Stokes phenomena and non-perturbative completion in the multi-cut two-matrix models

Chan, Chuan-Tsung; Irie, Hirotaka; Yeh, Chi-Hsien

doi:10.1016/j.nuclphysb.2011.08.021

Cited by 16 publications

(55 citation statements)

References 139 publications

(271 reference statements)

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“…Obtaining explicit solutions to the algebra is a first nontrivial preparation for the Riemann-Hilbert (shortly RH) calculus, and some recent progress for general k and r can be found in [23,24]. Importantly, the Stokes matrices S m in Eq.…”

Section: Riemann-hilbert Problem For the Baker-akhiezer Functionsmentioning

confidence: 99%

“…In other words, this is just a matter of how divide the BA function Ψ(ζ) into Z(ζ) andφ(ζ). In this sense, the RH approach can be interpreted as an (off-shell) background independent formulation of string theory [23].…”

Section: Riemann-hilbert Problem For the Baker-akhiezer Functionsmentioning

confidence: 99%

“…, and this background also preserves Z p -symmetry in the sense of [23]. Here following the discussion [23], we use the same notation.…”

Section: Cases Of Minimal String Theorymentioning

confidence: 99%

“…Around the singularity ζ → ∞, there are 2rp Stokes matrices {S n } 2rp−1 n=0 of p × p, and their algebraic relations [20,23] are expressed as…”

Section: Cases Of Minimal String Theorymentioning

confidence: 99%

“…Then, for completion of the non-perturbative information in the asymptotic expansion, there are mainly studied two ways to control fugacity: one is resurgent analysis (e.g. [11][12][13][14]); and the other is isomonodromy analysis (for mathematical developments on isomonodromy theory [18][19][20]; and with matrix models [21][22][23][24]). The former is based on connection formula (or Stokes phenomena) for analytic continuation of g; and the latter is based on Stokes phenomena of the Baker-Akhiezer (shortly BA) functions on the spectral curves.…”

mentioning

confidence: 99%

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Analytic study for the string theory landscapes via matrix models

2012

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We demonstrate a first-principle analysis of the string theory landscapes in the framework of noncritical string/matrix models. In particular, we discuss non-perturbative instability, decay rate and the true vacuum of perturbative string theories. As a simple example, we argue that the perturbative string vacuum of pure gravity is stable; but that of Yang-Lee edge singularity is inescapably a false vacuum. Surprisingly, most of perturbative minimal string vacua are unstable, and their true vacuum mostly does not suffer from non-perturbative ambiguity. Importantly, we observe that the instability of these tachyon-less closed string theories is caused by ghost D-instantons (or ghost ZZ-branes), the existence of which is determined only by non-perturbative completion of string theory.

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Section: Riemann-hilbert Problem For the Baker-akhiezer Functionsmentioning

confidence: 99%

Section: Riemann-hilbert Problem For the Baker-akhiezer Functionsmentioning

confidence: 99%

“…, and this background also preserves Z p -symmetry in the sense of [23]. Here following the discussion [23], we use the same notation.…”

Section: Cases Of Minimal String Theorymentioning

confidence: 99%

“…Around the singularity ζ → ∞, there are 2rp Stokes matrices {S n } 2rp−1 n=0 of p × p, and their algebraic relations [20,23] are expressed as…”

Section: Cases Of Minimal String Theorymentioning

confidence: 99%

mentioning

confidence: 99%

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Analytic study for the string theory landscapes via matrix models

2012

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Structure of Lefschetz thimbles in simple fermionic systems

Kanazawa¹,

Tanizaki

2015

J. High Energ. Phys.

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The Picard-Lefschetz theory offers a promising tool to solve the sign problem in QCD and other field theories with complex path-integral weight. In this paper the Lefschetz-thimble approach is examined in simple fermionic models which share some features with QCD. In zero-dimensional versions of the Gross-Neveu model and the NambuJona-Lasinio model, we study the structure of Lefschetz thimbles and its variation across the chiral phase transition. We map out a phase diagram in the complex four-fermion coupling plane using a thimble decomposition of the path integral, and demonstrate an interesting link between anti-Stokes lines and Lee-Yang zeros. In the case of nonzero mass, it is shown that the approach to the chiral limit is singular because of intricate cancellation between competing thimbles, which implies the necessity to sum up multiple thimbles related by symmetry. We also consider a Chern-Simons theory with fermions in 0 + 1-dimension and show how Lefschetz thimbles solve the complex phase problem caused by a topological term. These prototypical examples would aid future application of this framework to bona fide QCD.

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

Kuroki

Sugino

2019

J. High Energ. Phys.

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In the previous papers, the authors pointed out correspondence between a supersymmetric double-well matrix model and two-dimensional type IIA superstring theory on a Ramond-Ramond background. This was confirmed by agreement between planar correlation functions in the matrix model and tree-level amplitudes in the superstring theory. Furthermore, in the matrix model we computed one-point functions of single-trace operators to all orders of genus expansion in its double scaling limit, and found that the large-order behavior of this expansion is stringy and not Borel summable. In this paper, we discuss resurgence structure of these one-point functions and see cancellations of ambiguities in their trans-series. More precisely, we compute both series of ambiguities arising in a zero-instanton sector and in a one-instanton sector, and confirm how they cancel each other. In case that the original integration contour is a finite interval not passing through a saddle point, we have to choose an appropriate integration path in order for resurgence to work.1 Resurgence structure has been studied in various models and theories based on several motivations: see e.g. in quantum mechanics [9][10][11][12][13][14][15][16][17][18][19][20][21], string theories [22][23][24] as well as quantum field theories .

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Stokes phenomena and non-perturbative completion in the multi-cut two-matrix models

Cited by 16 publications

References 139 publications

Analytic study for the string theory landscapes via matrix models

Analytic study for the string theory landscapes via matrix models

Structure of Lefschetz thimbles in simple fermionic systems

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

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