Large N and double scaling limits in two dimensions

Abstract

Recently, the author has constructed a series of four dimensional non-critical string theories with eight supercharges, dual to theories of light electric and magnetic charges, for which exact formulas for the central charge of the space-time supersymmetry algebra as a function of the world-sheet couplings were obtained. The basic idea was to generalize the old matrix model approach, replacing the simple matrix integrals by the four dimensional matrix path integrals of N=2 supersymmetric Yang-Mills theory, and the Kazakov critical points by the Argyres-Douglas critical points. In the present paper, we study qualitatively similar toy path integrals corresponding to the two dimensional N=2 supersymmetric non-linear sigma model with target space CP^n and twisted mass terms. This theory has some very strong similarities with N=2 super Yang-Mills, including the presence of critical points in the vicinity of which the large n expansion is IR divergent. The model being exactly solvable at large n, we can study non-BPS observables and give full proofs that double scaling limits exist and correspond to universal continuum limits. A complete characterization of the double scaled theories is given. We find evidence for dimensional transmutation of the string coupling in some non-critical string theories. We also identify en passant some non-BPS particles that become massless at the singularities in addition to the usual BPS states.

38 pages, including an introductory section that makes the paper self-contained, two figures and one appendix; v2: typos corrected

References in corpus (4)

• The large Nc limit of N=2 super Yang-Mills, fractional instantons and infrared divergences
• A model for gauge theories with Higgs fields
• Exact amplitudes in four dimensional non-critical string theories
• A note on theta dependence

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