The super conformal field theories are above all conformal. Conformal theories are defined on flat space-times. Despite that, if one looks at the stress tensor trace of a SCFT in 4d you get a contribution from the field strength of the gauge sector and the Euler density, i.e. $$T_{\mu}^{\mu} \backsim F_{\mu \nu }^2 - a(R_{\mu \nu \rho \sigma})^2 + \text{other terms}$$ Where does this $R_{\mu \nu \rho \sigma}$ come from in a super-conformal field theory which, from what I know, it is defined in flat space-time? Why we call this $a$ "central charge" despite it looks like some coupling?

This post imported from StackExchange Physics at 2014-12-23 15:08 (UTC), posted by SE-user Marion