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Higher-Spin Interactions: three-point functions and beyond

Massimo Taronna

TL;DR

This work develops an ambient-space formulation for higher-spin interactions on constant-curvature backgrounds, focusing on the TT sector and the Noether procedure to connect HS vertices to Yang–Mills amplitudes. It builds cubic and quartic HS vertices from YM-like building blocks, analyzes flat-space limits and FV-type connections, and introduces a minimal nonlocal scheme to handle quartic consistency while preserving unitarity constraints. The results illuminate the role of nonlocalities, the inverse cosmological-constant expansion, and the string/HS correspondence, with implications for AdS/CFT and tensionless-string limits. Overall, the thesis provides a systematic, ambient-space-based framework for organizing HS interactions across spin, order, and background, highlighting both the potential consistency channels and the fundamental obstructions highlighted by Weinberg’s theorem.

Abstract

This Thesis reviews some recent developments about higher-spin interactions in flat and constant curvature backgrounds. Particular attention is given to the ambient-space formulation of the problem, both at the cubic and at the quartic order, with some emphasis on the structure of the solution to the Noether procedure that can be expressed in terms of powers of the standard Yang Mills amplitudes. We also highlight how some aspects of String Theory appear to reflect key properties of Field Theory that go beyond its low energy limit.

Higher-Spin Interactions: three-point functions and beyond

TL;DR

This work develops an ambient-space formulation for higher-spin interactions on constant-curvature backgrounds, focusing on the TT sector and the Noether procedure to connect HS vertices to Yang–Mills amplitudes. It builds cubic and quartic HS vertices from YM-like building blocks, analyzes flat-space limits and FV-type connections, and introduces a minimal nonlocal scheme to handle quartic consistency while preserving unitarity constraints. The results illuminate the role of nonlocalities, the inverse cosmological-constant expansion, and the string/HS correspondence, with implications for AdS/CFT and tensionless-string limits. Overall, the thesis provides a systematic, ambient-space-based framework for organizing HS interactions across spin, order, and background, highlighting both the potential consistency channels and the fundamental obstructions highlighted by Weinberg’s theorem.

Abstract

This Thesis reviews some recent developments about higher-spin interactions in flat and constant curvature backgrounds. Particular attention is given to the ambient-space formulation of the problem, both at the cubic and at the quartic order, with some emphasis on the structure of the solution to the Noether procedure that can be expressed in terms of powers of the standard Yang Mills amplitudes. We also highlight how some aspects of String Theory appear to reflect key properties of Field Theory that go beyond its low energy limit.

Paper Structure

This paper contains 34 sections, 391 equations, 2 figures.

Table of Contents

  1. Ambient Space Formulation
  2. (A)dS Geometry
  3. (A)dS Dynamics
  4. Massless representations
  5. Massive representations
  6. Partially-massless representations
  7. Ambient space measure
  8. Noether Procedure
  9. HS Free Theory on constant curvature backgrounds
  10. Free Ambient Lagrangians
  11. TT part of the action
  12. HS Interaction on constant curvature backgrounds
  13. Cubic interactions: general setting
  14. Consistent cubic interactions of massless HS fields
  15. Flat solution
  16. ...and 19 more sections

Figures (2)

  • Figure 1: Various cubic building blocks for the $G^{\,(i)}_{12\ldots n}$'s.
  • Figure 2: Various domain where to apply the Noether procedure. The TT domain is the smallest one for which one can keep a covariant description but it is well defined only on-shell or off-shell as an equivalence class.