Paulina Suchanek

Recursive representation of the torus 1-point conformal block

The recursive relation for the 1-point conformal block on a torus is derived and used to prove the identities between conformal blocks recently conjectured by Poghossian in [1]. As an illustration of the efficiency of the recurrence method the modular invariance of the 1-point Liouville correlation function is numerically analyzed.

Proving the AGT relation for N f = 0, 1, 2 antifundamentals

Using recursive relations satisfied by Nekrasov partition functions and by irregular conformal blocks we prove the AGT correspondence in the case of

Limits of Minimal Models and Continuous Orbifolds

\mathcal{N} = 2

Modular bootstrap in Liouville field theory

superconformal SU(2) quiver gauge theories with Nf = 0, 1, 2 antifundamental hypermultiplets.

Elliptic recurrence representation of the N = 1 Neveu-Schwarz blocks

A bstractThe λ = 0 ’t Hooft limit of the 2d

Elliptic recurrence representation of the N = 1 superconformal blocks in the Ramond sector

{\mathcal{W}_N}

Liouville’s imaginary shadow

minimal models is shown to be equivalent to the singlet sector of a free boson theory, thus paralleling exactly the structure of the free theory in the Klebanov-Polyakov proposal. In 2d, the singlet sector does not describe a consistent theory by itself since the corresponding partition function is not modular invariant. However, it can be interpreted as the untwisted sector of a continuous orbifold, and this point of view suggests that it can be made consistent by adding in the appropriate twisted sectors. We show that these twisted sectors account for the ‘light states’ that were not included in the original ’t Hooft limit. We also show that, for the Virasoro minimal models (N = 2), the twisted sector of our orbifold agrees precisely with the limit theory of Runkel & Watts. In particular, this implies that our construction satisfies crossing symmetry.

The universal Racah-Wigner symbol for U q (osp(1|2))

Abstract The modular matrix for the generic 1-point conformal blocks on the torus is expressed in terms of the fusion matrix for the 4-point blocks on the sphere. The modular invariance of the toric 1-point functions in the Liouville field theory with DOZZ structure constants is proved.

Elliptic recursion for 4-point superconformal blocks and bootstrap in N = 1 SLFT

Abstract We apply a suitably generalized method of Al. Zamolodchikov to derive an elliptic recurrence representation of the Neveu–Schwarz superconformal blocks.

Recurrence relations for toric N = 1 superconformal blocks

The structure of the 4-point N = 1 super-conformal blocks in the Ramond sector is analyzed. The elliptic recursion relations for these blocks are derived.