Noncommutative field theory from string theory: two-loop analysis

Abstract

Noncommutative phi (3) field theory in six dimensions exhibits the logarithmic UV/IR mixing at the two-loop order. We show that open string theory in the presence of constant background NS-NS two-form field yields the same amplitude upon taking: a decoupling limit. The stretched string picture proposed on the basis of one-loop analysis naturally generalizes to the two-loop amplitudes in consideration. Our string theory formulation can incorporate the closed string insertions as well as open string insertions. Furthermore, the analysis of the world-sheet partition function and propagators can be straightforwardly generalized to Riemann surfaces with genus zero but with an arbitrary number of boundaries. (C) 2001 Elsevier Science B.V. All rights reserved.