Non-perturbative large N trans-series for the Gross–Witten–Wadia beta function

Ahmed, Anees; Dunne, Gerald V.

doi:10.1016/j.physletb.2018.08.072

Cited by 10 publications

(19 citation statements)

References 41 publications

(103 reference statements)

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“…The resummation of a double series with variables " and n into a series with variables q and x is a problem in parametric resurgence. Parametric resurgence has been used in the Mathieu equation, in matrix models, and in other problems of mathematical physics; see [26,2,3]. In our case, the resurgence will be in the variable " (which upon resummation turns into q) and the role of parameter can be played either by n or x D e "n ; these should give the same answer.…”

Section: Resurgence For Knot Complementsmentioning

confidence: 93%

“…where the values " m are as in (3). By replacing q with q 1 and multiplying by the quantum integer OEn we obtain the unnormalized Jones polynomial for the mirror m.K/ D T .s; t /:…”

Section: Stability Seriesmentioning

confidence: 99%

“…This picture is related by S-duality to Witten's proposal from [91]; see [37,Section 2.10]. Furthermore, a similar set-up, in terms of BPS states, was used in [40] to describe Khovanov homology and HOMFLY-PT homology for knots in R 3 .…”

Section: Introductionmentioning

confidence: 99%

“…Conjecture 1.7. Let K S 3 be a knot, and S 3 p=r .K/ the result of Dehn surgery on K with coefficient p=r. Then, there exist " 2 ¹˙1º and d 2 Q such that…”

Section: Introductionmentioning

confidence: 99%

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A two-variable series for knot complements

2021

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The physical 3d N D 2 theory T OEY was previously used to predict the existence of some 3-manifold invariants y Z a .q/ that take the form of power series with integer coefficients, converging in the unit disk. Their radial limits at the roots of unity should recover the Witten-Reshetikhin-Turaev invariants. In this paper we discuss how, for complements of knots in S 3 , the analogue of the invariants y Z a .q/ should be a twovariable series F K .x; q/ obtained by parametric resurgence from the asymptotic expansion of the colored Jones polynomial. The terms in this series should satisfy a recurrence given by the quantum A-polynomial. Furthermore, there is a formula that relates F K .x; q/ to the invariants y Z a .q/ for Dehn surgeries on the knot. We provide explicit calculations of F K .x; q/ in the case of knots given by negative definite plumbings with an unframed vertex, such as torus knots. We also find numerically the first terms in the series for the figureeight knot, up to any desired order, and use this to understand y Z a .q/ for some hyperbolic 3-manifolds.

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Section: Resurgence For Knot Complementsmentioning

confidence: 93%

“…where the values " m are as in (3). By replacing q with q 1 and multiplying by the quantum integer OEn we obtain the unnormalized Jones polynomial for the mirror m.K/ D T .s; t /:…”

Section: Stability Seriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Conjecture 1.7. Let K S 3 be a knot, and S 3 p=r .K/ the result of Dehn surgery on K with coefficient p=r. Then, there exist " 2 ¹˙1º and d 2 Q such that…”

Section: Introductionmentioning

confidence: 99%

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A two-variable series for knot complements

2021

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“…In these two limits, the matrix model partition function is a tau function of Painlevé III', in the GWW case, or a tau function of Painlevé V for a generalization of (2.6) [2]. Among many other aspects, the connection with Painlevé is useful for resurgence computations [14,15].…”

Section: Jhep09(2020)081mentioning

confidence: 99%

Multiple phases in a generalized Gross-Witten-Wadia matrix model

Russo

Tierz

2020

J. High Energ. Phys.

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We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed Cauchy ensemble. Exact formulas for the partition function and Wilson loops are given in terms of Toeplitz determinants and minors and large N results are obtained by using Szegö theorem with a Fisher-Hartwig singularity. In the large N (planar) limit with two scaled couplings, the theory exhibits a surprisingly intricate phase structure in the two-dimensional parameter space.

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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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Non-perturbative large N trans-series for the Gross–Witten–Wadia beta function

Cited by 10 publications

References 41 publications

A two-variable series for knot complements

A two-variable series for knot complements

Multiple phases in a generalized Gross-Witten-Wadia matrix model

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

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