This paper provides a review of the literature on rigorous definitions and constructions in
quantum field theory (QFT), spanning the period of seven decades. Compared with the …

What follows is a broad-brush overview of the recent synergistic interactions between
mathematics and theoretical physics of quantum field theory and string theory. The …

A bstract We consider finite deformations of the Hull-Strominger system. Starting from the
heterotic superpotential, we identify complex coordinates on the off-shell parameter space …

The holomorphic sigma-model is a field theory that exists in any complex dimension that
describes the moduli space of holomorphic maps from one complex manifold to another. We …

We construct a trace map on the chiral homology of chiral Weyl algebra for any smooth
Riemann surface. Our trace map can be viewed as a chiral version of the deformed HKR …

We formulate a twisted version of the conjectured duality between heterotic and type I string
theories. Our formulation relates the chiral part of the heterotic string with a type I topological …

A bstract In this paper, inspired by the Costello's seminal work [11], we present a general
formulation of exact renormalization group (RG) within the Batalin-Vilkovisky (BV) …

We prove the existence of a homomorphism of vertex algebras, from the vacuum Verma
module over the loop algebra of an untwisted affine algebra, whose construction is …

In this article, taking inspiration from Costello's work on renormalization in Batalin–Vilkovisky
(BV) theory (KJ Costello, e-print arXiv: 0706.1533 [math. QA]), we present an abstract …