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-Neveu kink-antikink heat kernel.
New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We present a broad conceptual introduction to some new ideas in non-perturbative QFT. The large-$N$ orbifold-orientifold equivalence connects a natural large-$N$ limit of QCD to QCD with adjoint fermions. QCD(adj) with periodic boundary conditions and double-trace deformation of Yang-Mills theory satisfy large-$N$ volume independence, a type of orbifold equivalence. Certain QFTs that satisfy volume independence at $N=\infty$ exhibit adiabatic continuity at finite-$N$, and also become semi-classically calculable on small $\mathbb R^3 \times S^1$. We discuss the role of monopole-instantons, and magnetic and neutral bion saddles in connection to mass gap, and center and chiral symmetry realizations. Neutral bions also provide a weak coupling semiclassical realization of infrared-renormalons. These considerations help motivate the necessity of complexification of path integrals (Picard-Lefschetz theory) in semi-classical analysis, and highlights the importance of hidden topological angles. Finally, we briefly review the resurgence program, which potentially provides a novel non-perturbative continuum definition of QFT. All these ideas are continuously connected.
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UNVERDICTED 4representative citing papers
Numerical lattice study shows fractional instantons on twisted T^4 morph into monopole-instantons and center vortices as geometry interpolates between R^{4-k} x T^k, with some transitions discontinuous under deformation.
Presents explicit trans-series calculations for the double-well spectrum via exact WKB and path integral approaches up to four-instanton level.
Introductory lectures cover resurgent asymptotics using examples like the Airy function, nonlinear Stokes phenomenon, Heisenberg-Euler action, and resurgent continuation.
citing papers explorer
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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-Neveu kink-antikink heat kernel.
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Metamorphosis of fractional instantons on a twisted $T^4$ with a double-trace deformation: a numerical study
Numerical lattice study shows fractional instantons on twisted T^4 morph into monopole-instantons and center vortices as geometry interpolates between R^{4-k} x T^k, with some transitions discontinuous under deformation.
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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.