Effective Field Theory for a Three-Brane Universe

TL;DR

This work delivers a minimal, systematic effective field theory framework for a three-brane universe in a higher-dimensional bulk, with Standard Model fields confined to the brane and gravity propagating in the bulk. It constructs the bosonic sector, develops a robust treatment of fermions via an induced vierbein to realize four-dimensional chirality, and establishes gauge-fixing and power-counting procedures to sustain renormalization in the EFT context. By framing the brane as a spontaneous breaking of $d$-dimensional Poincaré symmetry, it connects the dynamics to the Volkov/CCWZ-like formalism and clarifies how brane fluctuations couple to bulk gravity and brane matter, including the handling of transverse momentum exchange. The framework provides a versatile, low-energy toolkit to study brane dynamics, gravity–brane couplings, and potential mechanisms for inter-brane mediation of symmetry breaking, without committing to a specific ultraviolet completion.

Abstract

A general effective field theory formalism is presented which describes the low-energy dynamics of a 3-brane universe. In this scenario an arbitrary four-dimensional particle theory, such as the Standard Model, is constrained to live on the world-volume of a (3+1)-dimensional hypersurface, or ``3-brane'', which in turn fluctuates in a higher-dimensional, gravitating spacetime. The inclusion of chiral fermions on the 3-brane is given careful treatment. The power-counting needed to renormalize quantum amplitudes of the effective theory is also discussed. The effective theory has a finite domain of validity, restricting it to processes at low enough energies that the internal structure of the 3-brane cannot be resolved.