arXiv subjects
Publications and source records attributed to Elena Apresyan.
In this paper we show how the Baxter Q-operator and the product formula for eigenfunctions of two-particle hyperbolic Ruijsenaars system can be derived from the genus one Moore-Seiberg duality identity in two-dimensional Liouville conformal field theory. We expect that this relation would reveal genuine role of the Moore-Seiberg identity in integrable systems.
In this paper we derive new symmetry and new expression for $6j$-symbols of the unitary principal series representations of the $SL(2,\mathbb{C})$ group. This allowed us to derive for them the analogue of the Regge symmetry.
In this paper we calculate matrix of modular transformations of the one-point toric conformal blocks in the Neveu-Schwarz sector of $N=1$ super Liouville field theory. For this purpose we use explicit expression for this matrix as integral of product of certain elements of fusion matrix. This integral is computed using the chain of integral identities for supersymmetric hyperbolic gamma functions derived by the degeneration of the integrals of parafermionic elliptic gamma functions.
We study properties of a parafermionic generalization of the hyperbolic hypergeometric function appearing as the most important part in the fusion matrix for Liouville field theory and the Racah-Wigner symbols for the Faddeev modular double. We show that this generalized hypergeometric function is a limiting form of the rarefied elliptic hypergeometric function $V^{(r)}$ and derive its transformation properties and a mixed difference-recurrence equation satisfied by it. At the intermediate level we describe symmetries of a more general rarefied hyperbolic hypergeometric function. An important $r=2$ case corresponds to the supersymmetric hypergeometric function given by the integral appearing in the fusion matrix of $N=1$ super Liouville field theory and the Racah-Wigner symbols of the quantum algebra ${\rm U}_q({\rm osp}(1|2))$. We indicate relations to the standard Regge symmetry and prove some previous conjectures for the supersymmetric Racah-Wigner symbols by establishing their different parametrizations.
We construct topological defects in the Liouville field theory producing jump in the value of cosmological constant. We construct them using the Cardy-Lewellen equation for the two-point function with defect. We show that there are continuous and discrete families of such kind of defects. For the continuous family of defects we also find the Lagrangian description and check its agreement with the solution of the Cardy-Lewellen equation using the heavy asymptotic semiclasscial limit.
The response of fermionic system to external gauge fields in presence of non-quantized magnetic field is determined by current-current correlation function $Π_{μν}({\bf B})$. We study $2D$ dimensional Dirac electron system and calculate current-current correlation function in a presence of magnetic field $B$, chemical potential $η$ and gap $m$.
We study mini-superspace semiclassical limit of the boundary three-point function in the Liouville field theory. We compute also matrix elements for the Morse potential quantum mechanics. An exact agreement between the former and the latter is found. We show that both of them are given by the generalized hypergeometric functions.