Genus two correlation functions in CFTs with TT deformation

Since the definition of TT deformation in the curved Riemann surface is obstructive in the literature,we propose a way to do the deformation in the genus two Riemann surfaces by sewing prescription.We construct the correlation functions of conformal field theories(CFTs)on genus two Riemann surfaces with the TT deformation in terms of the perturbative CFT approach.Thanks to sewing construction to form higher genus Riemann surfaces from lower genus ones and conformal symmetry,we systematically obtain the first-order TT correction to the genus two correlation functions in the TT deformed CFTs,e.g.,partition function and one/higher-point correlation functions.