The DBI and special galileon theories exhibit a conformal symmetry at unphysical values of the spacetime dimension. We find the Lagrangian form of this symmetry. The special conformal transformations are non-linearly realized on the fields, even though conformal symmetry is unbroken. Commuting the conformal transformations with the extended shift symmetries, we find new symmetries, which when taken together with the conformal and shift symmetries close into a larger algebra. For DBI this larger algebra is the conformal algebra of the higher dimensional bulk in the brane embedding view of DBI. For the special galileon it is a real form of the special linear algebra. We also find the Weyl transformations corresponding to the conformal symmetries, as well as the necessary improvement terms to make the theories Weyl invariant, to second order in the coupling in the DBI case and to lowest order in the coupling in the special galileon case.

DBI 和特殊伽利略理论在时空维度的非物理值上表现出共形对称性。我们找到了这种对称性的拉格朗日形式。特殊的共形变换是在场上非线性实现的，即使共形对称是不间断的。将共形变换与扩展的移位对称性进行交换，我们发现了新的对称性，当与共形对称性和移位对称性一起接近更大的代数时。对于 DBI，这个更大的代数是 DBI 的膜嵌入视图中更高维体的共形代数。对于特殊伽利略，它是特殊线性代数的实数形式。我们还找到了对应于共形对称性的 Weyl 变换，以及使 Weyl 理论不变的必要改进项，