Related papers: Quantization of string theory for $c \leq 1$

In recent years there has been considerable interest in theories over string equations, length function, and string-number conversion predicate within the formal verification, software engineering, and security communities. SMT solvers for…

We propose that the grand canonical topological string partition functions satisfy finite-difference equations in the closed string moduli. In the case of genus one mirror curve these are conjectured to be the q-difference Painlev\'e…

We find the precise relationship between the loop gas method and the matrix quantum mechanics approach to two-dimensional string theory. The two systems are distinguished by different target spaces ($\Z$ and $\R$, respectively) as far as…

We compute L\"uscher corrections to the effective string tension in the Pilch-Warner background, holographically dual to $\mathcal{N}=2^*$ supersymmetric Yang-Mills theory. The same quantity can be calculated directly from field theory by…

String theory is the most promising candidate for the theory unifying all interactions including gravity. It has an extremely difficult dynamics. Therefore, it is useful to study some its simplifications. One of them is non-critical string…

We develop further a new geometrical model of a discretized string, proposed in [1] and establish its basic physical properties. The model can be considered as the natural extention of the usual Feynman amplitude of the random walks to…

The Toda lattice hierarchy is discussed in connection with the topological description of the $c=1$ string theory compactified at the self-dual radius. It is shown that when special constraints are imposed on the Toda hierarchy, it…

Beginning with a review of the arguments leading to the so-called c=1 barrier in the continuum formulation of noncritical string theory, the pathology is then exhibited in a discretized version of the theory, formulated through dynamical…

We give an explicit demonstration of the equivalence between the Normal Matrix Model (NMM) of c=1 string theory at selfdual radius and the Kontsevich-Penner (KP) model for the same string theory. We relate macroscopic loop expectation…

We study the CPT theorem for a two-dimensional conformal field theory on an arbitrary Riemann surface. On the sphere the theorem follows from the assumption that the correlation functions have standard hermiticity properties and are…

We formulate and solve a class of two-dimensional matrix gauge models describing ensembles of non-folding surfaces covering an oriented, discretized, two-dimensional manifold. We interpret the models as string theories characterized by a…

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,…

We present a string theory realization for the correspondence between quantum integrable models and supersymmetric gauge theories. The quantization results from summing the effects of fundamental strings winding around a compact direction.…

Is string theory uniquely determined by self-consistency? Causality and unitarity seemingly permit a multitude of putative deformations, at least at the level of two-to-two scattering. Motivated by this question, we initiate a systematic…

We construct a string field theory for c=1 noncritical strings using the loop variables as the string field. We show how one can express the nonrelativistic free fermions which describes the theory, in terms of these string fields.

A few observations concerning topological string theories at the string-tree level are presented: (1) The tree-level, large phase space solution of an arbitrary model is expressed in terms of a variational problem, with an ``action'' equal,…

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…

Sequence theories are an extension of theories of strings with an infinite alphabet of letters, together with a corresponding alphabet theory (e.g. linear integer arithmetic). Sequences are natural abstractions of extendable arrays, which…

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 consider some questions of naturalness which arise when one considers conventional field theories in the presence of gravitation: the problem of global symmetries, the strong CP problem, and the cosmological constant problem. Using…