what does string theory have to say about the trace anomaly in the expectation value of the stress energy tensor of massless quantum fields on a curved background and its interpretation as the emergence of an extra scalar degree of freedom in the semiclassical limit of GR + QFT? Is it something that can be proved? that emerges naturally? Or that can be shown to be false?
The question has actually two quite distinct parts: 1) the presence of the anomaly and its form and 2) the possibility of interpreting it as the emergence of an extra degree of freedom at the classical level with its own EOM and a specific stress energy tensor satisfying the constraint Trace (T_mu_nu) = some function of the curvature.
Thanks a lot
NOTE ADDED As a warm-up I will reduce the scope of the question.
String theory and the triangle anomaly in Q.E.D.?
Are there examples where, starting from "first principles" in string theory, one compactifies to 3+1 dimensions and reproduce the physical effects of the so called/chiral triangle anomaly. When I say physical effects, I mean I don't care how it shows up, as long as it reproduces the final result in some approximation. Than we can think of the fact that there are different kind of anomalies etc.