Related papers: On the Liouville coupling constants
Nonassociative generalization of supersymmetry is suggested. 3- and 4-point associators for supersymmetric generators are considered. On the basis of zero Jacobiators for three supersymmetric generators, we have obtained the simplest form…
We suggest a dynamical vector model of entanglement in a three qubit system based on isomorphism between $su(4)$ and $so(6)$ Lie algebras. Generalizing Pl\"ucker-type description of three-qubit local invariants we introduce three pairs of…
We study generalized matrix models corresponding to n-point Virasoro conformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT correspondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge theories with generalized…
In this work, we study the discrete observables $$E_k = \sum_{i,j=1}^n (i-j)^k A_{i,j}$$ associated with $n\times n$ alternating sign matrices $A = (A_{i,j})$. This work develops exact formulas for expectations using Bernoulli polynomials,…
Let $(M,g)$ be a compact Riemann surface with no boundary and $u=(u_1,u_2)$ be a solution of the following singular Liouville system: $$\Delta_g u_i+\sum_{j=1}^2 a_{ij}\rho_j(\frac{h_je^{u_j}}{\int_M…
By analogy with the Lobachevsky space H_{3}, generalized parabolic coordinates (t_{1},t_{2},\phi) are introduced in Riemannian space model of positive constant curvature S_{3}. In this case parabolic coordinates turn out to be complex…
We establish the geometry behind the quantum $6j$-symbols under only the admissibility conditions as in the definition of the Turaev-Viro invariants of $3$-manifolds. As a classification, we show that the $6$-tuples in the quantum…
We study 6j-symbols, or Racah coefficients for tensor products of infinite-dimensional unitary principal series representations of the group SL(2,C). These symbols were constructed earlier by Ismagilov and we rederive his result (up to some…
We discuss the correlation functions of the SL(2,C)/SU(2) WZW model, or the CFT on the Euclidean AdS_3. We argue that their calculation is reduced to that of a free theory by taking into account the renormalization and integrating out a…
We calculate the three-point functions in the sine-Liouville theory explicitly. The same calculation was done in the (unpublished) work of Fateev, Zamolodchikov and Zamolodchikov to check the conjectured duality between the sine-Liouville…
We prove that general correlation functions of both ratios and products of characteristic polynomials of Hermitian random matrices are governed by integrable kernels of three different types: a) those constructed from orthogonal…
The first chapters introduce briefly conformal theories, Moore and Seiberg polynomial equations and Gervais-Neveu quantization of Liouville theory. The next chapters present the original results of this thesis. First, the algebra of the…
We use symbol correspondence and quantum normal form theory to develop a more general method for finding uniform asymptotic approximations. We then apply this method to derive a result we announced in an earlier paper, namely, the uniform…
The entanglement theory in quantum systems with internal symmetries is rich due to the spontaneous creation of entangled pairs of charge/anti-charge particles at the entangling surface. We call these pair creation operators the bi-local…
Central configurations are solutions of the equations $\lambda m_j\boldsymbol{q}_j = \frac{\partial U}{\partial \boldsymbol{q}_j}$, where $U$ denotes the potential function and each $\boldsymbol{q}_j$ is a point in the $d$-dimensional…
The Darboux-Koenigs metrics in 2D are an important class of conformally flat, non-constant curvature metrics with a single Killing vector and a pair of quadratic Killing tensors. In [arXiv:1804.06904] it was shown how to derive these by…
We introduce averaging operators on lattices $\mathbb{Z}^d$ and study the Liouville property for functions satisfying mean value properties associated to such operators. This framework encloses discrete harmonic, $p$-harmonic,…
Within the framework of the theory of irreducible tensor operators, using well-known general analytical results for double sums ($\sum_{jm}$) of products of two $3j$-Wigner symbols, analytical expressions for single sums ($\sum_m$) for the…
We present a new necessary condition for similarity of indefinite Sturm-Liouville operators to self-adjoint operators. This condition is formulated in terms of Weyl-Titchmarsh $m$-functions. Also we obtain necessary conditions for…
We briefly report our calculation of the 2-loop coefficient of the coupling constant renormalization function Z_g in lattice perturbation theory. The quantity under study is defined through g_0 = Z_g g, where g_0 (g) is the bare…