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Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
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Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
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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 also consider two applications of these techniques in string theory
Forward citations
Cited by 19 Pith papers
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Orientation Reversal and the Chern-Simons Natural Boundary
Resurgence provides a unique analytic continuation across natural boundaries for Chern-Simons q-series that matches 3-manifold orientation reversal via Mordell integral decompositions.
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Resurgence of Chern-Simons theory at the trivial flat connection
An extended square matrix of (x,q)-series indexed by boundary parabolic SL2(C) flat connections completely describes the resurgent structure, Stokes constants, and Borel transform of Chern-Simons perturbation theory a...
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From Matrix Models to Gaussian Molecules and the Einstein-Hilbert Action
The free energy of a D-dimensional matrix model with Gaussian heat-kernel propagator equals the Einstein-Hilbert action with cosmological constant, constants fixed by graph invariants of ribbon graphs.
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Derivation of the NS5-brane limit of the plane wave matrix model
A double-scaling limit of the BMN/plane-wave matrix model is derived analytically and produces an eigenvalue integral for the 1/4-BPS sector of IIA little string theory on R×S⁵.
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All-loop four-quark Bethe-Salpeter kernel
The all-loop bare perturbative part of the four-quark Bethe-Salpeter kernel is computed analytically in the large-Nf limit of massless QCD.
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Resurgence of high-energy string amplitudes
High-energy string amplitudes have asymptotic expansions governed by Bernoulli numbers, upgraded via resurgence to transseries whose Stokes data encode non-perturbative monodromy between kinematic regions.
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Resurgence of the Effective Action in Inhomogeneous Fields
Inhomogeneous background fields convert Borel poles in the effective action to branch points and introduce new ones, allowing resurgent extrapolation to recover non-perturbative information from perturbative input mor...
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From Fredholm Determinants to AdS/CFT Observables: A Universal Strong-Coupling Framework
The O(6) mass gap's strong-coupling trans-series is generated from Fredholm-determinant data via a conjectured alien calculus, yielding an all-orders relation to the cusp anomalous dimension.
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Weak-Strong Resurgence Duality
Establishes explicit resurgent duality between zero-radius weak-coupling and infinite-radius strong-coupling expansions, illustrated on Airy/Pearcey integrals and applied to phi^4 Dyson-Schwinger equations and Gross-N...
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Strong coupling structure of $\mathcal{N}=4$ SYM observables with matrix Bessel kernel
The strong-coupling transseries for matrix Bessel determinant observables is generated from its perturbative part by shifting a→a−Δ and replacing moments I_n, with all Stokes constants fixed by two recurrences.
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Strong coupling structure of $\mathcal{N}=4$ SYM observables with matrix Bessel kernel
Reorganizing the transseries of matrix Bessel kernel determinants at strong coupling yields a simple structure where non-perturbative corrections are directly determined by the perturbative series for N=4 SYM observables.
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$c_{\rm eff}$ from Resurgence at the Stokes Line
Resurgent cyclic orbits' algebraic structure plus the leading q-series term determines the asymptotic growth exponent of dual q-series coefficients, which equals an effective central charge c_eff in a related 3d N=2 QFT.
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Non-Perturbative Real Topological Strings
Extends operator formalism of closed topological strings to derive all-order trans-series solutions for real topological strings, with disk invariants as Stokes constants and numerical checks on local P2.
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All the D-Branes of Resurgence
Negative-tension ZZ-branes are required by resurgence to build complete transseries for minimal-string free energies, with analytic Stokes data and extensions to JT gravity and other string models.
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Coherent states versus Glauber-Sudarshan States: Bootstrapping, Schwinger-Keldysh Contours and Lefschetz Thimbles
Quasi-de Sitter spacetimes can be realized as Glauber-Sudarshan excited states built over supersymmetric Minkowski vacua, held consistent by a bootstrap self-consistency equation rather than by a potential minimum.
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Modular resurgence of topological string
Stokes constants of topological string non-perturbative contributions are invariant on monodromy orbits, reproduce the BPS spectrum, and satisfy the Kontsevich-Soibelman Lie algebra.
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From Matrix Models to Gaussian Molecules and the Einstein-Hilbert Action
The free energy of a D-dimensional matrix model on a curved background is the Einstein-Hilbert action with cosmological constant, where the constants are expectation values of graph invariants from ribbon graphs.
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The Double Well Done Doubly-Well
Presents explicit trans-series calculations for the double-well spectrum via exact WKB and path integral approaches up to four-instanton level.
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Introductory Lectures on Resurgence: CERN Summer School 2024
Introductory lectures cover resurgent asymptotics using examples like the Airy function, nonlinear Stokes phenomenon, Heisenberg-Euler action, and resurgent continuation.
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