms of the group Gamma(2), with the expected symmetry Weyl group of SO(8) semi-direct S_3. In the presence of an elementary surface operator, this symmetry is enhanced to an action of the affine Weyl group of SO(8) semi-direct S_4 on the instanton partition function, as we demonstrate via the link between the null vector decoupling equation and the quantum Painlevé VI equation.

31 pages, 1 figure; v2: typos corrected, references added

References in corpus (5)

• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks
• Multipoint correlation functions in Liouville field theory and minimal Liouville gravity
• Six results on Painleve VI
• Symmetries of quantum Lax equations for the Painlevé equations

Cited by in corpus (28)

• Classical Conformal Blocks and Painleve VI
• Modular anomaly equation, heat kernel and S-duality in N=2 theories
• A slow review of the AGT correspondence
• Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
• Exact WKB Analysis of N = 2 Gauge Theories
• BPS relations from spectral problems and blowup equations
• Quantum geometry from the toroidal block
• Modular and duality properties of surface operators in N=2* gauge theories
• Quantum spectral problems and isomonodromic deformations
• S-duality, triangle groups and modular anomalies in N=2 SQCD
• Quasimodular instanton partition function and the elliptic solution of Korteweg-de Vries equations
• Finite ${\epsilon }_2$-corrections to the $\mathcal{N}=2$ SYM prepotential
• S-duality and the prepotential in N=2* theories (I): the ADE algebras
• On the large $\Omega$-deformations in the Nekrasov-Shatashvili limit of $\mathcal{N}=2^{\ast }$ SYM
• Pure N=2 Super Yang-Mills and Exact WKB
• Chiral observables and S-duality in N = 2* U(N) gauge theories
• Recurrence relations for the ${\mathcal{W}}_3$ conformal blocks and $\mathcal{N}=2$ SYM partition functions
• Exact partition functions for the $\Omega$-deformed $\mathcal{N}=2^{\ast }$ $SU(2)$ gauge theory
• Modular anomaly equations and S-duality in N=2 conformal SQCD
• Chiral trace relations in $\Omega$-deformed $\mathcal{N}=2$ theories
• Virasoro blocks and quasimodular forms
• N=2 supersymmetric QCD and elliptic potentials
• Exact partition functions for deformed $\mathcal{N}=2$ theories with $N_f=4$ flavours
• Virasoro blocks at large exchange dimension
• Solving Heun's equation using conformal blocks
• Classical conformal blocks, Coulomb gas integrals and Richardson-Gaudin models
• Four-point correlation modular bootstrap for OPE densities
• Modular properties of surface operators in N=2 SQCD