Modular invariance and uniqueness of $T\bar{T}$ deformed CFT

Aharony, Ofer; Datta, Shouvik; Giveon, Amit; Jiang, Yunfeng; Kutasov, David

doi:10.1007/JHEP01(2019)086

Modular invariance and uniqueness of $T\bar{T}$ deformed CFT

Ofer Aharony
(
- Weizmann Inst.
)
,
Shouvik Datta
(
- Zurich, ETH
)
,
Amit Giveon
(
- Hebrew U.
)
,
Yunfeng Jiang
(
- Zurich, ETH
)
,
David Kutasov
(
- Chicago U. and
- Chicago U., EFI
)

Aug 7, 2018

21 pages

Published in:

JHEP 01 (2019) 086

Published: Jan 10, 2019

e-Print:

1808.02492 [hep-th]

DOI:

10.1007/JHEP01(2019)086

View in:

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Abstract: (Springer)

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}

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.

Note:

20 pages; v2 : minor improvements in presentation

Conformal Field Theory
Effective Field Theories
Field Theories in Lower Dimensions
field theory: conformal
invariance: modular
transformation: modular
dimension: 2
field theory
deformation
nonperturbative

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Modular invariance and uniqueness of TTˉT\bar{T}TTˉ deformed CFT

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Modular invariance and uniqueness of $T\bar{T}$ deformed CFT