Abstract
In this paper, we investigate the partition functions of conformal field theories (CFTs) with the T overline{T} deformation on a torus in terms of the perturbative QFT approach. In Lagrangian path integral formalism, the first- and second-order deformations to the partition functions of 2D free bosons, free Dirac fermions, and free Majorana fermions on a torus are obtained. The corresponding Lagrangian counterterms in these theories are also discussed. The first two orders of the deformed partition functions and the first-order vacuum expectation value (VEV) of the first quantum KdV charge obtained by the perturbative QFT approach are consistent with results obtained by the Hamiltonian formalism in literature.
Highlights
Where T λ depending on λ is stress tensor of the theory Lλ
In this paper, we investigate the partition functions of conformal field theories (CFTs) with the T Tdeformation on a torus in terms of the perturbative QFT approach
To evaluate the correlation functions and higher ordered partition functions perturbatively, the flow of stress tensor must be taken into consideration
Summary
We would like to compute the perturbation expansion of T Tdeformed partition function beyond the first-order. The procedure is based on the method first introduced in [2] ( see [50]), where deformed Lagrangian is obtained order by order. By comparing each order in the resulting expressions, eventually, we obtain the following recursion relations. By comparing each order in the resulting expressions, eventually, we obtain the following recursion relations1 Note this recursion relations allow us to obtain L(n) and Tμ(nν) for arbitrary n, once L(0), i.e. the un-deformed theory, is given. We will focus on the T Tdeformed free theories on a torus, including free bosons, Dirac fermions, and Majorana fermions, where the deformed partition functions up to the second-order (2.9)–(2.10) can be worked out analytically
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