Related papers: Do we need the $W^{(n>3)}$ constraints to solve th…

A topological procedure for computing correlation functions for any (1,q) model is presented. Our procedure can be used to compute any correlation function on the sphere as well as some correlation functions at higher genus. We derive new…

We study the $(1,q=-1)$ model coupled to topological gravity as a candidate to describing $2d$ string theory at the self-dual radius. We define the model by analytical continuation of $q>1$ topological recursion relations to $q=-1$. We show…

$q,t$-deformed matrix models give rise to representations of the deformed Virasoro algebra and more generally of the quantum toroidal $\mathfrak{gl}_1$ algebra. These representations are described in terms of finite difference equations…

We show how q-Virasoro constraints can be derived for a large class of (q,t)-deformed eigenvalue matrix models by an elementary trick of inserting certain q-difference operators under the integral, in complete analogy with full-derivative…

We give a new proof of the dilogarithm identities, associated to the (2,2n+1) minimal models of the Virasoro algebra.

We present a compact formula in Mellin space for the four-point tree-level holographic correlators of chiral primary operators of arbitrary conformal weights in $(2,0)$ supergravity on $AdS_3 \times S^3$, with two operators in tensor…

Using a superspace representation of the N=3 Neveau-Schwarz super Virasoro algebra, we find solutions of N=3 super Ward identities. Global transformations generated by the non-abelian supercurrent require not only superfields, but also…

In the first part of the talk, I review the applications of loop equations to the matrix models and to 2-dimensional quantum gravity which is defined as their continuum limit. The results concerning multi-loop correlators for low genera and…

The tree-level three-point correlation functions of local operators in the general $(p,q)$ minimal models coupled to gravity are calculated in the continuum approach. On one hand, the result agrees with the unitary series ($q=p+1$); and on…

The correspondence claimed by M. Douglas, between the multicritical regimes of the two-matrix model and 2D gravity coupled to (p,q) rational matter field, is worked out explicitly. We found the minimal (p,q) multicritical potentials U(X)…

From the defining exchange relations of the A_{q,p}(gl_{N}) elliptic quantum algebra, we construct subalgebras which can be characterized as q-deformed W_N algebras. The consistency conditions relating the parameters p,q,N and the central…

In order to study 3d loop quantum gravity coupled to matter, we consider a simplified model of abelian quantum gravity, the so-called U(1)^3 model. Abelian gravity coupled to a scalar field shares a lot of commonalities with parameterized…

We show that one can use some renormalized coupling constants to compute the free energy and correlation functions at all critical points of the two-dimensional topological gravity in a uniform way. In particular, one can derive the…

We consider the AGT relation, expressing conformal blocks for the Virasoro and W-algebras in terms of Nekrasov's special functions, in the simplest case of the 4-point functions for the first non-trivial W_3 algebra. The standard set of…

Infinite-dimensional Galilean conformal algebras can be constructed by contracting pairs of symmetry algebras in conformal field theory, such as $W$-algebras. Known examples include contractions of pairs of the Virasoro algebra, its $N=1$…

We investigate the supereigenvalue model in the Ramond sector. We prove that its partition function can be obtained by acting on elementary functions with exponents of the given operators. The Virasoro constraints for this supereigenvalue…

In this study, we explore the correlation functions of thin-shell operators, represented semiclassically by a homogeneous, thin interface of dust particles. Employing the monodromy method, we successfully compute the contribution from the…

We describe in detail the derivation of a superconformal off-shell formulation of the alternative $\mathcal{N}=2$, $d=5$ ungauged supergravity of Nishino and Rajpoot, coupled to $n$ Abelian vector multiplets, using a general dilaton-Weyl…

We study the double scaling limit of mKdV type, realized in the two-cut Hermitian matrix model. Building on the work of Periwal and Shevitz and of Nappi, we find an exact solution including all odd scaling operators, in terms of a hierarchy…

We investigate energy correlators in four-dimensional gravitational theories, which provide a simple class of infrared-finite observables. We compute the one- and two-point energy correlators at one loop in $\mathcal{N}=8$ supergravity and…