Related papers: Factorization algebras and abelian CS/WZW-type cor…
In this paper we relate two mathematical frameworks that make perturbative quantum field theory rigorous: perturbative algebraic quantum field theory (pAQFT) and the factorization algebras framework developed by Costello and Gwilliam. To…
Algebraic quantization has been applied on the class of globally hyperbolic spacetime for many decades, leading to remarkable results. Nonetheless, the presence of a boundary calls for a separate treatment, since, in general, it breaks…
Although in general there is no meaningful concept of factorization in fields, that in free associative algebras (over a commutative field) can be extended to their respective free field (universal field of fractions) on the level of…
Guided by the many-particle quantum theory of interacting systems, we develop a uniform classification scheme for topological phases of disordered gapped free fermions, encompassing all symmetry classes of the Tenfold Way. We apply this…
We present evidence for the factorization of the world-sheet path integrals for 2d conformal field theories on the disk into bulk and boundary contributions. This factorization is then used to reinterpret a shift in closed string…
We study a canonical quantization of the Wess--Zumino--Witten (WZW) model which depends on two integer parameters rather than one. The usual theory can be obtained as a contraction, in which our two parameters go to infinity keeping the…
A general solution of the Batalin-Vilkovisky master equation was formulated in terms of generalized fields. Recently, a superfields approach of obtaining solutions of the Batalin-Vilkovisky master equation is also established. Superfields…
We provide a mathematical formulation of the idea of a defect for a field theory, in terms of the factorization algebra of observables and using the BV formalism. Our approach follows a well-known ansatz identifying a defect as a boundary…
We extend the analysis of the canonical structure of the Wess-Zumino-Witten theory to the bulk and boundary coset G/H models. The phase spaces of the coset theories in the closed and in the open geometry appear to coincide with those of a…
We address the treatment of gauge theories within the framework that is formed from combining the machinery of noncommutative symplectic geometry, as introduced by Kontsevich, with Costello's approach to effective gauge field theories…
It has been recently discovered by Bell, Heinle and Levandovskyy that a large class of algebras, including the ubiquitous $G$-algebras, are finite factorization domains (FFD for short). Utilizing this result, we contribute an algorithm to…
Vertex algebras and factorization algebras are two approaches to chiral conformal field theory. Costello and Gwilliam describe how every holomorphic factorization algebra on the plane of complex numbers satisfying certain assumptions gives…
Both the physics and applications of fermionic symmetry-protected topological phases rely heavily on a principle known as bulk-boundary correspondence, which predicts the emergence of protected boundary-localized energy excitations…
The current algebra generated by fermions coupled to external gauge potentials and metrics on a manifold with boundary is discussed. It is shown that the previous methods, based on index theory arguments and used in the case without…
We review in detail the Batalin-Vilkovisky formalism for Lagrangian field theories and its mathematical foundations with an emphasis on higher algebraic structures and classical field theories. In particular, we show how a field theory…
In this paper we extend the classical BV framework to gauge theories on spacetime manifolds with boundary. In particular, we connect the BV construction in the bulk with the BFV construction on the boundary and we develop its extension to…
We show how the BV-BFV formalism provides natural solutions to descent equations, and discuss how it relates to the emergence of holographic counterparts of given gauge theories. Furthermore, by means of an AKSZ-type construction we…
For a finite group $D$, we study categorical factorisation homology on oriented surfaces equipped with principal $D$-bundles, which `integrates' a (linear) balanced braided category $\mathcal{A}$ with $D$-action over those surfaces. For…
This work forms a foundational study of factorization homology, or topological chiral homology, at the generality of stratified spaces with tangential structures. Examples of such factorization homology theories include intersection…
Some algebraic aspects of field quantization in space-time with boundaries are discussed. We introduce an associative algebra, whose exchange properties are inferred from the scattering processes in integrable models with reflecting…