# Gauging the higher-spin-like symmetries by the Moyal product

**Authors:** Maro Cvitan, Predrag Dominis Prester, Stefano Giaccari, Mateo Paulišić, Ivan Vuković  
**arXiv:** [2102.09254](https://arxiv.org/abs/2102.09254)  
**Date:** 2021-02-18  
**Summary page:** https://www.summarizepaper.com/en/paper/2102.09254v1/

## Key points

- The paper introduces a novel approach to analyzing rigid higher derivative symmetries in free relativistic actions on flat spacetime
- An off-shell definition is presented based on fields defined on a 2d-dimensional master space with a symplectic structure
- Utilizes the Moyal commutator to define an infinite dimensional Lie algebra of gauge transformations, allowing for well-defined weakly non-local actions in both the gauge and matter sectors
- Demonstrates the utility of their formalism by calculating basic 4-point tree-level amplitudes for matter fields, showing differences between ordinary spacetime matter and master matter behavior
- Introduces a covariant potential that acts as a generalised vielbein and expresses the theory in matrix model form, revealing additional phases within its structure
- Thoroughly analyzes the symmetries of the theory, leading to the explicit construction of conserved currents
- Focuses on the spin-2 sector to demonstrate emergent geometry exhibiting teleparallelism under disguise, with implications for theoretical physics.

## Summary

The paper "Gauging the higher-spin-like symmetries by the Moyal product" presents a novel approach to analyzing rigid higher derivative (higher spin) symmetries in free relativistic actions on flat spacetime. The authors introduce an off-shell definition based on fields defined on a 2d-dimensional master space with a symplectic structure, building upon previous work by Bonora et al. and Bekaert et al. They utilize the Moyal commutator to define an infinite dimensional Lie algebra of gauge transformations, allowing for well-defined weakly non-local actions in both the gauge and matter sectors. This approach is reminiscent of Yang-Mills theory and permits an off-shell description in Euclidean theory. The authors demonstrate the utility of their formalism by calculating basic 4-point tree-level amplitudes for matter fields, finding that ordinary spacetime matter does not scatter into non-trivial angles while amplitudes for master matter exhibit softer UV behavior compared to Quantum Electrodynamics (QED). Drawing parallels with non-commutative field theories, they introduce a covariant potential that acts as a generalised vielbein and express the theory in matrix model form, uncovering additional phases within its structure. The symmetries of the theory are thoroughly analyzed, leading to the explicit construction of conserved currents. By focusing on the spin-2 sector, the authors demonstrate that the emergent geometry exhibits teleparallelism under disguise, with a linear connection opposite to Weitzenböck's. This comprehensive study sheds light on new perspectives for understanding higher-spin-like symmetries and their implications in theoretical physics.