A pedagogical review on solvable irrelevant deformations of 2D quantum field theory

This is a pedagogical review on T (T) over bar deformation of two dimensional quantum field theories. It is based on three lectures which the author gave at ITP-CAS in December 2018. This review consists of four parts. The first part is a general introduction to T (T) over bar deformation. Special emphasises are put on the deformed classical Lagrangian and the exact solvability of the spectrum. The second part focuses on the torus partition sum of the T (T) over bar /J (T) over bar deformed conformal field theories and modular invariance/covariance. In the third part, different perspectives of T (T) over bar deformation are presented, including its relation to random geometry, 2D topological gravity and holography. We summarize more recent developments until January 2021 in the last part.

Automated summary

This is a pedagogical review on T (T) over bar deformation of two dimensional quantum field theories, based on lectures given at ITP-CAS in December 2018. The review consists of four parts: general introduction to T (T) over bar deformation, torus partition sum of T (T) over bar / J (T) over bar deformed conformal field theories, different perspectives of T (T) over bar deformation, and recent developments until January 2021.