Resurgence theory, ghost-instantons, and analytic continuation of path integrals

Abstract

A general quantum mechanical or quantum field theoretical system in the path integral formulation has both real and complex saddles (instantons and ghost-instantons). Resurgent asymptotic analysis implies that both types of saddles contribute to physical observables, even if the complex saddles are not on the integration path i.e., the associated Stokes multipliers are zero. We show explicitly that instanton-anti-instanton and ghost-antighost saddles both affect the expansion around the perturbative vacuum. We study a self-dual model in which the analytic continuation of the partition function to negative values of coupling constant gives a pathological exponential growth, but a homotopically independent combination of integration cycles (Lefschetz thimbles) results in a sensible theory. These two choices of the integration cycles are tied with a quantum phase transition. The general set of ideas in our construction may provide new insights into non-perturbative QFT, string theory, quantum gravity, and the theory of quantum phase transitions.

Tracy-Widom distribution as instanton sum of 2D IIA superstrings

“…7 The same result is obtained in a continuum formulation of the gauge theory [33,34]. 8 Methods of trans-series and resurgence have been recently investigated in matrix models [37][38][39][40] and in quantum field theory [41][42][43][44].…”

Neutral bions in the ℂ $$ \mathbb{C} $$ P N −1 model

“…In order to reach deeper understanding on bions and the associated physics, it is of great importance to study examples in the low-dimensional models such as CP N −1 models [12][13][14], principal chiral models [16,19] and quantum mechanics [15,17,18]. In particular, the CP N −1 model in 1+1 dimensions has been studied for a long time as a toy model of the Yang-Mills theory in 3+1 dimensions [48], because of similarities between them such as dynamical mass gap, asymptotic freedom and the existence of instantons [49].…”

“…It is stressed byÜnsal and his collaborators that these configurations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], which are termed "bions", have two physical significances associated with two types of topologically trivial bion configurations called "magnetic (charged) bions" and "neutral bions", as seen in the following examples: in the weak-coupling regime (L ≪ 1/Λ QCD ) in QCD(adj.) on R 3 × S 1 , or in the U(1) N −1 center-symmetric phase [20][21][22][23][24][25][26][27][28][29], condensation of magnetic bions (zero topological charge and nonzero magnetic charge) causes the confinement [3][4][5][6][7][8][9].…”

“…This argument is also of importance in terms of the recent progress in large-N volume reduction [30][31][32][33][34][35][36][37][38][39][40]. On the other side, neutral bions (zero topological charge and zero magnetic charge) can be identified as the infrared renormalon [10][11][12][13][14][15][16][17][18][19][41][42][43]. Here imaginary ambiguities arising in bion's amplitude and those arising in non-Borelsummable perturbative series cancel against each other, and it is expected that full semiclassical expansion including perturbative and non-perturbative sectors, which is called "resurgent" expansion [44], leads to unambiguous and self-consistent definition of field theories in the same manner as the Bogomolny-Zinn-Justin (BZJ) prescription in quantum mechanics [45][46][47].…”

Deconfinement in $ \mathcal{N}=1 $ super Yang-Mills theory on $ {{\mathbb{R}}^3}\times {{\mathbb{S}}^1} $ via dual-Coulomb gas and “affine” XY-model

“…A recent example is the argument that they are relevant to studies of the thermal deconfinement phase transition in pure YM theory, via the idea of "continuity". 2 Further, magnetic bions have been shown to be crucial for understanding the 1 The ongoing studies of "resurgence"-a generalization of Borel resummation-in field theories in various dimensions are shedding further light on the role of these molecules and other path integral saddle points, showing a fascinating interplay between perturbative and nonperturbative contributions at weak coupling (this is a currently active area of research, see, e.g., the recent work [17][18][19][20][21] and references therein).…”