Related papers: Non-critical superstrings: a comparison between co…
These are the lectures notes of the course given at the Eleventh Modave Summer School in Mathematical Physics, 2015, aimed at PhD candidates and junior researchers in theoretical physics. We review in details the result of…
The super Virasoro minimal string is defined by coupling spacelike and timelike super Liouville theories on the worldsheet. There are four different theories 0A$^\pm$ and 0B$^\pm$ depending on discrete choices on the worldsheet. We show…
Motivated by the study of self gravitating cosmic strings, we pursue the well known method by C. Bandle to obtain a weak version of the classical Alexandrov's isoperimetric inequality. In fact we derive some quantitative estimates for weak…
The correlation functions for models of minimal gravity are discussed. An algorithm is proposed for calculations of invariant ratios from formulas of residues that can be compared with the coefficients of expansion of the partition function…
Liouville theorems for scaling invariant nonlinear elliptic systems (saying that the system does not possess nontrivial entire solutions) guarantee a priori estimates of solutions of related, more general systems. Assume that $p=2q+3>1$ is…
The tiny graviton matrix theory [hep-th/0406214] is proposed to describe DLCQ of type IIB string theory on the maximally supersymmetric plane-wave or AdS_5xS^5 background. In this paper we provide further evidence in support of the tiny…
We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a…
We consider type II string theory compactified on a symmetric T^6/Z_2 orientifold. We study a general class of discrete deformations of the resulting four-dimensional supergravity theory, including gaugings arising from geometric and…
Liouville theory is shown to describe the asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant. This is because (i) Chern-Simons theory with a gauge group $SL(2,R) \times SL(2,R)$ on a space-time…
We study the origins of the five ten-dimensional ``matrix superstring'' theories, supplementing old results with new ones, and find that they all fit into a unified framework. In all cases the matrix definition of the string in the limit of…
The theory of embedded random surfaces, equivalent to two--dimensional quantum gravity coupled to matter, is reviewed, further developed and partly generalized to four dimensions. It is shown that the action of the Liouville field theory…
Using the Chern-Simon formulation of (2+1) gravity, we derive, for the general asymptotic metrics given by the Fefferman-Graham-Lee theorems, the emergence of the Liouville mode associated to the boundary degrees of freedom of (2+1)…
We establish the first connection between $2d$ Liouville quantum gravity and natural dynamics of random matrices. In particular, we show that if $(U_t)$ is a Brownian motion on the unitary group at equilibrium, then the measures $$…
The concept of self-dual supersymmetric nonlinear electrodynamics is generalized to a curved superspace of N = 1 supergravity, for both the old minimal and the new minimal versions of N = 1 supergravity. We derive the self-duality equation,…
In a previous paper with Gibbons [CMP 120 (1987) 295] we derived a list of three dimensional symmetric space $\sigma$-model obtained by dimensional reduction of a class of four dimensional gravity theories with abelian gauge fields and…
We propose a duality between the complex Liouville string and a two-matrix integral. The complex Liouville string is defined by coupling two Liouville theories with complex central charges $c = 13 \pm i \lambda$ on the worldsheet. The…
We discuss the connection between Matrix string theory and the DLCQ of string theory. Using this connection we describe the sense in which perturbative string amplitudes are reproduced in the Matrix string theory. Using recent realization…
We propose that the double scaling behavior of the unitary matrix models, and that of the complex matrix models, is related to type 0B and 0A fermionic string theories. The particular backgrounds involved correspond to $\hat c<1 $ matter…
In a series of recent papers, a special kind of AdS$_2$/CFT$_1$ duality was observed: the boundary correlators of elementary fields that appear in the Lagrangian of a 2d conformal theory in rigid AdS$_2$ background are the same as the…
We prove symmetry and uniqueness results for three classes of Liouville-type problems arising in geometry and mathematical physics: asymmetric Sinh-Gordon equation, cosmic string equation and Toda system, under certain assumptions on the…