Lectures on non‐perturbative effects in large N gauge theories, matrix models and strings

By Marcos Mariño. 2012

301 citations recorded by the source corpus.

In these lectures I present a review of non‐perturbative instanton effects in quantum theories, with a focus on large N gauge theories and matrix models. I first consider the structure of these effects in the case of ordinary differential equations, which provide a model for more complicated theories, and I introduce in a pedagogical way some technology from resurgent analysis, like trans‐series and the resurgent version of the Stokes phenomenon. After reviewing instanton effects in quantum mechanics and quantum field theory, I address general aspects of large N instantons, and then present a detailed review of non‐perturbative effects in matrix models. Finally, I consider two applications of these techniques in string theory.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b35c08f117de453e0559caa1a56706a56d25ee51

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In Nuclear and High Energy Physics

Citations in the corpus

JT gravity as a matrix integral (2019, methodology): “In this section we will use the density of eigenvalues in the forbidden region to predict the large genus asymptotics of the Weil-Petersson volumes, following a similar approach for other problems described by topological recursion in [111, 112, 61].”
An introduction to resurgence, trans-series and alien calculus (2014, unknown): “Resurgence theory was discovered in a different context by Ecalle in the early 80s [12] and since then it has been applied with success to quantum mechanics [4, 13–16], matrix models [17], supersymmetric localizable field theories [18] and topological string theory [19, 20].”
Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles (2014, methodology): “40) can be evaluated in multiple different ways [39, 80], for example, via the Gelfand-Yaglom method [95].”
Resurgence theory, ghost-instantons, and analytic continuation of path integrals (2013, background): “27) where Ẑ = ξ−1/2Z, and by a general result [15, 24], this means that Z has a three-term resurgent trans-series in the large ξ [small g2] limit, given in (2.”
Resurgence and trans-series in Quantum Field Theory: the $\mathbb{C}{{\mathbb{P}}^{N-1 }}$ model (2012, methodology): “We also note that some progress has recently been made in applying the ideas of resurgence to matrix models, and certain string theories and quantum field theories (which do not require renormalization) in the recent works of Schiappa et al [40], Mariño et al [41, 42], and Costin et al [43].”
Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity (2019, methodology): “The rules for including D-brane boundaries do not have a clear origin in gravity; we must rely upon the matrix integral description of JT gravity to understand how to properly (31)These branes are also closely related to branes in topological string theories described by matrix models [64, 65, 66, 6”