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High Energy Physics - Theory, hep-th,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
Abstract:
We construct the correlation functions of conformal field theories (CFTs) on
genus two Riemann surface with the $T\bar{T}$ deformation in terms of
perturbative CFT approach. Thanks to sewing construction to form higher genus
Riemann surface from lower genus ones and conformal symmetry, we systematically
obtain the first order $T\bar{T}$ correction to the higher genus correlation
functions in the $T\bar{T}$ deformed CFTs, e.g. partition function and
one/higher-point correlation functions. In the weak coupling limit, the higher
genus correlation functions can be decomposed by lower genus correlation
functions. Our results offer $T\bar{T}$ deformed field theories data to allow
us to extract quantum chaos signals and multiple-interval R\'{e}nyi entropies
in deformed field theories.
