TY - JOUR

T1 - Modular covariance and uniqueness of JT¯ deformed CFTs

AU - Aharony, Ofer

AU - Datta, Shouvik

AU - Giveon, Amit

AU - Jiang, Yunfeng

AU - Kutasov, David

N1 - Publisher Copyright:
© 2019, The Author(s).

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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 μJT¯ deformed conformal field theory (CFT). We derive a flow equation for the JT¯ 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.

AB - 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 μJT¯ deformed conformal field theory (CFT). We derive a flow equation for the JT¯ 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.

KW - Conformal Field Theory

KW - Effective Field Theories

KW - Field Theories in Lower Dimensions

UR - http://www.scopus.com/inward/record.url?scp=85059940899&partnerID=8YFLogxK

U2 - 10.1007/JHEP01(2019)085

DO - 10.1007/JHEP01(2019)085

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AN - SCOPUS:85059940899

SN - 1126-6708

VL - 2019

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 1

M1 - 85

ER -