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

Abstract

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.

arXiv comment50 pages, 4 figures, typos corrected

References in corpus (82)

• Level-Spacing Distributions and the Airy Kernel
• Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
• Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
• Open string amplitudes and large order behavior in topological string theory
• A Primer on Resurgent Transseries and Their Asymptotics
• An Introduction to Resurgence, Trans-Series and Alien Calculus
• The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
• Multi-Instantons and Exact Results I: Conjectures, WKB Expansions, and Instanton Interactions
• Uniform WKB, Multi-instantons, and Resurgent Trans-Series
• Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c=1 Matrix Models
• A semiclassical realization of infrared renormalons
• Nonperturbative Ambiguities and the Reality of Resurgent Transseries
• Non-Perturbative Effects in Matrix Models and Vacua of Two Dimensional Gravity
• Continuity and Resurgence: towards a continuum definition of the CP(N-1) model
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• Resurgence in QFT: Unitons, Fractons and Renormalons in the Principal Chiral Model
• Resurgence theory, ghost-instantons, and analytic continuation of path integrals
• Multi-Instantons and Exact Results II: Specific Cases, Higher-Order Effects, and Numerical Calculations
• New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence
• Asymptotics of the instantons of Painleve I
• Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2
• Multi-Instantons and Exact Results III: Unified Description of the Resonances of Even and Odd Anharmonic Oscillators
• Complexified path integrals, exact saddles and supersymmetry
• A note on perturbation series in supersymmetric gauge theories
• The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painleve II Equation
• Hidden topological angles and Lefschetz thimbles
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• Toward Picard-Lefschetz Theory of Path Integrals, Complex Saddles and Resurgence
• Cheshire Cat resurgence, Self-resurgence and Quasi-Exact Solvable Systems
• Multi-Instantons and Multi-Cuts
• Deconstructing zero: resurgence, supersymmetry and complex saddles
• Non-perturbative Contributions from Complexified Solutions in $\mathbb{C}{P}^{N-1}$ Models
• Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
• From 4d Yang-Mills to 2d ${\mathbb{CP}}^{N-1}$ model: IR problem and confinement at weak coupling
• Resumming the string perturbation series
• Loops versus Matrices - The nonperturbative aspects of noncritical string
• Resurgence in sine-Gordon quantum mechanics: Exact agreement between multi-instantons and uniform WKB
• The Power of Perturbation Theory
• Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
• Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}{P}^{N-1}$ models
• Complex Saddles in Two-dimensional Gauge Theory
• Resurgent Extrapolation: Rebuilding a Function from Asymptotic Data. Painleve I
• Exact Resurgent Trans-series and Multi-Bion Contributions to All Orders
• The grin of Cheshire cat resurgence from supersymmetric localization
• Borel summability of perturbative series in 4d N=2 and 5d N=1 theories
• Resurgence of the Cusp Anomalous Dimension
• Resurgence in $\eta$-deformed Principal Chiral Models
• Resurgence Matches Quantization
• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• The Resurgence of the Cusp Anomalous Dimension
• IR Renormalons vs. Operator Product Expansion in Supersymmetric and Related Gauge Theories
• Remark on the Dunne-Unsal relation in exact semi-classics
• Three-loop Correction to the Instanton Density. I. The Quartic Double Well Potential
• How to resum perturbative series in 3d N=2 Chern-Simons matter theories
• A new method to sum divergent power series: educated match
• Non-BPS exact solutions and their relation to bions in $\mathbb{C}{P}^{N-1}$ models
• Resurgence Structure to All Orders of Multi-bions in Deformed SUSY Quantum Mechanics
• Three-loop Correction to the Instanton Density. II. The Sine-Gordon potential
• Critical Points at Infinity, Non-Gaussian Saddles, and Bions
• Fractional instantons and bions in the principal chiral model on ${\mathbb{R}}^2\times S^1$ with twisted boundary conditions
• Instantons from Perturbation Theory
• Universality of Nonperturbative Effect in Type 0 String Theory
• Resurgence of the dressing phase for ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$
• On the Chemical Potential of D-instantons in c=0 Noncritical String Theory
• Neutral bions in the CP^{N-1} model for resurgence
• S-duality resurgence in SL(2) Chern-Simons theory
• Spontaneous supersymmetry breaking in matrix models from the viewpoints of localization and Nicolai mapping
• Spontaneous supersymmetry breaking in large-$N$ matrix models with slowly varying potential
• Universality of Nonperturbative Effects in c<1 Noncritical String Theory
• Stokes Phenomena and Non-perturbative Completion in the Multi-cut Two-matrix Models
• Stokes Phenomena and Quantum Integrability in Non-critical String/M Theory
• Convergence from Divergence
• Resurgence, Painleve Equations and Conformal Blocks
• T-duality of ZZ-brane
• SUSY breaking by nonperturbative dynamics in a matrix model for 2D type IIA superstrings
• Tracy-Widom distribution as instanton sum of 2D IIA superstrings
• New critical behavior in a supersymmetric double-well matrix model
• Resurgence and Lefschetz thimble in 3d N=2 supersymmetric Chern-Simons matter theories
• Supersymmetric double-well matrix model as two-dimensional type IIA superstring on RR background
• Non-Perturbative Large N Trans-series for the Gross-Witten-Wadia Beta Function
• One-point functions of non-SUSY operators at arbitrary genus in a matrix model for type IIA superstrings
• Resurgence of one-point functions in a matrix model for 2D type IIA superstrings

Cited by in corpus (2)

• Resurgence in Lorentzian quantum cosmology: No-boundary saddles and resummation of quantum gravity corrections around tunneling saddle points
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED