Transformations of Spherical Blocks

  • Amir-Kian Kashani-Poor
  • Jan Troost
Open Access


We further explore the correspondence between \( \mathcal{N} \) = 2 supersymmetric SU(2) gauge theory with four flavors on ϵ-deformed backgrounds and conformal field theory, with an emphasis on the ϵ-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 Γ(2), with the expected symmetry W(D 4) ⋊ S 3. In the presence of an elementary surface operator, this symmetry is enhanced to an action of \( W\left( {D_4^{(1) }} \right)\rtimes {S_4} \) on the instanton partition function, as we demonstrate via the link between the null vector decoupling equation and the quantum Painlevé VI equation.


Conformal and W Symmetry Supersymmetric gauge theory Topological Strings 


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Copyright information

© SISSA 2013

Authors and Affiliations

  1. 1.Laboratoire de Physique ThéoriqueEcole Normale SupérieureParisFrance

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