Constructing Conformal Double Field Theory through a Double Copy Map

TL;DR

This paper develops a new conformal double field theory (CDFT) by applying the classical double copy procedure to a four-derivative gauge theory, linking gauge theories with T-duality invariant models and Weyl gravity.

Contribution

It constructs a perturbative, T-duality invariant conformal double field theory from gauge theories using the double copy map, extending to cubic order without gauge fixing.

Findings

CDFT incorporates Weyl gravity, b-field, and dilaton at quadratic order.

CDFT and DFT are shown to be T-duality invariant theories derived from gauge theories.

The formulation extends to cubic order for specific conditions, maintaining key features.

Abstract

We follow the classical Double Copy (DC) procedure that links Yang-Mills and Double Field Theory (DFT), and we apply it on a four-derivative gauge theory which is known to be related to Weyl gravity at the level of the amplitudes. We obtain a perturbative T-duality invariant theory on a double geometry, or Conformal Double Field Theory (CDFT), incorporating Weyl gravity plus $b$-field and dilaton contributions at quadratic order, without the need to impose a gauge fixing condition. We also extend the formulation to cubic order for the case of vanishing generalized dilaton, which still incorporates Weyl gravity when $\Box h_{\mu \nu}=h=0$. CDFT, together with ordinary DFT, are examples of T-duality invariant theories constructed through classical DC maps, revealing a promising and deep connection between gauge theories and T-duality invariant models.