Weighted average over the Narain moduli space as a T T over line deformation of the CFT target space

We consider the weighted average of a two dimensional conformal field theory (CFT), whose target space is T2, over its Narain moduli space. We take as the weighing function the integral kernel which gives rise to TT?? deformation when applied to the world sheet moduli data of the partition function viewed as vacuum amplitude when the world sheet is a torus. We compute the smeared partition function where this kernel is applied to the target space moduli. Smearing the partition function over the parameter space of a field theory generally leads to the breakdown in the ability to write the partition function as a sum over Boltzmann factor with unit coefficients. The weight function inspired by the TT?? deformation appears to be an exception to this general expectation. We show that this smearing leads to a marginal deformation corresponding to the overall rescaling of the target space T2.

Automated summary

This study investigates the weighted average of a two-dimensional conformal field theory (CFT) with a T2 target space over its Narain moduli space, and computes the smeared partition function. The weight function inspired by the TT?? deformation turns out to be an exception, leading to a marginal deformation corresponding to the overall rescaling of the T2 target space.