Speaker
Description
$T\bar T$ deformations have been widely studied for 2d CFTs on the plane and the torus, and have many interesting implications for two and three dimensional quantum gravity. However, these deformations have not yet been extended to higher genus. Using ideas initiated by Friedan and Shenker in the 80s, we formulate the $T\bar T$ operator in terms of the Kähler form on the moduli space of higher genus Riemann surfaces, which provides a very natural interpretation of the solvability of such deformations and extends the deformation to arbitrary genus. We then explore what properties of the CFT partition function survive and what are modified by the deformation, for example factorization at degeneration limits. Finally we discuss how this formalism suggests how to reconstruct a bulk AdS$_3$ spacetime with a higher genus boundary.
