## Abstract

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.

Original language | American English |
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Article number | 85 |

Journal | Journal of High Energy Physics |

Volume | 2019 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 2019 |

### Bibliographical note

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

## Keywords

- Conformal Field Theory
- Effective Field Theories
- Field Theories in Lower Dimensions