Abstract

In the paper, we compute the correlation functions in 2D mathcal{N} = (1, 1) and mathcal{N} = (2, 2) superconformal field theories with Toverline{T} deformation up to the first order of the deformation in terms of perturbation theory. With the help of superconformal Ward identity in mathcal{N} = (1, 1) and mathcal{N} = (2, 2) theories and careful regularization, the correlation functions in the deformed theory can be obtained up to the first order perturbation. This study is the extension from previous bosonic Toverline{T} deformation to the supersymmetric one.

Highlights

  • The T Tdeformation as a special deformation, has attracted much attention [5–28]

  • Since we will work in the Euclidean signature, we will focus on the correlation functions of the deformed superconformal field theory with N = (1, 1) and N = (2, 2) SUSY

  • In the present paper we investigated the correlation functions with T Tdeformation for N = (1, 1) and N = (2, 2) superconformal field theory perturbatively to the first order of the deformation

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Summary

Φ1Φ2Φ3

As an example consider the OTOC involving two fields φ, ψ1, from (45) in [19], at first order one of the four-point functions needed to compute is φ In the bosonic CFT, four-point correlators can be expressed as conformal blocks whose universal properties are known in some cases, the OTOC can be computed [73], while in eq (2.58) the function f is unknown in general. Φ1(Z1, Z1)Φ2(Z2, Z2)Φ3(Z3, Z3) = Zi−j ∆ij exp θij θij Aij Zij δQ1+Q2+Q3,0 i

Dimensional regularization
Conclusions
N = (1, 1): 2-point case
N = (1, 1): 3-point case
N = (1, 1): n-point case Now evaluate
N = (2, 2): 2-point case
N = (2, 2): 3-point case
N = (2, 2): n-point case Let us first consider only holomorphic component J(Z) inserted
B Integrals in 2-point correlators
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