Related papers: Analytic properties of the Virasoro modular kernel
In this paper, we introduce a notion of $g$-twisted restricted conformal block on the three-pointed twisted projective line $\mathfrak{x}\colon\overline{C}\to\mathbb{P^1}$ associated with an untwisted module $M^1$ and the bottom levels of…
Let M(r) be the moduli space of rank r vector bundles with trivial determinant on a Riemann surface X . This space carries a natural line bundle, the determinant line bundle L . We describe a canonical isomorphism of the space of global…
The modular commutator is a recently discovered multipartite entanglement measure that quantifies the chirality of the underlying many-body quantum state. In this Letter, we derive a universal expression for the modular commutator in…
We describe several infinite series of rational conformal field theories whose conformal characters are modular units, i.e. which are modular functions having no zeros or poles in the upper complex half plane, and which thus possess simple…
Here we define a series of associative algebras attached to a vertex operator algebra $V$, called mode transition algebras, showing they reflect both algebraic properties of $V$ and geometric constructions on moduli of curves. One can…
In this paper a class of conformal field theories with nonabelian and discrete group of symmetry is investigated. These theories are realized in terms of free scalar fields starting from the simple $b-c$ systems and scalar fields on…
We introduce a formalism for handling general spaces of hierarchical tilings, a category that includes substitution tilings, Bratteli-Vershik systems, S-adic transformations, and multi-dimensional cut-and-stack transformations. We explore…
A class of non-semisimple extensions of Lie superalgebras is studied. They are obtained by adjoining to the superalgebra its adjoint representation as an abelian ideal. When the superalgebra is of affine Kac-Moody type, a generalisation of…
We develop the thermal shadow formalism to study the conformal blocks decomposition in $D$-dimensional conformal field theory on $\mathbb{S}_{\beta}^{1} \times \mathbb{S}^{D-1}$, where the temperature is $T = \beta^{-1}$. It is demonstrated…
For a module-finite algebra over a commutative noetherian ring, we give a complete description of flat cotorsion modules in terms of prime ideals of the algebra, as a generalization of Enochs' result for a commutative noetherian ring. As a…
In this paper the conformal Dirac operator on the sphere is defined to be operating on the space of square-integrable Clifford algebra-valued functions. The spinorial Laplacian of order d>0 is defined and used to establish Sobolev embedding…
The cosine transforms of functions on the unit sphere play an important role in convex geometry, the Banach space theory, stochastic geometry and other areas. Their higher-rank generalization to Grassmann manifolds represents an interesting…
We establish a correspondence between conformal partial waves on flat, thermal, and defect backgrounds using the shadow formalism. We demonstrate that scalar one-point thermal blocks can be systematically obtained from their four-point…
Recently, an intriguing family of the one-point toric conformal blocks AGT related to the $\mathcal{N}=2^*\,\, SU(2)$ Nekrasov functions was discovered by M. Beccaria and G. Macorini. Members of the family are distinguished by having only…
Black hole microstates and their approximate thermodynamic properties can be studied using heavy-light correlation functions in AdS/CFT. Universal features of these correlators can be extracted from the Virasoro conformal blocks in CFT2,…
Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction of the `bundle of conformal blocks', a representation of the mapping class groupoid of…
In this work we introduce KERNELIZED TRANSFORMER, a generic, scalable, data driven framework for learning the kernel function in Transformers. Our framework approximates the Transformer kernel as a dot product between spectral feature maps…
AGT correspondence gives an explicit expressions for the conformal blocks of $d=2$ conformal field theory. Recently an explanation of this representation inside the CFT framework was given through the assumption about the existence of the…
Explicit formulae describing the genus one characters and modular transformation properties of permutation orbifolds of arbitrary Rational Conformal Field Theories are presented, and their relation to the theory of covering surfaces is…
We determine the projectively flat unitary structure on abelian conformal blocks in terms of WZW-data.