Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Generating functions of (partially-)massless higher-spin cubic interactions

Euihun Joung, Luca Lopez, Massimo Taronna

TL;DR

This work develops generating functions for cubic interactions of (partially-)massless higher-spin fields in (A)dS via the ambient-space formalism. It reduces the problem to a factorized system of higher-order PDEs in invariants $Y_i$ and $Z_i$, whose solutions enumerate all consistent couplings; crucially, the solution space expands when mass-squared values hit integer values in units of the cosmological constant, revealing new $G$-type couplings that can yield non-Abelian gauge deformations. A key technical contribution is organizing the solutions with spin-independent bases $B_P$ and $B_Q$ (and their tilde{Q} and Q variants), and analyzing intersections of solution spaces when multiple (P)M fields participate. The results distinguish genuine (A)dS features from flat-space intuition, illustrate how mass patterns govern the presence of non-Abelian interactions, and provide concrete examples (notably 4-4-2) that recover and extend previous findings through explicit generating functions and basis correspondences.

Abstract

Generating functions encoding cubic interactions of (partially-)massless higher-spin fields are provided within the ambient-space formalism. They satisfy a system of higher-order partial differential equations that can be explicitly solved due to their factorized form. We find that the number of consistent couplings increases whenever the squares of the field masses take some integer values (in units of the cosmological constant) and satisfy certain conditions. Moreover, it is shown that only the supplemental solutions can give rise to non-Abelian deformations of the gauge symmetries. The presence of these conditions on the masses is a distinctive feature of (A)dS interactions that has in general no direct counterpart in flat space.

Generating functions of (partially-)massless higher-spin cubic interactions

TL;DR

This work develops generating functions for cubic interactions of (partially-)massless higher-spin fields in (A)dS via the ambient-space formalism. It reduces the problem to a factorized system of higher-order PDEs in invariants and , whose solutions enumerate all consistent couplings; crucially, the solution space expands when mass-squared values hit integer values in units of the cosmological constant, revealing new -type couplings that can yield non-Abelian gauge deformations. A key technical contribution is organizing the solutions with spin-independent bases and (and their tilde{Q} and Q variants), and analyzing intersections of solution spaces when multiple (P)M fields participate. The results distinguish genuine (A)dS features from flat-space intuition, illustrate how mass patterns govern the presence of non-Abelian interactions, and provide concrete examples (notably 4-4-2) that recover and extend previous findings through explicit generating functions and basis correspondences.

Abstract

Generating functions encoding cubic interactions of (partially-)massless higher-spin fields are provided within the ambient-space formalism. They satisfy a system of higher-order partial differential equations that can be explicitly solved due to their factorized form. We find that the number of consistent couplings increases whenever the squares of the field masses take some integer values (in units of the cosmological constant) and satisfy certain conditions. Moreover, it is shown that only the supplemental solutions can give rise to non-Abelian deformations of the gauge symmetries. The presence of these conditions on the masses is a distinctive feature of (A)dS interactions that has in general no direct counterpart in flat space.

Paper Structure

This paper contains 37 sections, 150 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Ambient-space formalism
  4. Cubic-interaction problem
  5. Summary of the results
  6. General structure of the solutions
  7. Cubic interactions as a vector space
  8. Choice of basis
  9. Solutions to one equation
  10. Massless equation
  11. General solution
  12. Change of basis
  13. $\tilde{Q}$ solutions
  14. $Q$ solutions
  15. Partially-massless equation
  16. ...and 22 more sections

Figures (2)

  • Figure 1: Unitary values of $\mu$ (for $s>0$) .
  • Figure 2: $\tilde{H}$- and $G$-couplings. Non-abelian couplings are a subset of the $G$-couplings that can not be written as $\tilde{H}$-couplings.