Any opinions if the equation 13.115 of Peskin and Schroeder is true on arbitrary manifolds in arbitrary dimensions for the same Lagrangian? I a priori see no problem.

The point I also want to ask is - if one evaluates that equation for spacetime >2 then one will miss the symmetry broken phase of the theory - right? - BUT isn't the saddle point obtained from it still the critical point of the corresponding theory on whatever is the (>2)-manifold?

Is this in general true that the large-N critical NLSM on a manifold $M$ is the same as the theory of $N$ non-interacting conformally coupled scalars on $M$?

Or in otherwords - will the Lagrange multiplier field in NLSM have to have at the large-N saddle point an expectation value which is the same as the conformally coupled mass for scalars on that manifold?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.