Arbitrary spin conformal fields in (A)dS

TL;DR

The paper develops an ordinary-derivative, gauge-invariant Lagrangian framework for totally symmetric arbitrary spin conformal fields in $(A)dS_{d+1}$ (with even $d+1\ge4$). It proves that the conformal Lagrangian can be decomposed into gauge-invariant sectors describing massless, partial-massless, and massive fields, and it derives the corresponding mass spectra, confirming conjectured spectra in the literature. A diagonal, two-derivative kinetic structure emerges in $(A)dS$, and the authors construct explicit conformal maps from flat-space conformal fields to $(A)dS$ fields, along with Lorentz-like and de Donder-like gauges that lead to BRST-invariant gauge-fixed Lagrangians and partition functions. The work extends to flat space $R^{d,1}$, elaborates detailed oscillator- and BRST-formulated generating-function formalisms, and provides a systematic method to obtain Lagrangians and gauge transformations for massless, partial-massless, massive, and conformal fields in $(A)dS_{d+1}$ via a unifying operator framework.

Abstract

Totally symmetric arbitrary spin conformal fields in (A)dS space of even dimension greater than or equal to four are studied. Ordinary-derivative and gauge invariant Lagrangian formulation for such fields is obtained. Gauge symmetries are realized by using auxiliary fields and Stueckelberg fields. We demonstrate that Lagrangian of conformal field is decomposed into a sum of gauge invariant Lagrangians for massless, partial-massless, and massive fields. We obtain a mass spectrum of the partial-massless and massive fields and confirm the conjecture about the mass spectrum made in the earlier literature. In contrast to conformal fields in flat space, the kinetic terms of conformal fields in (A)dS space turn out to be diagonal with respect to fields entering the Lagrangian. Explicit form of conformal transformation which maps conformal field in flat space to conformal field in (A)dS space is obtained. Covariant Lorentz-like and de-Donder like gauge conditions leading to simple gauge-fixed Lagrangian of conformal fields are proposed. Using such gauge-fixed Lagrangian, which is invariant under global BRST transformations, we explain how the partition function of conformal field is obtained in the framework of our approach.