Resurgence and dynamics of O(N) and Grassmannian sigma models

Dunne, Gerald V.; Unsal, Mithat

doi:10.1007/JHEP09(2015)199

Title: Resurgence and dynamics of O(N) and Grassmannian sigma models

Journal Article · Tue Sep 29 00:00:00 EDT 2015 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP09(2015)199· OSTI ID:1441165

Dunne, Gerald V. ^[1]; Unsal, Mithat ^[2]

Univ. of Connecticut, Storrs, CT (United States)
North Carolina State Univ., Raleigh, NC (United States)

Here, we study the non-perturbative dynamics of the two dimensional O(N) and Grassmannian sigma models by using compactification with twisted boundary conditions on R×S¹, semi-classical techniques and resurgence. While the O(N) model has no instantons for N > 3, it has (non-instanton) saddles on R², which we call 2d-saddles. On R×S¹, the resurgent relation between perturbation theory and non-perturbative physics is encoded in new saddles, which are associated with the affine root system of the o(N) algebra. These events may be viewed as fractionalizations of the 2d-saddles. The first beta function coefficient, given by the dual Coxeter number, can then be intepreted as the sum of the multiplicities (dual Kac labels) of these fractionalized objects. Surprisingly, the new saddles in O(N) models in compactified space are in one-to-one correspondence with monopole-instanton saddles in SO(N) gauge theory on R³×S¹. The Grassmannian sigma models Gr(N, M) have 2d instantons, which fractionalize into N kink-instantons. The small circle dynamics of both sigma models can be described as a dilute gas of the one-events and two-events, bions. One-events are the leading source of a variety of non-perturbative effects, and produce the strong scale of the 2d theory in the compactified theory. We show that in both types of sigma models the neutral bion emulates the role of IR-renormalons. We also study the topological theta angle dependence in both the O(3) model and Gr(N, M), and describe the multi-branched structure of the observables in terms of the theta-angle dependence of the saddle amplitudes, providing a microscopic argument for Haldane’s conjecture.

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Research Organization:: Univ. of Connecticut, Storrs, CT (United States); North Carolina State University, Raleigh, NC (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0010339; SC0013036

OSTI ID:: 1441165

Journal Information:: Journal of High Energy Physics (Online), Vol. 2015, Issue 9; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 45 works

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