Constructing conformal double field theory through a double copy map

We follow the classical double copy (DC) procedure that links Yang-Mills and double field theory (DFT), and 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>b</a:mi></a:math>-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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mo>□</c:mo><c:msub><c:mi>h</c:mi><c:mrow><c:mi>μ</c:mi><c:mi>ν</c:mi></c:mrow></c:msub><c:mo>=</c:mo><c:mi>h</c:mi><c:mo>=</c:mo><c:mn>0</c:mn></c:math>. 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.