Working Seminar on Mathematical Physics of HSE University and Skoltech Krichever Center Alexey Bychkov (Skoltech, HSE Univ.)
RG flows in nonlinear sigma models (continuation)
The talk will be centered around the calculation of 1-loop beta-function in a nonlinear sigma model of a general kind. We will show that RG flow coincides with Ricci flow for sigma models without a Kalb-Ramond B-field. Addition of a B-field results in modification of this Ricci flow equation. Namely, instead of the usual Ricci tensor constructed from a metric (Levi-Civita) connection, in the r.h.s. of a generalized Ricci flow there appears a Ricci tensor constructed from a connection that is compatible with a Riemannian metric as well as with a certain torsion depending on a B-field. Along the way we will remind a listener of the basic constructions needed for a calculation: normal geodesic coordinates, covariant Taylor series, background field method, and some geometry of torsionfull connections. The main application of this calculation is the celebrated Wess-Zumino-Witten model. We will show that the 1-loop counterterm is cancelled out at any level k and a special value of a coupling constant g = 1/k
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