The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painlevé II Equation

Schiappa, Ricardo; Vaz, Ricardo Zambarda

doi:10.1007/s00220-014-2028-7

Cited by 63 publications

(134 citation statements)

References 108 publications

Supporting

Mentioning

129

Contrasting

Order By: Relevance

“…For the case of the topological-string free energy, the general construction of its resurgent transseries-out of a nonperturbative extension of the holomorphic anomaly equations-was set-up in [4]; with the explicit example of the local P 2 toric Calabi-Yau threefold being fully worked out in [5]. These results were obtained based upon earlier stringy constructions [6][7][8][9][10][11][12][13][14][15], and have since led to a few further developments, e.g., [16,17]. In principle, this construction allows us to obtain fully nonperturbative results for the string-theoretic free energy, at any value of the string coupling constant.…”

Section: Introductionmentioning

confidence: 99%

Resurgence matches quantization

Couso-Santamaría¹,

Mariño²,

Schiappa³

2017

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

Abstract:The quest to find a nonperturbative formulation of topological string theory has recently seen two unrelated developments. On the one hand, via quantization of the mirror curve associated to a toric Calabi-Yau background, it has been possible to give a nonperturbative definition of the topological-string partition function. On the other hand, using techniques of resurgence and transseries, it has been possible to extend the string (asymptotic) perturbative expansion into a transseries involving nonperturbative instanton sectors. Within the specific example of the local P 2 toric Calabi-Yau threefold, the present work shows how the Borel-Padé-Ecalle resummation of this resurgent transseries, alongside occurrence of Stokes phenomenon, matches the string-theoretic partition function obtained via quantization of the mirror curve. This match is highly non-trivial, given the unrelated nature of both nonperturbative frameworks, signaling at the existence of a consistent underlying structure.

show abstract

Section: Introductionmentioning

confidence: 99%

Resurgence matches quantization

Couso-Santamaría¹,

Mariño²,

Schiappa³

2017

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

show abstract

“…there is no phase transition any longer in the double scaling limit. 7 That issue is discussed in the context of trans-series and resurgence in [35,36]. 8 • In the double scaling limit of our model, aspects of nonperturbative SUSY breaking for the region s > 0 carry over to the region s < 0 where SUSY is broken at the classical level.…”

Section: Jhep09(2014)104mentioning

confidence: 98%

“…It would be interesting to understand the difference from the point of view of resurgence. As discussed in [36], two-parameter trans-series would play a central role in order to perform such a resurgent analysis, which could give an insight into the global structure of the free energy for a complex variable s.…”

Section: Jhep09(2014)104mentioning

confidence: 99%

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

Nishigaki

Sugino

2014

J. High Energ. Phys.

View full text Add to dashboard Cite

We present an analytic expression of the nonperturbative free energy of a double-well supersymmetric matrix model in its double scaling limit, which corresponds to two-dimensional type IIA superstring theory on a nontrivial Ramond-Ramond background. To this end we draw upon the wisdom of random matrix theory developed by Tracy and Widom, which expresses the largest eigenvalue distribution of unitary ensembles in terms of a Painlevé II transcendent. Regularity of the result at any value of the string coupling constant shows that the third-order phase transition between a supersymmetry-preserving phase and a supersymmetry-broken phase, previously found at the planar level, becomes a smooth crossover in the double scaling limit. Accordingly, the supersymmetry is always broken spontaneously as its order parameter stays nonzero for the whole region of the coupling constant. Coincidence of the result with the unitary one-matrix model suggests that one-dimensional type 0 string theories partially correspond to the type IIA superstring theory. Our formulation naturally allows for introduction of an instanton chemical potential, and reveals the presence of a novel phase transition, possibly interpreted as condensation of instantons.

show abstract

“…Adding to it are results for the free energy in minimal (super)string theory [ASVo12,SchiVa14] and topological string theory [CESVo15,CESVo16], for which transseries ansätze proved viable. Furthermore, we mention the results for the transseries representations of the cusp anomalous dimension in N = 4 SUSY Yang-Mills theory which have been explored in [An15,DoH15].…”

Section: Analysable Functions and Resurgent Transseriesmentioning

confidence: 99%

Resurgent transseries & Dyson–Schwinger equations

Klaczynski

2016

Annals of Physics

View full text Add to dashboard Cite

Abstract. We employ resurgent transseries as algebraic tools to investigate two self-consistent Dyson-Schwinger equations, one in Yukawa theory and one in quantum electrodynamics. After a brief but pedagogical review, we derive fixed point equations for the associated anomalous dimensions and insert a moderately generic log-free transseries ansatz to study the possible strictures imposed. While proceeding in various stages, we develop an algebraic method to keep track of the transseries' coefficients. We explore what conditions must be violated in order to stay clear of fixed point theorems to eschew a unique solution, if so desired, as we explain. An interesting finding is that the flow of data between the different sectors of the transseries shows a pattern typical of resurgence, ie the phenomenon that the perturbative sector of the transseries talks to the nonperturbative ones in a one-way fashion. However, our ansatz is not exotic enough as it leads to trivial solutions with vanishing nonperturbative sectors, even when logarithmic monomials are included. We see our result as a harbinger of what future work might reveal about the transseries representations of observables in fully renormalised four-dimensional quantum field theories and adduce a tentative yet to our mind weighty argument as to why one should not expect otherwise.This paper is considerably self-contained. Readers with little prior knowledge are let in on the basic reasons why perturbative series in quantum field theory eventually require an upgrade to transseries. Furthermore, in order to acquaint the reader with the language utilised extensively in this work, we also provide a concise mathematical introduction to grid-based transseries.

show abstract

The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painlevé II Equation

Cited by 63 publications

References 108 publications

Resurgence matches quantization

Resurgence matches quantization

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

Resurgent transseries & Dyson–Schwinger equations

Contact Info

Product

Resources

About