相关论文: Instantons and Merons in Matrix Models
Differential reformulations of field theories are often used for explicit computations. We derive a one-matrix differential formulation of two-matrix models, with the help of which it is possible to diagonalize the one- and two-matrix…
We review some relations occurring between the combinatorial intersection theory on the moduli spaces of stable curves and the asymptotic behavior of the 't Hooft-Kontsevich matrix integrals. In particular, we give an alternative proof of…
A new combinatorial object is introduced, the part-frequency matrix sequence of a partition, which is elementary to describe and is naturally motivated by Glaisher's bijection. We prove results that suggest surprising usefulness for such a…
We construct type $g\ell(n)$ Yangian algebra evaluations of order $N$ embedded in Heisenberg algebras and consider their representations having a highest weight. These Yangian algebra presentations depend on $nN$ parameters. We construct…
We construct a matrix model that reproduces the topological string partition function on arbitrary toric Calabi-Yau 3-folds. This demonstrates, in accord with the BKMP "remodeling the B-model" conjecture, that Gromov-Witten invariants of…
We describe the moduli space of SU(N) instantons in the presence of a general surface operator of type N=n_1+ ... +n_M in terms of the representations of the so-called chain-saw quiver, which allows us to write down the instanton partition…
M-theoretic construction of N=2 gauge theories implies that the instanton partition function is expressed as the scalar product of coherent states (Whittaker states) in the Verma module of an appropriate two dimensional conformal field…
The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such…
The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…
The role of integrable systems in string theory is discussed. We remind old examples of the correspondence between stringy partition functions or effective actions and integrable equations, based on effective application of the matrix model…
In the conformal field theories given by the Ising and Dirac models, when the system is in the ground state, the moments of the reduced density matrix of two disjoint intervals and of its partial transpose have been written as partition…
We study a matrix model obtained by dimensionally reducing Chern-Simon theory on S^3. We find that the matrix integration is decomposed into sectors classified by the representation of SU(2). We show that the N-block sectors reproduce SU(N)…
Partition of unities appear in many places in analysis. Typically they are generated by compactly supported functions with a certain regularity. In this paper we consider partition of unities obtained as integer-translates of entire…
A unitary matrix model is proposed as the large-N matrix formulation of M theory on flat space with toroidal topology. The model reproduces the motion of elementary D-particles on the compact space, and admits membrane states with nonzero…
AGT relations imply that the four-point conformal block admits a decomposition into a sum over pairs of Young diagrams of essentially rational Nekrasov functions - this is immediately seen when conformal block is represented in the form of…
We characterize all real matrix semigroups satisfying a mild boundedness assumption, without assuming continuity. Besides the continuous solutions of the semigroup functional equation, we give a description of solutions arising from…
This paper intends to lay the theoretical foundation for the method of functional maps, first presented in 2012 by Ovsjanikov, Ben-Chen, Solomon, Butscher and Guibas in the field of the theory and numerics of maps between shapes. We show…
In this paper, we consider an extended Kazakov-Migdal model defined on an arbitrary graph. The partition function of the model, which is expressed as the summation of all Wilson loops on the graph, turns out to be represented by the…
Given an associative multiplication in matrix algebra compatible with the usual one or, in other words, linear deformation of matrix algebra, we construct a solution to the classical Yang-Baxter equation. We also develop a theory of such…
We compute the decomposition of representations of Yangians into g-modules for simply-laced Lie algebras g. The decomposition has an interesting combinatorial tree structure. Results depend on a conjecture of Kirillov and Reshetikhin.