Searcharxiv⌕ Search

arXiv subjects

Paulina Suchanek

Publications and source records attributed to Paulina Suchanek.

13 recordsLinked to original sources
arXiv2015

Non-rational su(2) cosets and Liouville field theory

We propose an su(2) WZNW model with a non-rational level and a continuous spectrum based on the non-unitary hermitian representations of the chiral algebra su(2)_k. It is conjectured that for this model the continuous spectra counterpart of the Goddard-Kent-Olive (GKO) coset construction yields the Liouville and the imaginary Liouville field theories. We support the conjecture by a number of nontrivial tests based on analytic calculations.

hep-th↗
arXiv2014

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

We propose a new and elegant formula for the Racah-Wigner symbol of self-dual continuous series of representations of Uq(osp(1|2)). It describes the entire fusing matrix for both NS and R sector of N=1 supersymmetric Liouville field theory. In the NS sector, our formula is related to an expression derived in [1]. Through analytic continuation in the spin variables, our universal expression reproduces known formulas for the Racah-Wigner coefficients of finite dimensional representations.

hep-th↗
arXiv2012

Liouville's Imaginary Shadow

N=1 super Liouville field theory is one of the simplest non-rational conformal field theories. It possesses various important extensions and interesting applications, e.g. to the AGT relation with 4D gauge theory or the construction of the OSP(1|2) WZW model. In both setups, the N=1 Liouville field is accompanied by an additional free fermion. Recently, Belavin et al. suggested a bosonization of the product theory in terms of two bosonic Liouville fields. While one of these Liouville fields is standard, the second turns out to be imaginary (or time-like). We extend the proposal to the R sector and perform extensive checks based on detailed comparison of 3-point functions involving several super-conformal primaries and descendants. On the basis of such strong evidence we sketch a number of interesting potential applications of this intriguing bosonization.

hep-th↗
arXiv2012

Limits of minimal models and continuous orbifolds

The lambda=0 't Hooft limit of the 2d W_N 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.

hep-th↗
arXiv2011

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

All types of 4-point spheric conformal blocks in both sectors of N=1 superconformal field theory are introduced and analyzed. The elliptic recurrence formulae are derived for all the types of blocks not previously discussed in the literature. The results are used for numerical verification of the crossing symmetry of some 4-point functions in the N=1 superconformal Liouville field theory.

hep-th↗
arXiv2010

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 N=2 superconformal SU(2) quiver gauge theories with N_f = 0,1,2 antifundamental hypermultiplets

hep-th↗
arXiv2009

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 R. Poghossian. As an illustration of the efficiency of the recurrence method the modular invariance of the 1-point Liouville correlation function is numerically analyzed.

hep-th↗
arXiv2009

Modular bootstrap in Liouville field theory

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.

hep-th↗
arXiv2007

Conformal blocks related to the R-R states in the \hat c =1 SCFT

We derive an explicit form of a family of four-point Neveu-Schwarz blocks with $\hat c =1,$ external weights $Δ_i = 1/8$ and arbitrary intermediate weight. The derivation is based on a set of identities obeyed in the free superscalar theory by correlation functions of fields satisfying Ramond condition with respect to the bosonic (dimension 1) and the fermionic (dimension 1/2) currents.

hep-th↗
arXiv2006

Recursion representation of the Neveu-Schwarz superconformal block

Four-point super-conformal blocks for the N = 1 Neveu-Schwarz algebra are defined in terms of power series of the even super-projective invariant. Coefficients of these expansions are represented both as sums over poles in the "intermediate" conformal weight and as sums over poles in the central charge of the algebra. The residua of these poles are calculated in both cases. Closed recurrence relations for the block coefficients are derived.

hep-th↗