Abstract
We study perturbative renormalization of the composite operators in the Toverline{T} -deformed two-dimensional free field theories. The pattern of renormalization for the stress-energy tensor is different in the massive and massless cases. While in the latter case the canonical stress tensor is not renormalized up to high order in the perturbative expansion, in the massive theory there are induced counterterms at linear order. For a massless theory our results match the general formula derived recently in [1].
Highlights
Dual of the T Tdeformed theories is an interesting question studied, for instance, in [14,15,16], see [17,18,19,20,21] for recent developments on T Tand string theory, and [22] for studies of dS
We study perturbative renormalization of the composite operators in the T Tdeformed two-dimensional free field theories
At large N one expects the T Tdeformation to represent a change in boundary conditions [23], whereas the Hagedorn behavior and partition function of the T Ttheories is an interesting question by itself [2, 3, 24,25,26,27]
Summary
We consider T Tdeformation of the free massless scalar field. To the linear order in the T Tcoupling λ the action is given by. In all of our calculations we are looking for logarithmically divergent terms, which (to linear order in the coupling λ) in dimensional regularization correspond to only simple poles in. Consider renormalization of the composite operator φn, n ≥ 2 in the theory of massless scalar field φ to the linear order in the T Tcoupling λ, φn = [φn] + ∆φn ,. Using the O(λ0) order equations of motion ∂2φ = 0, one can show that in d = 2 the O(λ) expression (2.20) is equivalent to in agreement with (1.2). First of all we notice that in massless theory the term ∂μφ∂νφ(∂φ) does not get renormalized to zeroth order in λ. Since to linear order in λ the renormalization of ∂μφ∂νφ defines renormalization of Tμν, we conclude that the O(λ0) equations of motion imply.
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