Cubic Interactions of Massless Bosonic Fields in Three Dimensions

Area of Science:

• Theoretical Physics
• Quantum Gravity
• String Theory

Background:

• Higher-spin gravity theories are challenging to formulate, especially with matter interactions.
• Existing formulations often lack a clear way to incorporate matter.
• A metric-like approach offers a promising avenue for constructing interacting theories.

Purpose of the Study:

• To construct nontrivial Lagrangian theories of higher-spin gravity in three dimensions using a metric-like formulation.
• To classify cubic interactions for arbitrary triples of massless fields.
• To derive universal coupling to gravity for any spin.

Main Methods:

• Development of a metric-like formulation for higher-spin gravity.
• Derivation of a complete classification of cubic interactions for massless fields.
• Analysis of spin values and triangle inequalities for interaction vertices.

Main Results:

• At most one cubic interaction vertex exists for any given triple of spins (with one exception).
• No vertices exist for spin values violating strict triangle inequalities with at least two spins greater than one.
• Universal coupling to gravity for any spin is derived.

Conclusions:

• The classification of cubic interactions provides selection rules for three-point functions in 2D conformal field theory.
• The derived classification is argued to persist in arbitrary Einstein backgrounds.
• This work represents a significant step towards building interacting higher-spin gravity theories.