Related papers: The operator algebra of cyclic orbifolds
The rationality and C_2-cofiniteness of the orbifold vertex operator algebra V_{L_{2}}^{A_{4}} are established and all the irreducible modules are constructed and classified. This is part of classification of rational vertex operator…
We prove convergence and compatibility of iterated bulk and boundary operator product expansions (OPEs) in two-dimensional conformal field theory with locally $C_1$-cofinite chiral symmetry. For each tree, we give an explicit domain of…
The chiral algebra of a 4D $N\geq2$ superconformal field theory is a vertex operator algebra generated by the Schur subsector of the 4D theory and its rigid (yet rich) structure has been useful in constraining and classifying 4D N=2 SCFTs.…
We use computational linear algebra and commutative algebra to study spaces of relations satisfied by quadrilinear operations. The relations are analogues of associativity in the sense that they are quadratic (every term involves two…
These notes survey the theory of (twisted) conformal blocks from an algebro-geometric perspective and have two main goals. The first one is to summarize the construction of conformal blocks from vertex operator algebras, and to describe…
The explicit computation of higher-point conformal blocks in any dimension is usually a challenging task. For two-dimensional conformal field theories in Euclidean signature, the oscillator formalism proves to be very efficient. We…
We show how to compute conformal blocks of operators in arbitrary Lorentz representations using the formalism described in arXiv:1905.00036 and arXiv:1905.00434, and present several explicit examples of blocks derived via this method. The…
An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.
We carry out a systematic study of primary operators in the conformal field theory of a free Weyl fermion. Using SO(4,2) characters we develop counting formulas for primaries constructed using a fixed number of fermion fields. By…
We study some aspects of 2d supersymmetric sigma models on orbifolds. It turns out that independently of whether the 2d QFT is conformal the operator products of twist operators are non-singular, suggesting that massive (non-conformal)…
In this paper, we introduce the concept of L-dendriform conformal algebras, which arise naturally from the study of $\mathcal{O}$-operators on left-symmetric conformal algebras and solutions to the conformal $S$-equation. These algebras…
The Verlinde formula computes the dimension of conformal blocks associated to simple Lie algebras and stable pointed curves. If a simply-laced simple Lie algebra admits a nontrivial diagram automorphism, then this automorphism acts on the…
We extend the geometric approach to vertex algebras developed by the first author to twisted modules, allowing us to treat orbifold models in conformal field theory. Let $V$ be a vertex algebra, $H$ a finite group of automorphisms of $V$,…
Quaternionic and octonionic realizations of Clifford algebras and spinors are classified and explicitly constructed in terms of recursive formulas. The most general free dynamics in arbitrary signature space-times for both quaternionic and…
The chiral algebra of 4D $\mathcal{N}=4$ SU$(N)$ super-Yang-Mills theory is an $\mathcal{N}=4$ superconformal vertex operator algebra. We analyse the structure of this algebra by studying recursively the constraints that are required by the…
We consider chiral fermionic conformal field theories (CFTs) constructed from lattices and investigate their orbifolds under reflection and shift $\mathbb{Z}_2$ symmetries. For lattices based on binary error-correcting codes, we show the…
We construct symmetry generators and operators for $J\bar{T}$-deformed conformal field theories by generalizing the framework established for $T\bar{T}$ deformations. Working in the Hamiltonian formalism on the plane, we derive the symmetry…
This thesis describes a new approach to conformal field theory. This approach combines the method of coadjoint orbits with resolutions and chiral vertex operators to give a construction of the correlation functions of conformal field…
We apply the factorization and vector bundle propositionerty of the sheaves of conformal blocks on $\overline{\mathscr{M}}_{g,n}$. defined by vertex operator algebras (VOAs) and give geometric proofs of essential results in the…
We take first steps toward a theory of ``conformal twists'' for superconformal field theories in dimension 3 to 6, extending the well-known analysis of twists for supersymmetric theories. A conformal twist is a square-zero odd element in…