Related papers: Two-Matrix String Model as Constrained (2+1)-Dimen…
The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Discrete 1-matrix, 2-matrix, ``conformal'' (multicomponent) and Kontsevich models are considered in some detail, together with the…
String equations of the $p$-th generalized Kontsevich model and the compactified $c = 1$ string theory are re-examined in the language of the Toda lattice hierarchy. As opposed to a hypothesis postulated in the literature, the generalized…
We consider a new 3-parameter class of exact 4-dimensional solutions in closed string theory and solve the corresponding string model, determining the physical spectrum and the partition function. The background fields (4-metric,…
The recent developments in string theory suggest that the space-time coordinates should be generalized to non-commuting matrices. Postulating this suggestion as the fundamental geometrical principle, we formulate a candidate for covariant…
We investigate self-similar solutions of the extended discrete KP hierarchy. It is shown that corresponding ansatzes lead to purely discrete equations with dependence on some number of parameters together with equations governing…
We study the structure of the normal matrix model (NMM). We show that all correlation functions of the model with axially symmetric potentials can be expressed in terms of holomorphic functions of one variable. This observation is used to…
Recently, Arutyunov, Bassi and Lacroix have shown that 2D non-linear sigma model with a deformed $T^{1,1}$ background is classically integrable [arXiv:2010.05573 [hep-th]]. This background includes a Kalb-Ramond two-form with a critical…
We discuss different formulations and approaches to string theory and $ 2d$ quantum gravity. The generic idea to get a unique description of {\it many} different string vacua altogether is demonstrated on the examples in $ 2d$ conformal,…
In this paper a list of $R$-matrices on a certain coupled Lie algebra is obtained. With one of these $R$-matrices, we construct infinitely many bi-Hamiltonian structures for each of the two-component BKP and the Toda lattice hierarchies. We…
We consider the $(2+1)$-d $SU(2)$ quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the Kagom\'e lattice. The model has crystalline confined phases with spontaneously broken translation…
A direct relation between the conformal formalism for 2d-quantum gravity and the W-constrained KP hierarchy is found, without the need to invoke intermediate matrix model technology. The Kontsevich-Miwa transform of the KP hierarchy is used…
We study the relation between topological string theory and singularity theory using the partition function of $A_{N-1}$ topological string defined by matrix integral of Kontsevich type. Genus expansion of the free energy is considered, and…
(Lecture at the workshop "Basic Problems in String Theory", Yukawa Institute for Theoretical Physics, Kyoto, October 19-21) In this talk, we first review the possibility of matrix models toward a nonperturbative (critical) string theory. We…
We formulate matrix models for strings in ten dimensional pp-wave backgrounds and for particles in eleven dimensional ones. This is done by first characterizing the deformations of ten dimensional {\cal N}=1 SYM which are induced by a…
We show how the two--matrix model and Toda lattice hierarchy presented in a previous paper can be solved exactly: we obtain compact formulas for correlators of pure tachyonic states at every genus. We then extend the model to incorporate a…
We extend the system of ungauged N=2, d=4 supergravity coupled to vector multiplets and hypermultiplets with 2-form potentials. The maximal number of 2-form potentials that one may introduce is equal to the number of isometries of either…
Given a super-integrable system in $n$ degrees of freedom, possessing an integral which is linear in momenta, we use the "Kaluza-Klein construction" in reverse to reduce to a lower dimensional super-integrable system. We give two examples…
I investigate the Kazakov-Migdal (KM) model -- the Hermitean gauge-invariant matrix model on a D-dimensional lattice. I utilize an exact large-N solution of the KM model with a logarithmic potential to examine its critical behavior. I find…
We study the large $N$ limit of an interacting \td\ matrix field theory, whose perturbative expansion generates the sum over planar random graphs embedded in two dimensions. In the \lc\ quantization the theory possesses closed string…
We construct the Generalized Monodromy matrix $\mathcal{\hat{M}}(\omega)$ of two dimensional string effective action by introducing the T-duality group properties.The integrability conditions with general solutions depending on spectral…