Nonlocal field theory driven by a deformed product. Generalization of Kalb-Ramond duality

TL;DR

This paper introduces a new class of nonlocal field theories using an associative deformed product, which varies by spin and exhibits supersymmetry and duality, extending the Kalb-Ramond duality.

Contribution

It proposes a novel associative deformed product for local field theories that induces nonlocality and generalizes duality concepts, including Kalb-Ramond duality.

Findings

Deformed products are constructed for spins 0, 1/2, 1.

The resulting theories are naturally supersymmetric.

The theories exhibit an intriguing duality.

Abstract

A modification of the standard product used in local field theory by means of an associative deformed product is proposed. We present a class of deformed products, one for every spin S=0,1/2,1, that induces a nonlocal theory, displaying different form for different fields. This type of deformed product is naturally supersymmetric and it has an intriguing duality.