Toward frame-like gauge invariant formulation for massive mixed symmetry bosonic fields

TL;DR

This work tackles the problem of formulating a frame-like, gauge-invariant description for massive mixed-symmetry bosonic fields in $(A)dS_d$. By extending known massless frame-like constructions with a Goldstone tower and carefully chosen cross terms, the authors derive complete Lagrangians and gauge transformations for $Y(2,1)$, $Y(3,1)$, and the general $Y(k,1)$, including all massless and partially massless limits. The key contributions are the explicit Lagrangian structures ${\cal L} = {\cal L}_0 + {\cal \ L}_1$, the necessary corrections to gauge transformations, and the recursive relations that fix the massive theory in terms of curvature $\kappa$ and a mass scale $M^2$, revealing rich partially massless sectors in $(A)dS$ as well as constraints on unitary regions. This framework enables controlled deformations of higher-spin mixed-symmetry fields to curved backgrounds and clarifies when PM phases arise, enhancing understanding of massive higher-spin dynamics in diverse dimensions.

Abstract

In this paper, as a first step toward frame-like gauge invariant formulation for massive mixed symmetry bosonic fields, we consider mixed tensors, corresponding to Young tableau with two rows with k >= 2 boxes in the first row and only one box in the second one. We construct complete Lagrangian and gauge transformations describing massive particles in (anti) de Sitter space-time with arbitrary dimension d >= 4 and investigate all possible massless and partially massless limits.

Figures (9)

• Figure 1: General massive theory for $Y(2,1)$ tensor
• Figure 2: General massive theory for $Y(3,1)$ tensor
• Figure 3: Partially massless limit in $dS$ space
• Figure 4: Non-unitary partially massless theory
• Figure 5: Partially massless limit in $AdS$ space