Dyson instability for 2D nonlinear O(N) sigma models
- Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242 (United States)
For lattice models with compact field integration (nonlinear sigma models over compact manifolds and gauge theories with compact groups) and satisfying some discrete symmetry, the change of sign of the bare coupling g{sub 0}{sup 2} at zero results in a mere discontinuity in the average energy rather than the catastrophic instability occurring in theories with integration over arbitrarily large fields. This indicates that the large order of perturbative series and the nonperturbative contributions should have unexpected features. Using the large-N limit of two-dimensional nonlinear O(N) sigma model, we discuss the complex singularities of the average energy for complex 't Hooft coupling {lambda}{sup t}=g{sub 0}{sup 2}N. A striking difference with the usual situation is the absence of the cut along the negative real axis. We show that the zeros of the partition function can only be inside a clover shape region of the complex {lambda}{sup t} plane. We calculate the density of states and use the result to verify numerically the statement about the zeros. We propose dispersive representations of the derivatives of the average energy for an approximate expression of the discontinuity. The discontinuity is purely nonperturbative and contributions at small negative coupling in one dispersive representation are essential to guarantee that the derivatives become exponentially small when {lambda}{sup t}{yields}0{sup +}. We discuss the implications for gauge theories.
- OSTI ID:
- 21322596
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 80, Issue 5; Other Information: DOI: 10.1103/PhysRevD.80.054020; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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