arXiv:1909.11118 · Physics Letters B

Strings, symmetric products, TT¯ deformations and Hecke operators

Akikazu Hashimoto, David Kutasov

Published May 12, 2020• 22 citations

Abstract

We derive a formula for the torus partition sum of the symmetric product of TT¯ deformed CFT's, using previous work on long strings in (deformed) AdS3, and universality. The result is given by an integral transform of the partition function for the block of the symmetric product, summed over its Hecke transforms, and is manifestly modular invariant. The spectrum is interpretable as a gas of multiply wound long strings with a particular orientation.

DOI: 10.1016/j.physletb.2020.135479

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arXiv:1909.11118 · Physics Letters B

Strings, symmetric products, TT¯ deformations and Hecke operators

Akikazu Hashimoto, David Kutasov

Published May 12, 2020• 22 citations

arXiv HTML PDF

Abstract

DOI: 10.1016/j.physletb.2020.135479

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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

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 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.