Gravitational and higher-derivative interactions of massive spin 5/2 field in (A)dS space

TL;DR

This work develops an on-shell gauge-invariant framework to classify and construct cubic interactions of a massive spin $\frac{5}{2}$ Dirac field with gravity in $(A)dS_d$ for $d\ge 4$, identifying a gravitational vertex plus two higher-derivative vertices with up to three derivatives. In $d>4$ the gravitational vertex contains contributions up to $3$ derivatives and two independent higher-derivative vertices with $k_{\min}=2$, $k_{\max}=3$ exist, while in $d=4$ the derivative structure simplifies and a uniform vertex can accommodate massive, massless, and partial-massless limits. The paper provides explicit coefficient solutions $m_{a,b}$ and $m_{a,b}^{\rm im}$ dictated by on-shell gauge invariance, analyzes flat-space limits, and extends the construction to vertices involving lower-spin fields, yielding a detailed map between AdS/dS and flat-space higher-spin interactions. These results illuminate the structure of consistent gravitational couplings for massive higher-spin fermions and supply ingredients potentially relevant to string theory and higher-spin holography in AdS.

Abstract

Using on-shell gauge invariant formulation of relativistic dynamics we study interaction vertices for a massive spin 5/2 Dirac field propagating in (A)dS space of dimension greater than or equal to four. Gravitational interaction vertex for the massive spin 5/2 field and all cubic vertices for the massive spin 5/2 field and massless spin 2 field with two and three derivatives are obtained. In dimension greater that four, we demonstrate that the gravitational vertex of the massive spin 5/2 field involves, in addition to the standard minimal gravitational vertex, contributions with two and three derivatives. We find that for the massive spin 5/2 and massless spin 2 fields one can build two higher-derivative vertices with two and three derivatives. Limits of massless and partial massless spin 5/2 fields in (A)dS space and limits of massive and massless spin 5/2 fields in flat space are discussed.