Quantum Field Theory in Singular Limits
Abstract
This is a short summary of the phase structure of vector O(N) symmetric quantum field theories in a singular limit, the double scaling limit.It is motivated by the fact that summing up dynamically triangulated random surfaces using Feynman graphs of the O(N) matrix model results in a genus expansion and it provides,in some sense, a nonperturbative treatment of string theory when the double scaling limit is enforced. The main point emphasized here is that this formal singular limit, recently discussed mainly in d=0 O(N) matrix models, has an intriguing physical meaning in d>2 O(N) vector theories. In this limit all orders in {1\over N} are of equal importance since at each order infrared divergences compensate for the decrease in powers of {1\over N}. The infrared divergences are due to the tuning of the strength of the force {g \to g_c} between the O(N) quanta so that a massless O(N) singlet appears in the spectrum. At the critical dimension an interesting phase structure is revealed, the massless excitation has the expected physical meaning: it is the Goldston boson of spontaneous breaking of scale invariance - the dilaton.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 1998
- DOI:
- 10.48550/arXiv.hep-th/9812029
- arXiv:
- arXiv:hep-th/9812029
- Bibcode:
- 1998hep.th...12029M
- Keywords:
-
- High Energy Physics - Theory
- E-Print:
- This is a short summary of Lecture 16 - Les-Houches, February 1997 (Latex file,7 pages, no figures)