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Register a new userMultiple phases in a generalized Gross-Witten-Wadia matrix model
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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 Szego 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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We study Yang-Baxter deformations of the Nappi-Witten model with a prescription invented by Delduc, Magro and Vicedo. The deformations are specified by skew-symmetric classical $r$-matrices satisfying (modified) classical Yang-Baxter equations. We show that the sigma-model metric is invariant under arbitrary deformations (while the coefficient of $B$-field is changed) by utilizing the most general classical $r$-matrix. Furthermore, the coefficient of $B$-field is determined to be the original value from the requirement that the one-loop $beta$-function should vanish. After all, the Nappi-Witten model is the unique conformal theory within the class of the Yang-Baxter deformations preserving the conformal invariance.
New finite energy traveling wave solutions with small speed are constructed for the three dimensional Gross-Pitaevskii equation begin{equation*} iPsi_t= Delta Psi+(1-|Psi|^2)Psi, end{equation*} where $Psi$ is a complex valued function defined on ${mathbb R}^3times{mathbb R}$. These solutions have the shape of $2n+1$ vortex rings, far away from each other. Among these vortex rings, $n+1$ of them have positive orientation and the other $n$ of them have negative orientation. The location of these rings are described by the roots of a sequence of polynomials with rational coefficients. The polynomials found here can be regarded as a generalization of the classical Adler-Moser polynomials and can be expressed as the Wronskian of certain very special functions. The techniques used in the derivation of these polynomials should have independent interest.
We introduce a log-gas model that is a generalization of a random matrix ensemble with an additional interaction, whose strength depends on a parameter $gamma$. The equilibrium density is computed by numerically solving the Riemann-Hilbert problem associated with the ensemble. The effect of the additional parameter $gamma$ associated with the two-body interaction can be understood in terms of an effective $gamma$-dependent single-particle confining potential.
We give a pedagogical review of the computation of Gromov-Witten invariants via localization in 2D gauged linear sigma models. We explain the relationship between the two-sphere partition function of the theory and the Kahler potential on the conformal manifold. We show how the Kahler potential can be assembled from classical, perturbative, and non-perturbative contributions, and explain how the non-perturbative contributions are related to the Gromov-Witten invariants of the corresponding Calabi-Yau manifold. We then explain how localization enables efficient calculation of the two-sphere partition function and, ultimately, the Gromov-Witten invariants themselves.
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.
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