Working Seminar on Mathematical Physics on Wednesdays. Speaker: Maxim Gritskov (Skoltech, HSE Univ.)

The stress–energy tensor in conformal perturbation theory and topological CFTs 

In the first part, I will discuss a formula derived by Ashoke Sen and Philip Nelson in the early 1990s. This rather counterintuitive result answers the question of how the stress–energy tensor of a conformal field theory deforms under a marginal perturbation. We will examine this formula through a simple yet illustrative example - the free bosonic field.  

In the second part, I will introduce the concept of topological conformal field theories. We will consider the main basic example - the critical bosonic string theory. Then, we will study marginal deformations of the general theory and, using the result on the deformation of the stress–energy tensor from the first part, derive Witten’s formula for the deformation of the BRST charge. In this framework, the cohomological obstruction to the second-order deformation of the BRST charge will turn out to be the one-loop beta function