Super-Virasoro Anomaly, Super-Weyl Anomaly, and the Super-Liouville Action for 2D Supergravity

Abstract

The relation between super-Virasoro anomaly and super-Weyl anomaly in N = 1 NSR superstring coupled with 2D supergravity is investigated from canonical theoretical view point. The WZW action canceling the super-Virasoro anomaly is explicitly constructed.It is super-Weyl invariant but nonlocal functional of 2D supergravity. The nonlocality can be remedied by the super-Liouvlle action, which in turn recovers the super-Weyl anomaly. The final gravitational effective action turns out to be local but noncovariant super-Liouville action, describing the dynamical behavior of the super-Liouville fields.The BRST invariance of this approach is examined in the superconformal gauge and in the light-cone gauge.

Nonrelativistic string theory sigma model and its canonical formulation

“…The presence of two dimensional vielbeins e a α makes the analysis slightly complicated and hence it is important to choose suitable parametrization. To do this we use convention introduced in [28,29]. Explicitly, let us define e α and ēα as…”