A geometric South-East rule combined with Borel-plane values and resurgence adjacency identifies contributing critical points for asymptotics of integrals e^{i k f(x)} over R^d without Picard-Lefschetz flows.
Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
5 Pith papers cite this work. Polarity classification is still indexing.
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abstract
This work is a step towards a non-perturbative continuum definition of quantum field theory (QFT), beginning with asymptotically free two dimensional non-linear sigma-models, using recent ideas from mathematics and QFT. The ideas from mathematics are resurgence theory, the trans-series framework, and Borel-Ecalle resummation. The ideas from QFT use continuity on R^1 x S^1_L, i.e, the absence of any phase transition as N \to infinity, or rapid-crossovers for finite-N, and the small-L weak coupling limit to render the semi-classical sector well-defined and calculable. We classify semi-classical configurations with actions 1/N (kink-instantons), 2/N (bions and bi-kinks), in units where the 2d instanton action is normalized to one. Perturbation theory possesses the IR-renormalon ambiguity that arises due to non-Borel summability of the large-orders perturbation series (of Gevrey-1 type), for which a microscopic cancellation mechanism was unknown. This divergence must be present because the corresponding expansion is on a singular Stokes ray in the complexified coupling constant plane, and the sum exhibits the Stokes phenomenon crossing the ray. We show that there is also a non-perturbative ambiguity inherent to certain neutral topological molecules (neutral bions and bion-anti-bions) in the semiclassical expansion. We find a set of "confluence equations" that encode the exact cancellation of the two different type of ambiguities. We show that a new notion of "graded resurgence triangle" is necessary to capture the path integral approach to resurgence, and that graded resurgence underlies a potentially rigorous definition of general QFTs. The mass gap and the Theta angle dependence of vacuum energy are calculated from first principles, and are in accord with large-N and lattice results.
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Renormalons can be understood as saddle points of the 1-loop effective action in toy models, enabled by the quantum scale anomaly.
Simulations of a partially reduced twisted Eguchi-Kawai model with one adjoint Dirac fermion show the Polyakov loop remains near zero for periodic boundary conditions as the compactified circle shrinks, supporting adiabatic continuity of the confined phase.
Instanton condensation in the matrix model for the BPS index reveals a new instability and dominant phase for small black holes, connected to partial deconfinement.
Presents explicit trans-series calculations for the double-well spectrum via exact WKB and path integral approaches up to four-instanton level.
citing papers explorer
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Which Saddles Contribute? The South-East Rule for Multidimensional Integrals
A geometric South-East rule combined with Borel-plane values and resurgence adjacency identifies contributing critical points for asymptotics of integrals e^{i k f(x)} over R^d without Picard-Lefschetz flows.
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Renormalons as Saddle Points
Renormalons can be understood as saddle points of the 1-loop effective action in toy models, enabled by the quantum scale anomaly.
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Adiabatic continuity in a partially reduced twisted Eguchi-Kawai model with one adjoint Dirac fermion
Simulations of a partially reduced twisted Eguchi-Kawai model with one adjoint Dirac fermion show the Polyakov loop remains near zero for periodic boundary conditions as the compactified circle shrinks, supporting adiabatic continuity of the confined phase.
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Instanton condensation and a new phase of BPS black holes
Instanton condensation in the matrix model for the BPS index reveals a new instability and dominant phase for small black holes, connected to partial deconfinement.
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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.