Auxiliary-Field Formalism for Higher-Derivative Boundary CFTs

We study the conformal field theory defined by the fourth-order operator on four-dimensional manifolds with boundaries, reformulating it through an auxiliary field so that the dynamics become second order. Within this framework, we compute the heat kernel of $\Box^2$ in flat space exactly, together with the associated Seeley-DeWitt coefficients for a broad class of non-standard boundary conditions. On curved backgrounds, we further construct the Weyl-invariant completion of the auxiliary field action with boundary terms and identify the corresponding conformal boundary conditions. Finally, we compute the boundary charges in the trace anomaly from the displacement operator correlators.