The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

By P. Argyres, M. Unsal. 2012

211 citations recorded by the source corpus.

A bstractWe study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are magnetic bions which carry net magnetic charge and induce a mass gap for gauge fluctuations. Another type are neutral bions which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics — which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription — to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion-anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Écalle’s resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.

Subfields: Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/fe856f953f967ebf409bce8291ee13af8d28730f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Condensed Matter Physics

1. G. Dunne
2. Daniele Dorigoni
3. A. Cherman
4. M. Unsal

In Nuclear and High Energy Physics

1. G. Dunne
2. Daniele Dorigoni
3. A. Cherman
4. M. Unsal
5. P. Argyres
6. Simon Catterall
7. D. Kaplan
8. R. Schiappa

Citations in the corpus

• Lectures on non‐perturbative effects in large N gauge theories, matrix models and strings (2012, unknown): “The ideas of resurgence, which have been very powerful in the context of ODEs and Quantum Mechanics, have scarcely been used in QFT (see however [11] for recent work in this direction).”
• Resurgence and trans-series in Quantum Field Theory: the $\mathbb{C}{{\mathbb{P}}^{N-1 }}$ model (2012, methodology): “[17], in theories with massless fermions, both charged and neutral bion events are unambiguous.”
• Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles (2014, methodology): “2.1 Borel analysis and Stokes Phenomena 13 2.2 Stokes automorphism and alien derivative 15 2.3 Reality of resurgent trans-series for real λ and BE-summability 16 2.4 Lefschetz thimbles and geometrization of ambiguity cancellation 17 2.5 NP-data in late terms of P-expansion 19”
• Uniform WKB, Multi-instantons, and Resurgent Trans-Series (2014, methodology): “For CPN−1 models, the N dependence matches precisely the N dependence coming from the IR renormalons [25], while for 4D gauge theory the dependence is parametrically correct[24].”