Related papers: On pq-duality and explicit solutions in $c \le 1$ …
We discuss the non--perturbative formulation for $c \leq 1$ string theory. The field theory like formulation of topological and non--topological models is presented. The integral representation for arbitrary $(p,q)$ solutions is derived…
A generalisation of the non--perturbatively stable solutions of string equations which respect the KdV flows, obtained recently for the $(2m-1,2)$ conformal minimal models coupled to two--dimensional quantum gravity, is presented for the…
Nonperturbative effects in c<1 noncritical string theory are studied using the two-matrix model. Such effects are known to have the form fixed by the string equations but the numerical coefficients have not been known so far. Using the…
We consider the canonical quantization scheme for $c \leq 1$ ($(p,q)$ -) string theories and compare it with what is known from matrix model approach. We derive explicitly a trivial ($\equiv $ topological) solution. We discuss a ``dressing"…
The main results for the two-dimensional quantum gravity, conjectured from the matrix model or integrable approach, are presented in the form to be compared with the world-sheet or Liouville approach. In spherical limit the integrable side…
We compute exact solutions of two--matrix models, i.e. detailed genus by genus expressions for the correlation functions of these theories, calculated without any approximation. We distinguish between two types of models, the unconstrained…
We consider a low energy effective theory of $p$-branes in a $D$-dimensional spacetime, and impose two conditions: 1) the theory is scale invariant, and 2) the electric-magnetic dual $(D-p-4)$-branes exist and they obey the same type of…
We construct two new classes of exact solutions to string theory which are not of the standard plane wave or gauged WZW type. Many of these solutions have curvature singularities. The first class includes the fundamental string solution,…
A 1-matrix model is proposed, which nicely interpolates between double-scaling continuum limits of all multimatrix models. The interpolating partition function is always a KP $\tau $-function and always obeys ${\cal L}_{-1}$-constraint and…
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,…
The strongest version of the gauge/gravity duality conjecture relates the 1/N correction in super Yang-Mills theory and the quantum correction in superstring theory. We perform a quantitative test of this conjecture at finite temperature,…
We discuss the large order behaviour and Borel summability of the topological expansion of models of 2D gravity coupled to general $(p,q)$ conformal matter. In a previous work it was proven that at large order $k$ the string susceptibility…
We discuss the interpertation of the $c=1$ matrix model as two-dimensional string theory in a dilaton-black hole background. The nonperturbative formulation of $c=1$ matrix model in terms of an integrable model of nonrelativistic fermions…
By a mapping to the bosonic string theory, we present an exact solution to the O(26) sigma model coupled to 2-D quantum gravity. In particular, we obtain the exact gravitational dressing to the various matter operators classified by the…
We study an implication of $p-q$ duality (spectral duality or T-duality) on non-perturbative completion of $(p,q)$ minimal string theory. According to the Eynard-Orantin topological recursion, spectral $p-q$ duality was already checked for…
Continuum and discrete approaches to 2d gravity coupled to $c<1$ matter are reviewed.
The string equation for the $[{\tilde P},Q]=Q$ formulation of non--perturbatively stable 2D quantum gravity coupled to the $(2m-1,2)$ models is studied. Global KdV flows between the appropriate solutions are considered as deformations of…
We review known exact classical solutions in (bosonic) string theory. The main classes of solutions are `cosets' (gauged WZW models), `plane wave'-type backgrounds (admitting a covariantly constant null Killing vector) and `$F$-models'…
We reformulate two dimensional string-inspired gravity with point particles as a gauge theory of the extended Poincar\'e group. A non-minimal gauge coupling is necessary for the equivalence of the two descriptions. The classical…
The set of solutions to the string equation $[P,Q]=1$ where $P$ and $Q$ are differential operators is described.It is shown that there exists one-to-one correspondence between this set and the set of pairs of commuting differential…