arXiv:2104.00281 · Journal of High Energy Physics

Characters of irrelevant deformations

Shouvik Datta, Yunfeng Jiang

Published Jul 1, 2021• 6 citations

Abstract

Abstract We analyse the $$ T\overline{T} $$ T T ¯ deformation of 2d CFTs in a special double-scaling limit, of large central charge and small deformation parameter. In particular, we derive closed formulae for the deformation of the product of left and right moving CFT characters on the torus. It is shown that the 1/c contribution takes the same form as that of a CFT, but with rescalings of the modular parameter reflecting a state-dependent change of coordinates. We also extend the analysis for more general deformations that involve $$ T\overline{T} $$ T T ¯ , $$ J\overline{T} $$ J T ¯ and $$ T\overline{J} $$ T J ¯ simultaneously. We comment on the implications of our results for holographic proposals of irrelevant deformations.

DOI: 10.1007/jhep07(2021)162

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

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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.

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

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Sep 27, 202217 citations

$$ T\overline{T} $$ deformed partition functions

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A bstract We demonstrate the presence of modular properties in partition functions of $$ T\overline{T} $$ 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 $$ T\overline{T} $$ T T ¯ flow. Finally, we comment on the deformation of the CFT vacuum character and its implications for the holographic dual.

arXiv:1806.07426Journal of High Energy PhysicsAug 1, 2018162 citations

TT¯ deformed partition functions

Shouvik Datta, Yunfeng Jiang

Journal of High Energy PhysicsAug 1, 201850 citations

Modular covariance and uniqueness of $$ J\overline{T} $$ deformed CFTs

Ofer Aharony A, Shouvik Datta, Amit Giveon +2 more

arXiv:1808.08978Journal of High Energy PhysicsJan 1, 201955 citations

arXiv:2104.00281 · Journal of High Energy Physics

Characters of irrelevant deformations

Shouvik Datta, Yunfeng Jiang

Published Jul 1, 2021• 6 citations

arXiv HTML PDF

Abstract

Abstract We analyse the

T\overline{T}

T T ¯ deformation of 2d CFTs in a special double-scaling limit, of large central charge and small deformation parameter. In particular, we derive closed formulae for the deformation of the product of left and right moving CFT characters on the torus. It is shown that the 1/c contribution takes the same form as that of a CFT, but with rescalings of the modular parameter reflecting a state-dependent change of coordinates. We also extend the analysis for more general deformations that involve

T\overline{T}

T T ¯ ,

J\overline{T}

J T ¯ and

T\overline{J}

T J ¯ simultaneously. We comment on the implications of our results for holographic proposals of irrelevant deformations.

DOI: 10.1007/jhep07(2021)162

Related papers

On correlation functions in J T ¯ -deformed CFTs

Monica Guica

Abstract The deformation, built from the components of the stress tensor and of a current, is a universal irrelevant deformation of two-dimensional CFTs that preserves the left-moving conformal symmetry, while breaking locality on the right-moving side. Operators in the -deformed CFT are naturally labeled by the left-moving position and right-moving momentum and transform in representations of the one-dimensional extended conformal group. We derive an all-orders formula for the spectrum of conformal dimensions and charges of the deformed CFT, which we cross-check at leading order using conformal perturbation theory. We also compute the linear corrections to the one-dimensional OPE coefficients and comment on the extent to which the correlation functions in -deformed CFTs can be obtained from field-dependent coordinate transformations.Abstract The deformation, built from the components of the stress tensor and of a current, is a universal irrelevant deformation of two-dimensional CFTs that preserves the left-moving conformal symmetry, while breaking locality on the right-moving side. Operators in the -deformed CFT are naturally labeled by the left-moving position and right-moving momentum and transform in representations of the one-dimensional extended conformal group. We derive an all-orders formula for the spectrum of conformal dimensions and charges of the deformed CFT, which we cross-check at leading order using conformal perturbation theory. We also compute the linear corrections to the one-dimensional OPE coefficients and comment on the extent to which the correlation functions in -deformed CFTs can be obtained from field-dependent coordinate transformations.

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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, David Kutasov

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.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.

arXiv:1907.07221Journal of High Energy PhysicsFeb 1, 202051 citations

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

Akikazu Hashimoto A

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.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.

Sep 27, 202217 citations

$T\overline{T}$ deformed partition functions$$ T\overline{T} $$ deformed partition functions

Shouvik Datta, Yunfeng Jiang

A bstract We demonstrate the presence of modular properties in partition functions of $T\overline{T}$ 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 $T\overline{T}$ T T ¯ flow. Finally, we comment on the deformation of the CFT vacuum character and its implications for the holographic dual.A bstract We demonstrate the presence of modular properties in partition functions of $$ T\overline{T} $$ 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 $$ T\overline{T} $$ T T ¯ flow. Finally, we comment on the deformation of the CFT vacuum character and its implications for the holographic dual.

arXiv:1806.07426Journal of High Energy PhysicsAug 1, 2018162 citations

TT¯ deformed partition functions

Shouvik Datta, Yunfeng Jiang

We demonstrate the presence of modular properties in partition functions of TT 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 flow. Finally, we comment on the deformation of the CFT vacuum character and its implications for the holographic dual.We demonstrate the presence of modular properties in partition functions of TT 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 flow. Finally, we comment on the deformation of the CFT vacuum character and its implications for the holographic dual.

Journal of High Energy PhysicsAug 1, 201850 citations

Modular covariance and uniqueness of $J\overline{T}$ deformed CFTsModular covariance and uniqueness of $$ J\overline{T} $$ deformed CFTs

Ofer Aharony A, Shouvik Datta, Amit Giveon +2 more

A bstract We study families of two dimensional quantum field theories, labeled by a dimensionful parameter μ , that contain a holomorphic conserved U(1) current J ( z ). We assume that these theories can be consistently defined on a torus, so their partition sum, with a chemical potential for the charge that couples to J , is modular covariant. We further require that in these theories, the energy of a state at finite μ is a function only of μ , and of the energy, momentum and charge of the corresponding state at μ = 0, where the theory becomes conformal. We show that under these conditions, the torus partition sum of the theory at μ = 0 uniquely determines the partition sum (and thus the spectrum) of the perturbed theory, to all orders in μ , to be that of a $\mu J\overline{T}$ 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.A bstract We study families of two dimensional quantum field theories, labeled by a dimensionful parameter μ , that contain a holomorphic conserved U(1) current J ( z ). We assume that these theories can be consistently defined on a torus, so their partition sum, with a chemical potential for the charge that couples to J , is modular covariant. We further require that in these theories, the energy of a state at finite μ is a function only of μ , and of the energy, momentum and charge of the corresponding state at μ = 0, where the theory becomes conformal. We show that under these conditions, the torus partition sum of the theory at μ = 0 uniquely determines the partition sum (and thus the spectrum) of the perturbed theory, to all orders in μ , to be that of a $$ \mu J\overline{T} $$ 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.

arXiv:1808.08978Journal of High Energy PhysicsJan 1, 201955 citations

Abstract We analyse the

T\overline{T}

T\overline{T}

T T ¯ ,

J\overline{T}

J T ¯ and

T\overline{J}

T J ¯ simultaneously. We comment on the implications of our results for holographic proposals of irrelevant deformations.

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\overline{T}

deformed partition functions

A bstract We demonstrate the presence of modular properties in partition functions of

T\overline{T}

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

T\overline{T}

T T ¯ flow. Finally, we comment on the deformation of the CFT vacuum character and its implications for the holographic dual.

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.