Vertex Constraints in 3D Higher Spin Theories.

Area of Science:

• Theoretical Physics
• Quantum Field Theory
• String Theory

Background:

• Higher-spin gravities extend Einstein's theory with fields of increasing spin.
• Gauge invariance is a fundamental principle in physics, ensuring physical quantities are independent of certain transformations.
• Understanding interactions in higher-spin theories is crucial for developing a complete theory of quantum gravity.

Purpose of the Study:

• To investigate the constraints imposed by gauge invariance on higher-order interactions.
• To determine the structure of nonlinear interactions between massless bosonic fields in 3D higher-spin gravities.
• To identify which fields can participate in quartic and higher-order interaction vertices independent of cubic ones.

Main Methods:

• Analysis of gauge invariance conditions.
• Focus on the transverse-traceless part of field interactions.
• Derivation of interaction vertices for massless bosonic fields.

Main Results:

• Gauge invariance significantly constrains higher-order interaction vertices.
• Vertices independent of the cubic ones can only involve scalar and Maxwell fields.
• The full nonlinear interactions of massless higher-spin fields are completely determined by the cubic vertex.

Conclusions:

• The structure of nonlinear interactions in 3D higher-spin gravities is highly constrained.
• The cubic vertex plays a pivotal role in defining all higher-order interactions.
• These findings simplify the study of higher-spin theories and their potential applications.