Related papers: Analytic properties of the Virasoro modular kernel
We compute the automorphism groups of the Torelli complex and the complex of separating curves for all but finitely many compact orientable surfaces. As an application, we show that the abstract commensurators of the Torelli group and the…
We analyse the fusion of representations of the triplet algebra, the maximally extended symmetry algebra of the Virasoro algebra at c=-2. It is shown that there exists a finite number of representations which are closed under fusion. These…
We consider the symplectic vortex equations for a linear Hamiltonian torus action. We show that the associated genus zero moduli space itself is homotopic (in the sense of a homotopy of regular G-moduli problems) to a toric manifold with…
We discuss some basic problems and conjectures in a program to construct general orbifold conformal field theories using the representation theory of vertex operator algebras. We first review a program to construct conformal field theories.…
We numerically investigate the mechanical and geometrical properties of dense wet granular particles with irreversible attractive interaction. The shear modulus exhibits two inflection points as the packing fraction increases, and the bulk…
It is shown how to obtain conformal blocks from embedding space with the help of the operator product expansion. The minimal conformal block originates from scalar exchange in a four-point correlation functions of four scalars. All…
A new characterization of conformal transformations is given. By use of this, the general form of conformal transformation on two-dimensional Minkowski space is given and its conformal structure is analyzed.
A discussion of character formulae for positive energy unitary irreducible representations of the the conformal group is given, employing Verma modules and Weyl group reflections. Product formulae for various conformal group representations…
We investigate the constraints of crossing symmetry on CFT correlation functions. Four point conformal blocks are naturally viewed as functions on the upper-half plane, on which crossing symmetry acts by PSL(2,Z) modular transformations.…
We review and systematize two (analytic) bootstrap techniques in two-dimensional conformal field theories using the S-modular transformation. The first one gives universal results in asymptotic regimes by relating extreme temperatures.…
Recall that the moduli space of smooth (that is, stable) cubic curves is isomorphic to the quotient of the upper half plane by the group of fractional linear transformations with integer coefficients. We establish a similar result for…
We show that the grading of fields by conformal weight, when built into the initial group symmetry, provides a discrete, non-central conformal extension of any group containing dilatations. We find a faithful vector representation of the…
A new set of realizations of the Virasoro algebra on a bosonic Fock space are found by explicitly computing the Virasoro representations associated with coadjoint orbits of the form (Diff S1) / S1. Some progress is made in understanding the…
In this paper we show that the worldline reparametrization for particles with higher derivative interactions appears as a higher dimensional symmetry, which is generated by the truncated Virasoro algebra. We also argue that for generic…
We compute the exact thermal partition functions of a massive scalar field on flat spacetime backgrounds of the form $\mathbb R^{d-q}\times \mathbb T^{q+1}$ and show that they possess an ${\rm SL}(q+1,\mathbb Z)$ symmetry. Non-trivial…
We study general properties of the conformal basis, the space of wavefunctions in $(d+2)$-dimensional Minkowski space that are primaries of the Lorentz group $SO(1,d+1)$. Scattering amplitudes written in this basis have the same symmetry as…
In [arXiv:2008.04625] the authors constructed a classifying space for polystable holomorphic vector bundles on a compact K\"ahler manifold using analytic GIT theory. The aim of this article is to show that this classifying space taken in…
We derive recursive representations in the internal weights of N-point Virasoro conformal blocks in the sphere linear channel and the torus necklace channel, and recursive representations in the central charge of arbitrary Virasoro…
The use of kernels for nonlinear prediction is widespread in machine learning. They have been popularized in support vector machines and used in kernel ridge regression, amongst others. Kernel methods share three aspects. First, instead of…
Aimed at complex geometers and representation theorists, this survey explores higher dimensional analogues of the rich interplay between Riemann surfaces, Virasoro and Kac-Moody Lie algebras, and conformal blocks. We introduce a panoply of…