Three loop calculations of B-functions for string associated non-linear sigma models

Foakes, Andrew Paul (1988) Three loop calculations of B-functions for string associated non-linear sigma models. University of Southampton, Doctoral Thesis.

Abstract

We calculate the three loop β-function for the purely metric bosonic non-linear sigma model by calculating the residue of the simple pole at three loops. We check this calculation by showing that the residue of the double pole at three loops is the same as (up to terms that can be absorbed by a diffeomorphism) the prediction from the renormalisation group equation. The condition that Weyl invariance is preserved after quantisation is that the β-function is set to zero. We show that setting this β-function to zero is equivalent (again, up to terms that can be absorbed by a diffeomorphism) to the equations of motion of the O(α'2) low energy effective action being obeyed. We also calculate the three loop β-function for the supersymmetric purely metric non-linear sigma model using a choice of fermionic quantum field that preserves the supersymmetry. The renormalisation group equation predicts that the double pole residue should vanish in this case. We show that at three loops, the double and simple pole residues both cancel between the bosonic and fermionic contributions diagram by diagram, whereas the triple pole has no fermionic contribution. We go on to show that we can choose a fermionic quantum field that does not preserve the explicit supersymmetry. We also calculate the β-function to three loops uisng this quantum field and show that the simple and double pole residues still cancel. (DX86451)

This record has no associated files available for download.

Contributors

Download statistics