arXiv subjects

Nikolai Reshetikhin

Publications and source records attributed to Nikolai Reshetikhin.

5 recordsLinked to original sources

arXiv2003

Quantum Calabi-Yau and Classical Crystals

We propose a new duality involving topological strings in the limit of large string coupling constant. The dual is described in terms of a classical statistical mechanical model of crystal melting, where the temperature is inverse of the string coupling constant. The crystal is a discretization of the toric base of the Calabi-Yau with lattice length $g_s$. As a strong evidence for this duality we recover the topological vertex in terms of the statistical mechanical probability distribution for crystal melting. We also propose a more general duality involving the dimer problem on periodic lattices and topological A-model string on arbitrary local toric threefolds. The $(p,q)$ 5-brane web, dual to Calabi-Yau, gets identified with the transition regions of rigid dimer configurations.

hep-th↗

arXiv2003

Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram

Schur process is a time-dependent analog of the Schur measure on partitions studied in math.RT/9907127. Our first result is that the correlation functions of the Schur process are determinants with a kernel that has a nice contour integral representation in terms of the parameters of the process. This general result is then applied to a particular specialization of the Schur process, namely to random 3-dimensional Young diagrams. The local geometry of a large random 3-dimensional diagram is described in terms of a determinantal point process on a 2-dimensional lattice with the incomplete beta function kernel (which generalizes the discrete sine kernel). A brief discussion of the universality of this answer concludes the paper.

math.CO↗

arXiv1997

Towards Deformed Chiral Algebras

We describe a new algebraic structure of "deformed chiral algebra" motivated by the study of the deformed W-algebras. We use it to gain some insights into the deformed Virasoro algebra.

q-alg↗

arXiv1995

Quantum Affine Algebras and Deformations of the Virasoro and W-algebras

We generalize some results concerning affine algebras at the critical level to the corresponding quantum algebras. In particular, we show that the Wakimoto realization provides a homomorphism of Poisson algebras from the center of a quantum affine algebra to a Heisenberg-Poisson algebra. This homomorphism is a q-deformation of the Miura transformation. It is given by the same formulas as the spectra of transfer-matrices of the corresponding quantum integrable models. The image of the center in the Heisenberg-Poisson algebra is a Poisson subalgebra of the latter, which is a q-deformation of the corresponding classical W-algebra. The relations in this Poisson algebra are explicitly computed in the case of sl(n)^.

q-alg↗

arXiv1994

Gaudin Model, Bethe Ansatz and Critical Level

We propose a new method of diagonalization of hamiltonians of the Gaudin model associated to an arbitrary simple Lie algebra, which is based on Wakimoto modules over affine algebras at the critical level. We construct eigenvectors of these hamiltonians by restricting certain invariant functionals on tensor products of Wakimoto modules. In conformal field theory language, the eigenvectors are given by certain bosonic correlation functions. Analogues of Bethe ansatz equations naturally appear as Kac-Kazhdan type equations on the existence of certain singular vectors in Wakimoto modules. We use this construction to expalain a connection between Gaudin's model and correlation functions of WZNW models.

hep-th↗