Shift Symmetries in (Anti) de Sitter Space

TL;DR

The paper identifies discrete-mass shift symmetries for bosonic fields of all spins in maximally symmetric (A)dS spaces, showing they originate from partial masslessness and can be understood via ambient-space and PM reducibility parameters.It extends the flat-space tower of shifts (constant, galileon, and special galileon) to (A)dS, and classifies how these symmetries can be deformed for scalar theories, yielding (A)dS analogues of galileons and special galileons with second-order equations of motion.For interacting scalars, the authors construct invariant actions for $k=0,1,2$ under undeformed and deformed algebras, including deformations to $rak{so}(D+2)$ and $rak{sl}(D+1)$, and provide detailed ambient/coset formulations of the resulting theories.The work suggests deep connections to PM higher-spin algebras, AdS/CFT boundary symmetries, and enhanced soft limits, and outlines directions for extending the framework to massive higher-spin interactions and to fermionic or mixed-symmetry fields.

Abstract

We construct a class of extended shift symmetries for fields of all integer spins in de Sitter (dS) and anti-de Sitter (AdS) space. These generalize the shift symmetry, galileon symmetry, and special galileon symmetry of massless scalars in flat space to all symmetric tensor fields in (A)dS space. These symmetries are parametrized by generalized Killing tensors and exist for fields with particular discrete masses corresponding to the longitudinal modes of massive fields in partially massless limits. We construct interactions for scalars that preserve these shift symmetries, including an extension of the special galileon to (A)dS space, and discuss possible generalizations to interacting massive higher-spin particles.

Figures (4)

• Figure 1: Masses in dS space in units of $H^2$ (masses in AdS space are the negatives of these, in units of $1/L^2$). Theories along the (red) diagonal have no apparent symmetry, but the $s=0$ case in $D=4$ corresponds to the conformally coupled scalar. Each (blue) square below the diagonal is a PM field labelled by spin $s$ and depth $t$. The corresponding longitudinal mode is the theory reflected across the diagonal, and has a shift symmetry of level $k$. The parameter $k$ is uniform along diagonal lines in the top half of the square.
• Figure 2: Conformal dimensions of the PM and shift-symmetric fields. Each (blue) filled circle below the diagonal line is a PM field and the corresponding shift-symmetric longitudinal mode is the (black) circle obtained by reflecting about the dotted line $\Delta=s+d-1$. The open circles on the dotted line belong to the same family as the conformally coupled scalar in $D=4$, corresponding to the diagonal squares in Figure \ref{['masstablegeneralD']}.
• Figure 3: Plots of $H^2V(\phi)/\Lambda^{D+2}$ for the special galileon in dS space in various dimensions. The horizontal axes show the dimensionless combination $H^2\phi/ \Lambda^{(D+2)/2}$.
• Figure 4: Potential for the $D=4$ special galileon in dS space.