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Journal of High Energy Physics

, 2012:20 | Cite as

Liouville’s imaginary shadow

  • Volker Schomerus
  • Paulina Suchanek
Open Access
Article

Abstract

\( \mathcal{N}=1 \) 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 \( \mathcal{N}=1 \) 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.

Keywords

Field Theories in Lower Dimensions Conformal and W Symmetry 

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Copyright information

© SISSA 2012

Authors and Affiliations

  1. 1.DESY Theory Group, DESY HamburgHamburgGermany
  2. 2.Institute for Theoretical PhysicsUniversity of WroclawWroclawPoland

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