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arXiv:1508.06302 · Journal of High Energy Physics

Warped Weyl fermion partition functions

Alejandra Castro, Diego M. Hofman A, Gábor Sárosi

Published Nov 1, 2015• 54 citations
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Abstract

Warped conformal field theories (WCFTs) are a novel class of non-relativistic theories. A simple, yet non-trivial, example of such theory is a massive Weyl fermion in (1 + 1)-dimensions, which we study in detail. We derive general properties of the spectrum and modular properties of partition functions of WCFTs. The periodic (Ramond) sector of this fermionic system is non-trivial, and we build two novel partition functions for this sector which have no counterpart in a CFT2. The thermodynamical properties of WCFTs are revisited in the canonical and micro-canonical ensemble.

DOI
10.1007/jhep11(2015)129

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Warped conformal field theories (WCFTs) are two-dimensional non-relativistic systems, with a chiral scaling and shift symmetry. We present a detailed derivation of the near-extremal limit for their torus partition function. This limit requires large values of the central charge, and is only consistent for non-unitary WCFT. We compare our analysis with previous studies of WCFT and its relation to a one-dimensional warped-Schwarzian theory. We discuss different ensembles of warped CFTs and contrast our results with analogous limits in two-dimensional CFTs.
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TT‾ T\overline{T} TT deformed partition functions
A bstract We demonstrate the presence of modular properties in partition functions of TT‾ T\overline{T} TT T T ¯ deformed conformal field theories. These properties are verified explicitly for the deformed free boson. The modular features facilitate a derivation of the asymptotic density of states in these theories, which turns out to interpolate between Cardy and Hagedorn behaviours. We also point out a sub-sector of the spectrum that remains undeformed under the TT‾ T\overline{T} TT T T ¯ flow. Finally, we comment on the deformation of the CFT vacuum character and its implications for the holographic dual.