Shift-symmetric spin-1 theories

Abstract

We study interacting massive spin-1 theories in de Sitter (dS) and anti-de Sitter (AdS) space that possess shift symmetries parametrized by (A)dS Killing vectors. We show how they emerge from the massless limit of massive spin-2 theories on (A)dS space. In the case of massive gravity, the corresponding spin-1 theory realizes a symmetry breaking pattern that takes two copies of the (A)dS isometry group down to a diagonal subgroup. By taking the flat space limit of this theory, we find a new symmetry of the decoupling limit of massive gravity in flat space. This symmetry acts on the vector modes, is parametrized by an antisymmetric tensor, and fixes the nonlinear structure of the scalar-vector sector of the decoupling limit.

Multi-spin soft bootstrap and scalar-vector Galileon

“…Assume the Lagrangian which couple the general Galileon with massless vector that has been derived in [55] as the most general scalar-vector sector of the decoupling limit of the massive spin-2 pseudolinear theory, namely…”

“…as well as with respect to the Galileon symmetry (6.26). Such theories correspond to the scalar-vector sector of the decoupling limit of the massive gravity as discussed in details in [55]. The Lagrangian of these theories can be obtained from the "seed" Lagrangian (6.24) by the deformation procedure which produces infinite tower of descendant terms from each scalar-vector interacting terms of the Lagrangian (6.24).…”

“…We focus on the case of scalar-vector theories with fixed power-counting and demonstrate that there is a unique theory fixed by these soft theorems which we call Special scalar-vector Galileon as the scalar part of this theory corresponds to the Special Galileon. We end with the discussion of more general vector Galileon theories which are related to theories studied in [55].…”

EFT of interacting spin-2 fields

“…through terms being total derivatives. Hence we either have 27) assuming the helicity-two modes interact with other modes at the same Λ 3 scale or 28) assuming the helicity-two interactions are additionally suppressed, as is natural in models which for we may diagonalize/demix the helicity-2 interactions at leading order in the decoupling limit (as in eq. (6.18)).…”

“…Massive spin-1 generalizations to the classic Proca action that restrict to second order equations of motion have been studied, for example, in [24][25][26][27], but general EFTs allow for infinitely more interactions. A novel shift-symmetric extension to interacting massive spin-1 theories in de Sitter and anti-de Sitter spacetimes has recently been made in [28]. In the case of a single massive spin-2 which can be coupled to matter, the most general ghost-free (two derivative, five propagating degrees of freedom) nonlinear theory in four spacetime dimensions is the de Rham-Gabadadze-Tolley theory of massive gravity [29].…”