Neutral bions in the CP^{N-1} model for resurgence

Abstract

Classical configurations in the CP^{N-1} model on R^1 x S^1 is studied with twisted boundary conditions. Starting from fractional instantons with the Z_N twisted boundary conditions, we review briefly the relevance of our study to resurgence phenomenon in field theory. We consider primarily configurations composed of multiple fractional instantons, called "neutral bions", which are identified as "perturbative infrared renormalons". We construct an explicit ansatz corresponding to topologically trivial configurations containing one fractional instanton (nu=1/N) and one fractional anti-instanton (nu=-1/N), which is guaranteed to become a solution of field equations asymptotically for large separations. The attractive interactions between the instanton constituents from small to large separations are found to be consistent with the standard separated-instanton calculus. Our results suggest that the ansatz enables us to study bions and the related physics for a wide range of separations. This talk is mainly based on our recent work published in JHEP 1406, 164 (2014) [arXiv:1404.7225 [hep-th]].

arXiv comment10 pages, 3 figures, submitted to the Proceedings of the 30th International Colloquium on Group Theoretical Methods in Physics, Ghent, 14-18 July 2014 to appear in the Journal of Physics: Conference Series (JPCS)

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• Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}{P}^{N-1}$ models
• Exact Resurgent Trans-series and Multi-Bion Contributions to All Orders
• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• The curious incident of multi-instantons and the necessity of Lefschetz thimbles
• Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on $S^1$
• Relations among topological solitons
• Non-BPS exact solutions and their relation to bions in $\mathbb{C}{P}^{N-1}$ models
• Resurgence Structure to All Orders of Multi-bions in Deformed SUSY Quantum Mechanics
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• Josephson instantons and Josephson monopoles in a non-Abelian Josephson junction
• Resurgence and Lefschetz thimble in 3d N=2 supersymmetric Chern-Simons matter theories
• Resurgence and semiclassical expansion in two-dimensional large-$N$ sigma models
• Resurgence of one-point functions in a matrix model for 2D type IIA superstrings
• Two-point functions at arbitrary genus and its resurgence structure in a matrix model for 2D type IIA superstrings
• Exact WKB in all sectors II: Potentials with non-degenerate saddles