The spin one-point function in the critical Ising chain has a natural boundary of analyticity on the negative real axis after Borel resummation, with singularities matching those of an odd-divisor sum series.
Les Houches lectures on matrix models and topological strings
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abstract
In these lecture notes for the Les Houches School on Applications of Random Matrices in Physics we give an introduction to the connections between matrix models and topological strings. We first review some basic results of matrix model technology and then we focus on type B topological strings. We present the main results of Dijkgraaf and Vafa describing the spacetime string dynamics on certain Calabi-Yau backgrounds in terms of matrix models, and we emphasize the connection to geometric transitions and to large N gauge/string duality. We also use matrix model technology to analyze large N Chern-Simons theory and the Gopakumar-Vafa transition.
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Negative-tension ZZ-branes are required by resurgence to build complete transseries for minimal-string free energies, with analytic Stokes data and extensions to JT gravity and other string models.
The large-N limit of a QCD-inspired unitary matrix model admits analytic solutions for spectral density, Wilson loops, and free energy in the ungapped phase, reproducing low-T QCD, with a third-order phase transition at μ=0 and a continuous transition of at least second order at finite μ.
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Analyticity, asymptotics and natural boundary for a one-point function of the finite-volume critical Ising chain
The spin one-point function in the critical Ising chain has a natural boundary of analyticity on the negative real axis after Borel resummation, with singularities matching those of an odd-divisor sum series.
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All the D-Branes of Resurgence
Negative-tension ZZ-branes are required by resurgence to build complete transseries for minimal-string free energies, with analytic Stokes data and extensions to JT gravity and other string models.
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Large-$N$ Dynamics of a QCD-Inspired Unitary Matrix Model
The large-N limit of a QCD-inspired unitary matrix model admits analytic solutions for spectral density, Wilson loops, and free energy in the ungapped phase, reproducing low-T QCD, with a third-order phase transition at μ=0 and a continuous transition of at least second order at finite μ.