arXiv:2002.04824 · Nuclear Physics B

KdV charges and the generalized torus partition sum in TT‾ deformation

Meseret Asrat

Published Jul 27, 2020• 14 citations

Abstract

We consider KdV currents in a quantum field theory obtained by deforming a two dimensional conformal field theory via the irrelevant operator TT‾. In this paper we determine their torus one–point functions modular properties. We find that the one–point functions decompose into a direct sum of two non–holomorphic modular forms. We also obtain a general differential equation that the KdV generalized torus partition sum satisfies. The differential equation provides a non–perturbative description of TT‾ deformed theories.

DOI: 10.1016/j.nuclphysb.2020.115119

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arXiv:2002.04824 · Nuclear Physics B

KdV charges and the generalized torus partition sum in TT‾ deformation

Meseret Asrat

Published Jul 27, 2020• 14 citations

arXiv HTML PDF

Abstract

DOI: 10.1016/j.nuclphysb.2020.115119

Related papers

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T\bar{T}

deformed CFT. Non-perturbatively, we find that for one sign of t (for which the energies are real) the partition sum is uniquely determined, while for the other sign we find non-perturbative ambiguities. We characterize these ambiguities and comment on their possible relations to holography.

Modular covariance and uniqueness of

J\overline{T}

deformed CFTs

\mu J\overline{T}

μ J T ¯ deformed conformal field theory (CFT). We derive a flow equation for the

J\overline{T}

J T ¯ deformed partition sum, and use it to study non-perturbative effects. We find non-perturbative ambiguities for any non-zero value of μ , and comment on their possible relations to holography.

Modular invariance and uniqueness of

T\overline{T}

deformed CFT

T\overline{T}

T T ¯ deformed CFT. Non-perturbatively, we find that for one sign of t (for which the energies are real) the partition sum is uniquely determined, while for the other sign we find non-perturbative ambiguities. We characterize these ambiguities and comment on their possible relations to holography.

\overline{T}

-flow effects on torus partition functions

Abstract In this paper, we investigate the partition functions of conformal field theories (CFTs) with the T

\overline{T}

T ¯ deformation on a torus in terms of the perturbative QFT approach. In Lagrangian path integral formalism, the first- and second-order deformations to the partition functions of 2D free bosons, free Dirac fermions, and free Majorana fermions on a torus are obtained. The corresponding Lagrangian counterterms in these theories are also discussed. The first two orders of the deformed partition functions and the first-order vacuum expectation value (VEV) of the first quantum KdV charge obtained by the perturbative QFT approach are consistent with results obtained by the Hamiltonian formalism in literature.

T\overline{T},J\overline{T},T\overline{J}

partition sums from string theory

A bstract We calculate the torus partition sum of a general CFT 2 with left and right moving conserved currents J and

\overline{J}

J ¯ , perturbed by a combination of the irrelevant operators

T\overline{T},J\overline{T}

T T ¯ , J T ¯ and

T\overline{J}

T J ¯ . We use string theory techniques to write it as an integral transform of the partition sum of the unperturbed CFT with chemical potentials for the left and right moving conserved charges. The resulting expression transforms in the right way under the modular group, and reproduces the known spectrum of these models. We also derive a formula for the partition function of deformed CFT 2 with non-vanishing chemical potentials.

T\overline{T},J\overline{T},T\overline{J}

partition sums from string theory