Related papers: Liouville conformal blocks and Stokes phenomena
Three explicit and equivalent representations for the monodromy of the conformal blocks in the SL(2,C)/SU(2) WZNW model are proposed in terms of the same quantity computed in Liouville field theory. We show that there are two possible…
Following Boardman-Vogt, McDuff, Segal, and others, we construct a monoidal topological groupoid or space of finite subsets of the plane, and interpret the Burau representation of knot theory as a topological quantum field theory defined on…
We study interacting massive N=(2,2) supersymmetric field theories in two dimensions which arise from deforming conformal field theories with a continuous spectrum. Firstly, we deform N=2 superconformal Liouville theory with relevant…
One of the most challenging problems in the domain of 2-D image or 3-D shape is to handle the non-rigid deformation. From the perspective of transformation groups, the conformal transformation is a key part of the diffeomorphism. According…
We discuss the resummation procedure of the superpotential in 4d $\mathcal{N}=2$ SYM theory without matter from the point of view of 2d Liouville conformal field theory, utilizing the AGT correspondence. We identify contributions of…
We analytically study the Fermi-gas formulation of sphere correlation functions of the Coulomb branch operators for 3d $\mathcal{N}=4$ ADHM theory with a gauge group $U(N)$, an adjoint hypermultiplet and $l$ hypermultiplets which can…
The Coulomb-gas description of minimal models is considered on the half plane. Screening prescriptions are developed by the perturbative expansion of the Liouville theory with imaginary coupling and with Neumann boundary condition on the…
The conjecture about the correspondence between instanton partition functions in the N=2 SUSY Yang-Mills theory and conformal blocks of two-dimensional conformal field theories is extended to the case of the N=1 supersymmetric conformal…
Analytic expressions for the two dimensional $\mathcal{N}=1$ SLFT blocks in the light semi-classical limit are found for both Neveu-Schwarz and Ramond sectors. The calculations are done by using the duality between $SU(2)$ $\mathcal{N}=2$…
Sturm-Liouville oscillation theory is studied for Jacobi operators with block entries given by covariant operators on an infinite dimensional Hilbert space. It is shown that the integrated density of states of the Jacobi operator is…
We use time-independent canonical transformation methods to discuss the energy eigenfunctions for the simple linear potential, pedagogically setting the stage for some field theory calculations to follow. We then discuss the Schr\"odinger…
We study magnetic geodesic flows invariant under rotations on the 2-sphere. The dynamical system is given by a generic pair of functions $(f,\Lambda)$ in one variable. Topology of the Liouville fibration of the given integrable system near…
A recently proposed correspondence between 4-dimensional N=2 SUSY SU(k) gauge theories on R^4/Z_m and SU(k) Toda-like theories with Z_m parafermionic symmetry is used to construct four-point N=1 super Liouville conformal block, which…
We show how general principles of symmetry in quantum mechanics lead to twisted notions of a group representation. This framework generalizes both the classical 3-fold way of real/complex/quaternionic representations as well as a…
Topology of Liouville foliations for an analogue of the Kovalevskaya integrable case on Lie algebra so(4) is discussed. Fomenko-Zieschang invariants (i.e. marked molecules) were calculated for these foliations on every regular isoenergy…
We point out that there is a generalization to higher dimensions $d=2h>2$ of the two-dimensional Dotsenko-Fateev formula \DF\ for particular Coulomb gas conformal invariant integrals. These expressions represent structure constants of…
We introduce a method for computing conformal blocks of operators in arbitrary Lorentz representations in any spacetime dimension, making it possible to apply bootstrap techniques to operators with spin. The key idea is to implement the…
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…
We study the solution of the Schlesinger system for the 4-point $\mathfrak{sl}_N$ isomonodromy problem and conjecture an expression for the isomonodromic $\tau$-function in terms of 2d conformal field theory beyond the known $N=2$…
The Laguerre functions constitute one of the fundamental basis sets for calculations in atomic and molecular electron-structure theory, with applications in hadronic and nuclear theory as well. While similar in form to the Coulomb…