$$ T\overline{T},J\overline{T},T\overline{J} $$ partition sums from string theory

Akikazu Hashimoto A

Published Sep 27, 2022• 17 citations

Abstract

We calculate the torus partition sum of a general CFT2with left and right moving conserved currentsJand $ \overline{J} $ J¯ , perturbed by a combination of the irrelevant operators $ T\overline{T},J\overline{T} $ TT¯,JT¯ and $ T\overline{J} $ TJ¯ . 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 CFT2with non-vanishing chemical potentials.

DOI: 10.1007/jhep02%282020%29080

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$T\overline{T},J\overline{T},T\overline{J}$ partition sums from string theory$$ T\overline{T},J\overline{T},T\overline{J} $$ partition sums from string theory

Akikazu Hashimoto A

Published Sep 27, 2022• 17 citations

Publisher

Abstract

We calculate the torus partition sum of a general CFT2with left and right moving conserved currentsJand

\overline{J}

J¯ , perturbed by a combination of the irrelevant operators

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

TT¯,JT¯ and

T\overline{J}

TJ¯ . 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 CFT2with non-vanishing chemical potentials.

DOI: 10.1007/jhep02%282020%29080

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Any two dimensional quantum field theory that can be consistently defined on a torus is invariant under modular transformations. In this paper we study families of quantum field theories labeled by a dimensionful parameter t, that have the additional property that the energy of a state at finite t is a function only of t and of the energy and momentum of the corresponding state at t = 0, where the theory becomes conformal. We show that under this requirement, the partition sum of the theory at t = 0 uniquely determines the partition sum (and thus the spectrum) of the perturbed theory, to all orders in t, to be that of a $T\bar{T}$ 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.Any two dimensional quantum field theory that can be consistently defined on a torus is invariant under modular transformations. In this paper we study families of quantum field theories labeled by a dimensionful parameter t, that have the additional property that the energy of a state at finite t is a function only of t and of the energy and momentum of the corresponding state at t = 0, where the theory becomes conformal. We show that under this requirement, the partition sum of the theory at t = 0 uniquely determines the partition sum (and thus the spectrum) of the perturbed theory, to all orders in t, to be that of a $T\bar{T}$ 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.

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Abstract Any two dimensional quantum field theory that can be consistently defined on a torus is invariant under modular transformations. In this paper we study families of quantum field theories labeled by a dimensionful parameter t, that have the additional property that the energy of a state at finite t is a function only of t and of the energy and momentum of the corresponding state at t = 0, where the theory becomes conformal. We show that under this requirement, the partition sum of the theory at t = 0 uniquely determines the partition sum (and thus the spectrum) of the perturbed theory, to all orders in t, to be that of a $T\overline{T}$ 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.Abstract Any two dimensional quantum field theory that can be consistently defined on a torus is invariant under modular transformations. In this paper we study families of quantum field theories labeled by a dimensionful parameter t, that have the additional property that the energy of a state at finite t is a function only of t and of the energy and momentum of the corresponding state at t = 0, where the theory becomes conformal. We show that under this requirement, the partition sum of the theory at t = 0 uniquely determines the partition sum (and thus the spectrum) of the perturbed theory, to all orders in t, to be that of a $$ T\overline{T} $$ 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.

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

partition sums from string theory

We calculate the torus partition sum of a general CFT2with left and right moving conserved currentsJand

\overline{J}

J¯ , perturbed by a combination of the irrelevant operators

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

TT¯,JT¯ and

T\overline{J}

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.

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.

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.