BRST invariant effective action of shadow fields, conformal fields, and AdS/CFT

TL;DR

This paper develops BRST invariant effective actions for shadow and conformal fields in AdS space, linking bulk massless and massive fields to boundary conformal fields through the AdS/CFT correspondence.

Contribution

It introduces BRST invariant Lagrangians for arbitrary spin fields in AdS, connecting bulk actions to boundary conformal fields and elucidating the geometric role of Nakanishi-Laudrup fields.

Findings

BRST invariant bulk actions lead to boundary effective actions for shadow fields.

Leading logarithmic divergence yields BRST invariant conformal field action.

Nakanishi-Laudrup fields are boundary values of massless AdS fields.

Abstract

Totally symmetric arbitrary spin massless and massive fields in AdS space are studied. For such fields, we obtain Lagrangians which are invariant under global BRST transformations. The Lagrangians are used for computation of partition functions and effective actions. We demonstrate that BRST invariant bulk action for massless field evaluated on the solution of Dirichlet problem for gauge massless fields and Faddeev-Popov fields leads to BRST invariant effective action for canonical shadow gauge fields and shadow Faddeev-Popov fields, while the BRST invariant bulk action for massive field evaluated on the solution of Dirichlet problem for gauge massive fields and Faddeev-Popov fields leads to BRST invariant effective action for anomalous shadow gauge fields and shadow Faddeev-Popov fields. The leading logarithmic divergence of the regularized effective action for the canonical shadow field leads to simple BRST invariant action of conformal field. We demonstrate that the Nakanishi-Laudrup fields entering the BRST invariant Lagrangian of conformal field can geometrically be interpreted as boundary values of massless AdS fields.