Related papers: c=1 Matrix Models: Equivalences and Open-Closed St…

We derive a Kontsevich-type matrix model for the c=1 string directly from the W-infinity solution of the theory. The model that we obtain is different from previous proposals, which are proven to be incorrect. Our matrix model contains the…

We show that the most general two--matrix model with bilinear coupling underlies $c=1$ string theory. More precisely we prove that $W_{1+\infty}$ constraints, a subset of the correlation functions and the integrable hierarchy characterizing…

This is a review of some beautiful matrix models related to the moduli space of Riemann surfaces as well as to noncritical c=1 string theory at self-dual radius. These include the Penner model and the W-infinity model, which have different…

It is generally accepted that the double-scaled 1D matrix model is equivalent to the $c=1$ string theory with tachyon condensation. There remain however puzzles that are to be clarified in order to utilize this connection for our quest…

We show that the $c=1$ bosonic string theory at finite temperature has two matrix-model realizations related by a kind of duality transformation. The first realization is the standard one given by the compactified matrix quantum mechanics…

We argue that topological matrix models (matrix models of the Kontsevich type) are examples of exact open/closed duality. The duality works at finite N and for generic `t Hooft couplings. We consider in detail the paradigm of the Kontsevich…

The same complex matrix model calculates both tachyon scattering for the c=1 non-critical string at the self-dual radius and certain correlation functions of half-BPS operators in N=4 super-Yang-Mills. It is dual to another complex matrix…

We propose a random matrix model as a representation for $D=1$ open strings. We show that the model is equivalent to $N$ fermions with spin in a central potential that also includes a long-range ferromagnetic interaction between the…

We sharpen the duality between open and closed topological string partition functions for topological gravity coupled to matter. The closed string partition function is a generalised Kontsevich matrix model in the large dimension limit. We…

We show that the 2-matrix string model corresponds to a coupled system of $2+1$-dimensional KP and modified KP ($\KPm$) integrable equations subject to a specific ``symmetry'' constraint. The latter together with the Miura-Konopelchenko map…

We study the perturbative $S$-matrix of the $c=1$ string and show that it admits a description in terms of a double-scaled (0+0)-dimensional matrix integral based on the spectral curve $\mathsf{x}(z) = 2\sqrt{2}\cos(z)$,…

We show the existence of a duality between the c-map space describing the universal hypermultiplet at tree level and the matrix model description of two-dimensional string theory compactified at a self-dual radius and perturbed by a…

For correlators in $\mathcal{N}=4$ Super Yang-Mills preserving half the supersymmetry, we manifestly recast the gauge theory Feynman diagram expansion as a sum over dual closed strings. Each individual Feynman diagram maps on to a Riemann…

String theory in two-dimensional spacetime illuminates two main threads of recent development in string theory: (1) Open/closed string duality, and (2) Tachyon condensation. In two dimensions, many aspects of these phenomena can be explored…

We propose a new interpretation of the c=1 matrix model as the world-line theory of N unstable D-particles, in which the hermitian matrix is provided by the non- abelian open string tachyon. For D-particles in 1+1-d string theory, we find a…

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 lay out an approach to derive the closed string dual to the simplest possible gauge theory, a single hermitian matrix integral, in the conventional 't Hooft large $N$ limit. In this first installment of three papers, we propose and…

The collective behavior of the SL(2,R) covariant brane states of non-critical c=1 string theory found in a previous work, is studied in the Fermi liquid approximation. It is found that such states mimick the coset WZW model, whereas only by…

The exact FZZT brane partition function for topological gravity with matter is computed using the dual two-matrix model. We show how the effective theory of open strings on a stack of FZZT branes is described by the generalized Kontsevich…

I present a short review of our results with S.Kharchev, A.Mironov, A.Morozov and A.Zabrodin on Generalized Kontsevich model which in a sense can be interpreted as unifying ``string field theory'' for $c < 1$ minimal series coupled to 2d…