An Introduction to Higher-Spin Theories: The Case of Spin-4

• Grant number: 25/18083-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: December 01, 2025
• End date: November 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Elias Leite Mendonça
• Grantee: Maria Isabel Coelho Maués
• Host Institution: Faculdade de Engenharia (FEG). Universidade Estadual Paulista (UNESP). Campus de Guaratinguetá. Guaratinguetá , SP, Brazil

Abstract

The formulation of consistent theories for higher-spin particles remains a central challenge in theoretical physics, especially in four dimensions, where the presence of auxiliary fields and the preservation of unitarity hinder progress. In $D=2+1$, however, it is possible to construct local self-dual models with higher-order derivatives that propagate physical degrees of freedom without auxiliary fields. Recent works have shown that, through the generalized soldering procedure, massive spin-3 models analogous to \textit{New Massive Gravity} can be obtained. This project aims to extend such an approach to the investigation of geometric structures for higher spins, in particular spin-4, analyzing the formulation of gauge-invariant actions and exploring generalizations of the Ricci, Einstein, and Schouten tensors. In addition to consolidating the student's training in classical field theory and relativity, the project is expected to pave the way for future studies on massive higher-spin theories and their extensions to interactive and curved contexts.