Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-04-03
Nucl.Phys. B635 (2002) 505-524
Physics
High Energy Physics
High Energy Physics - Theory
21 pages, 4 figures using axodraw, 2 appendices; version 2: a new ref item [9] added to cite efforts to all orders, typos fixe
Scientific paper
The scalar theory is ultraviolet (UV) quadratically divergent on ordinary spacetime. On noncommutative (NC) spacetime, this divergence will generally induce pole-like infrared (IR) singularities in external momenta through the UV/IR mixing. In spontaneous symmetry breaking theory this would invalidate the Goldstone theorem which is the basis for mass generation when symmetry is gauged. We examine this issue at two loop level in the U(N) linear sigma model which is known to be free of such IR singularities in the Goldstone self-energies at one loop. We analyze the structures in the NC parameter (\theta_{\mu\nu}) dependence in two loop integrands of Goldstone self-energies. We find that their coefficients are effectively once subtracted at the external momentum p=0 due to symmetry relations between 1PI and tadpole contributions, leaving a final result proportional to a quadratic form in p. We then compute the leading IR terms induced by NC to be of order p^2\ln(\theta_{\mu\nu})^2 and p^2\ln\tilde{p}^2 (\tilde{p}_{\mu}=\theta_{\mu\nu}p^{\nu}) which are much milder than naively expected without considering the above cancellation. The Goldstone bosons thus keep massless and the theorem holds true at this level. However, the limit of \theta\to 0 cannot be smooth any longer as it is in the one loop Goldstone self-energies, and this nonsmooth behaviour is not necessarily associated with the IR limit of the external momentum as we see in the term of p^2\ln(\theta_{\mu\nu})^2.
No associations
LandOfFree
Validity of Goldstone Theorem at Two Loops in Noncommutative U(N) Linear Sigma Model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Validity of Goldstone Theorem at Two Loops in Noncommutative U(N) Linear Sigma Model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Validity of Goldstone Theorem at Two Loops in Noncommutative U(N) Linear Sigma Model will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-340402