Resurgence of one-point functions in a matrix model for 2D type IIA superstrings

Kuroki, Tsunehide; Sugino, Fumihiko

doi:10.1007/jhep05(2019)138

Cited by 4 publications

(14 citation statements)

References 119 publications

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“…From these motivations, in the previous papers, we considered a supersymmetric double-well matrix model [97,98] and derived one-point functions at arbitrary genus [99]. Then we confirmed resurgence works for the one-point functions by calculating both their perturbative expansion and one-instanton contribution [100]. This model is proposed as nonperturbative formulation of type IIA superstring theory on a Ramond-Ramond background [101,102].…”

Section: Jhep07(2020)118mentioning

confidence: 52%

“…In this paper we extend the results in [99,100] and study resurgence structure of two-point functions of non-SUSY operators in our model under the double scaling limit. More precisely, we compute the two-point functions both at arbitrary genus and on the one-instanton background.…”

Section: Jhep07(2020)118mentioning

confidence: 54%

“…Then the problem is reduced to the one-point function by (5.10). However, as mentioned in [100], in the case of the one-point function,…”

Section: Application To Our Modelmentioning

confidence: 99%

“…In this section, we give a brief review of the supersymmetric double-well matrix model which has been proposed as a nonperturbative formulation of type IIA superstring theory in two dimensions. Definitions and notations are exactly the same as in [100]. Most of the review in this section overlaps with section 2 there.…”

Section: Review Of the Supersymmetric Matrix Modelmentioning

confidence: 99%

“…Extending the derivation in [99,100], we begin with the connected K-point function of the φ 2 -resolvent in the filling fraction (1, 0)…”

Section: φ 2 -Resolventmentioning

confidence: 99%

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Two-point functions at arbitrary genus and its resurgence structure in a matrix model for 2D type IIA superstrings

Kuroki

2020

J. High Energ. Phys.

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In the previous papers, it is pointed out that a supersymmetric double-well matrix model corresponds to a two-dimensional type IIA superstring theory on a Ramond-Ramond background at the level of correlation functions. This was confirmed by agreement between their planar correlation functions. The supersymmetry in the matrix model corresponds to the target space supersymmetry and it is shown to be spontaneously broken by nonperturbative effect. Furthermore, in the matrix model we computed one-point functions of single-trace operators to all order of genus expansion in its double scaling limit. We found that this expansion is stringy and not Borel summable and hence there arises an ambiguity in applying the Borel resummation technique. We confirmed that resurgence works here, namely this ambiguity in perturbative series in a zero-instanton sector is exactly canceled by another ambiguity in a one-instanton sector obtained by instanton calculation. In this paper we extend this analysis and study resurgence structure of the two-point functions of the single trace operators. By using results in the random matrix theory, we derive two-point functions at arbitrary genus and see that the perturbative series in the zero-instanton sector again has an ambiguity. We find that the two-point functions inevitably have logarithmic singularity even at higher genus. In this derivation we obtain a new result of the two-point function expressed by the one-point function at the leading order in the soft-edge scaling limit of the random matrix theory. We also compute an ambiguity in the one-instanton sector by using the Airy kernel, and confirm that ambiguities in both sectors cancel each other at the leading order in the double scaling limit. We thus clarify resurgence structure of the two-point functions in the supersymmetric double-well matrix model.

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Section: Jhep07(2020)118mentioning

confidence: 52%

Section: Jhep07(2020)118mentioning

confidence: 54%

“…Then the problem is reduced to the one-point function by (5.10). However, as mentioned in [100], in the case of the one-point function,…”

Section: Application To Our Modelmentioning

confidence: 99%

Section: Review Of the Supersymmetric Matrix Modelmentioning

confidence: 99%

“…Extending the derivation in [99,100], we begin with the connected K-point function of the φ 2 -resolvent in the filling fraction (1, 0)…”

Section: φ 2 -Resolventmentioning

confidence: 99%

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Two-point functions at arbitrary genus and its resurgence structure in a matrix model for 2D type IIA superstrings

Kuroki

2020

J. High Energ. Phys.

Self Cite

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Borel resummation of secular divergences in stochastic inflation

Honda

Jinno

Pinol

et al. 2023

J. High Energ. Phys.

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We make use of Borel resummation to extract the exact time dependence from the divergent series found in the context of stochastic inflation. Correlation functions of self-interacting scalar fields in de Sitter spacetime are known to develop secular IR divergences via loops, and the first terms of the divergent series have been consistently computed both with standard techniques for curved spacetime quantum field theory and within the framework of stochastic inflation. We show that Borel resummation can be used to interpret the divergent series and to correctly infer the time evolution of the correlation functions. In practice, we adopt a method called Borel-Padé resummation where we approximate the Borel transformation by a Padé approximant. We also discuss the singularity structures of Borel transformations and mention possible applications to cosmology.

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Quantum phase transition and resurgence: Lessons from three-dimensional $\mathcal{N}=4$ supersymmetric quantum electrodynamics

Fujimori

Honda

Kamata

et al. 2021

Progress of Theoretical and Experimental Physics

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We study a resurgence structure of a quantum field theory with a phase transition to uncover relations between resurgence and phase transitions. In particular, we focus on three-dimensional N = 4 supersymmetric quantum electrodynamics (SQED) with multiple hypermultiplets, where a second-order quantum phase transition has been recently proposed in the large-flavor limit. We provide interpretations of the phase transition from the viewpoints of Lefschetz thimbles and resurgence. For this purpose, we study the Lefschetz thimble structure and properties of the large-flavor expansion for the partition function obtained by the supersymmetric localization. We show that the second-order phase transition is understood as a phenomenon where a Stokes and anti-Stokes phenomenon occurs simultaneously. The order of the phase transition is determined by how saddles collide at the critical point. In addition, the phase transition accompanies an infinite number of Stokes phenomena due to the supersymmetry. These features are appropriately mapped to the Borel plane structures as the resurgence theory expects. Given the lessons from the SQED, we provide a more general discussion on the relationship between the resurgence and phase transitions. In particular, we show how the information on the phase transition is decoded from the Borel resummation technique.

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Resurgence of one-point functions in a matrix model for 2D type IIA superstrings

Cited by 4 publications

References 119 publications

Two-point functions at arbitrary genus and its resurgence structure in a matrix model for 2D type IIA superstrings

Two-point functions at arbitrary genus and its resurgence structure in a matrix model for 2D type IIA superstrings

Borel resummation of secular divergences in stochastic inflation

Quantum phase transition and resurgence: Lessons from three-dimensional $\mathcal{N}=4$ supersymmetric quantum electrodynamics

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