# 2-form gauge theory dual to scalar-tensor theory

## TL;DR

This paper extends electromagnetic duality to scalar-tensor theories, deriving dual 2-form gauge actions for shift symmetric K-essence and Horndeski theories, revealing complex interactions and modified duality relations.

## Contribution

It introduces a duality framework between scalar-tensor theories and 2-form gauge fields, including nonlinear and gravity-interacting cases, expanding the scope of electromagnetic duality.

## Key findings

- Derived dual 2-form actions for shift symmetric K-essence and Horndeski theories.
- Found the dual 2-form has nonlinear kinetic terms and gravity interactions.
- Discovered the duality relation is modified from the standard case.

## Abstract

We generalize the electromagnetic duality between a massless, canonical scalar field and a 2-form gauge field in 4-dimensional spacetime to scalar-tensor theories. We derive the action of 2-form gauge field that is dual to two kinds of scalar-tensor theories: shift symmetric K-essence theory and the shift symmetric Horndeski theory up to quadratic in scalar field. The former case, the dual 2-form has a nonlinear kinetic term. The latter case, the dual 2-form has non-trivial interactions with gravity through Einstein tensor. In both case, the duality relation is modified from usual case, that is, the dual 2-form field is not simply given by the Hodge dual of the gradient of the scalar field.