Related papers: H(3)+ correlators from Liouville theory
The problem of the structure constants of the operator product expansions in the minimal models of conformal field theory is revisited. We rederive these previously known constants and present them in the form particularly useful in the…
We show that any bounded smooth helically symmetric solution $(\Bu, \Bh)$ in $\mathbb{R}^3$ must be constant vectors. This is an extension of previous result \cite[Theorem 1.1]{HWXAHE} from Navier-Stokes system to MHD system. The proof…
The Hamiltonians of $SU(2)$ and $SU(3)$ gauge theories in 3+1 dimensions can be expressed in terms of gauge invariant spatial geometric variables, i.e., metrics, connections and curvature tensors which are simple local functions of the…
We construct Euclidean Liouville conformal field theories in odd number of dimensions. The theories are nonlocal and non-unitary with a log-correlated Liouville field, a ${\cal Q}$-curvature background, and an exponential Liouville-type…
Liouville, SL(2,R)/U(1) and SL(2,R)/R_+ coset structures are completely described by gauge invariant Hamiltonian reduction of the SL(2,R) WZNW theory.
This is the first part of an investigation concerning the formulation of 2D gravity in the framework of the uniformization theory of Riemann surfaces. As a first step in this direction we show that the classical Liouville action appears in…
We compute the exact path integral of $\mathcal{N}=2$ supersymmetric gauge theories with general gauge group on $\mathbb{RP}^4$ and a $\mathbb{Z}_2$-quotient of the hemi-$S^4$. By specializing to $SU(2)$ superconformal quivers, we show that…
The aim of this paper is to present a complete description of all rotational linear Weingarten surface into the Euclidean sphere S3. These surfaces are characterized by a linear relation aH+bK=c, where H and K stand for their mean and…
It is shown that time-independent solutions to the (2+1)-dimensional non- linear O(3) sigma model may be placed in correspondence with surfaces of constant mean curvature in three-dimensional Euclidean space. The tools required to establish…
We determine the spectrum and correlation functions of Liouville theory with a central charge less than (or equal) one. This completes the definition of Liouville theory for all complex values of the central charge. The spectrum is always…
Since the work of Bershadsky and Ooguri and Feigin and Frenkel it is well known that correlators of $SL(2)$ current algebra for admissible representations should reduce to correlators for conformal minimal models. A precise proposal for…
We present a relation between N=2 quiver gauge theories on the ALE space O_{P^1}(-2) and correlators of N=1 super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for…
For $n\geq2,$ we obtain Liouville type theorems for minimal surface equations in half space $\mathbf R^n_+$ with affine Dirichlet boundary value or constant Neumann boundary value.
An explicit construction of surfaces with flat normal bundle in the Euclidean space (unit hypersphere) in terms of solutions of certain linear system is proposed. In the case of 3-space our formulae can be viewed as the direct Lie sphere…
Recently, two of us argued that the probability that an FK cluster in the Q-state Potts model connects three given points is related to the time-like Liouville three-point correlation function. Moreover, they predicted that the FK…
We propose a definition of irregular vertex operators in the H3+ WZW model. Our definition is compatible with the duality [1] between the H3+ WZW model and Liouville theory, and we provide the explicit map between correlation functions of…
In three dimensions, the construction of bi-Hamiltonian structure can be reduced to the solutions of a Riccati equation with the arclength coordinate of a Frenet-Serret frame being the independent variable. Explicit integration of conserved…
We formulate the $O(3) \s-$ model on fuzzy sphere and construct the Hopf term. We show that the field can be expanded in terms of the ladder operators of Holstein-Primakoff realisation of SU(2) algebra and the corresponding basis set can be…
In this paper we provide a proof of the Riemann Hypothesis by relating the non-trivial zeros of the zeta function to a certain Sturm-Liouville eigenvalue problem on a finite interval.
We study the connection between Zamolodchikov operator-valued relations in Liouville field theory and in the SL(2,R)_k WZNW model. In particular, the classical relations in SL(2,R)_k can be formulated as a classical Liouville hierarchy in…