Auxiliary-Field Formalism for Higher-Derivative Boundary CFTs

TL;DR

The paper develops an auxiliary-field approach to four-dimensional higher-derivative boundary CFTs, recasting the $\Box^2$ biharmonic theory as a second-order system to enable exact flat-space heat-kernel computations and a Weyl-invariant curved-space extension. It identifies a precise mapping between boundary conditions in the original fourth-order theory and the auxiliary formulation, derives Seeley–DeWitt coefficients for general boundary data, and computes boundary charges from displacement-operator correlators, finding $b_1=8b$ with $b=-1/15$ and $c=-104/315$ under appropriate BC. The work validates the auxiliary-field framework off-shell and demonstrates its consistency with conformal and anomaly structures, while clarifying which conformal BC survive the reformulation and highlighting potential links to logarithmic CFTs and RG flows. These results offer a computationally efficient path to study higher-derivative boundary CFTs and set the stage for extensions to more general GJMS operators and spinorial cases.

Abstract

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.