相关论文: Chiral Rings and Integrable Systems for Models of …
Talk given at the 26th Workshop: ``From Superstrings to Supergravity", Erice - Sicily, 5-12 December 1992. We review the superconformal properties of 2d matter coupled to gravity, and extensions thereof. Focusing on topological strings, we…
We investigate the algebraic structure of integrable hierarchies that, we propose, underlie models of $W$-gravity coupled to matter. More precisely, we concentrate on the dispersionless limit of the topological subclass of such theories, by…
We show that almost all string theories, including the bosonic string, the superstring and $W$-string theories, possess a twisted N=2 superconformal symmetry. This enables us to establish a connection between topological gravity and the…
A review of the appearence of integrable structures in the matrix model description of $2d$-gravity is presented. Most of ideas are demonstrated at the technically simple but ideologically important examples. Matrix models are considered as…
A $D>2$ topological string is presented by coupling the $2d$ topological gravity with the twisted version of the $N=2$ superconformal matter with $c=3k/(k-2)$. The latter is shown to admit $k+1$ chiral primary fields from the…
We study the equivariant cohomology of a class of multi-field topological LG models, and find that such systems carry intrinsic information about $W$-gravity. As a result, we can construct the gravitational chiral ring in terms of LG…
We review recent progress in 2D gravity coupled to $d<1$ conformal matter, based on a representation of discrete gravity in terms of random matrices. We discuss the saddle point approximation for these models, including a class of related…
The tree-level S-matrix of type II supergravity can be computed in scattering equation form by correlators in a worldsheet theory analogous to a chiral, infinite tension limit of the pure spinor formalism. By defining a non-minimal version…
After a short review of the algebraic setting of N=2 superconformal field theories, their chiral ring and their perturbations, I present some recent results on curious relations between the integrability of their perturbations and algebraic…
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 these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a…
The KdV and modified KdV integrable hierarchies are shown to be different descriptions of the same 2D gravitational system -- open-closed string theory. Non-perturbative solutions of the multi-critical unitary matrix models map to…
An infinite number of topological conformal algebras with varying central charges are explicitly shown to be present in $2d$ gravity (treated both in the conformal gauge and in the light-cone gauge) coupled to minimal matter. The central…
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 show that the connection between certain integrable perturbations of $N=2$ superconformal theories and graphs found by Lerche and Warner extends to a broader class. These perturbations are such that the generators of the perturbed chiral…
We provide a unified description of the three covariant superspace approaches to ${\cal N}=2$ conformal supergravity in four dimensions: (i) conformal superspace; (ii) $\mathsf{U}(2)$ superspace; and (iii) $\mathsf{SU}(2)$ superspace. Each…
I summarize some recent results obtained in collaboration with P.~Bouwknegt and K.~Pilch on the spectrum of physical states in $\cW_3$ gravity coupled to $c=2$ matter. In particular, it is shown that the algebra of operators corresponding…
We study effective gravitational F-terms, obtained by integrating an $U(N)$ adjoint chiral superfield $\Phi$ coupled to the ${\cal N}=1$ gauge chiral superfield $W_\alpha$ and supergravity, to arbitrary orders in the gravitational…
By using a bosonization we uncover the topological gravity structure of Labastida, Pernici and Witten in ordinary $2d$ gravity coupled to $(p,q)$ minimal models. We study the cohomology class associated with the fermionic charge of the…
The aim of this paper is to discuss a kinematical algebraic structure of a theory of gravity, that would be unitary, renormalizable and coupled in the same manner to both spinorial and tensorial matter fields. An analysis of the common…