Towards frame-like gauge invariant formulation for massive mixed symmetry bosonic fields. II. General Young tableau with two rows

TL;DR

This work completes a frame-like gauge-invariant description of massive mixed-symmetry bosonic fields corresponding to two-row Young tableaux, for arbitrary ($A$)dS cosmological constant. It systematically builds massless data, extends to massive theories via Goldstone towers, and fixes all interaction parameters in terms of a single mass parameter $M$, while revealing a rich structure of (partially) massless limits in both $AdS$ and $dS$ spaces. The results unify the massive theories for $Y(k+1,k+1)$ and $Y(k+1,l+1)$ and generalize to arbitrary two-row tableaux, with clear decoupling patterns that reflect the underlying Young diagram geometry. The framework supports smooth deformations to ($A$)dS, clarifies unitary windows, and provides a groundwork for potential interactions among higher-spin mixed-symmetry fields.

Abstract

In this paper we complete our construction of frame-like gauge invariant description for massive mixed symmetry tensor fields corresponding to arbitrary Young tableau with two rows started in [1]. We consider general massive theory in (A)dS spaces with arbitrary cosmological constant as well as all special limits which exist both in de Sitter and in anti-de Sitter spaces.

Figures (11)

• Figure 1: General massive $Y(k+1,k+1)$ theory
• Figure 2: Massless limit in $AdS$ space
• Figure 3: Unitary partially massless limit in $dS$ space
• Figure 4: Example of non-unitary partially massless limit in $dS$ space
• Figure 5: General massive $Y(k+1,l+1)$ theory