Ray-Singer introduced the concept of holomorphic analytic torsion. One key step to define the analytic torsion is small time asymptotics of the heat kernel. 
In this talk, we establish the small time asymptotics of the kernel of the difference of the heat operator and Szegő projector, then give the definition of the analytic torsion on a non-degenerate CR manifold, which answers Bismut’s question. 
We also establish Bismut-Vasserot type asymptotics of the analytic torsion associated with high powers of a CR line bundle. 
This is a joint work with C.-Y. Hsiao and R.-T. Huang.