Aspects of braided field theories from homotopy algebras and the double copy of noncommutative gauge theories

Abstract

The quantum Batalin–Vilkovisky (BV) formalism and its connection to homotopy Lie algebras is reviewed. The Drinfel’d twist deformation procedure is used to define braided homotopy Lie algebras, leading us to perform a detailed study of the braided cubic scalar and the braided quantum electrodynamics model in the first part of this thesis. The braided BV formalism is used to compute correlation functions for these models and we show the absence of UV/IR mixing up to one-loop order and three-point multiplicity. New homological techniques are presented to study the Schwinger–Dyson equation and the Ward–Takahashi identities of these braided theories respectively. In the later theory, the braided gauge symmetry is verified to be non-anomalous. We next study how conventional noncommutative field theories fit into the ho motopy double copy paradigm whose central idea is the factorisation of homotopy algebras. To perform this operation, a new twisted colour-kinematics duality is identified. This twist captures the (conventional) noncommutativity of the theory, hence the double copied theories are shown to match with their commutative coun terparts; a result that is expected from open-closed string duality in the presence of a background B-field. We conjecture that performing the homotopy double copy within the category of braided L∞-algebras is the correct way to probe twisted noncommutative gravity.