The coset construction for particles of arbitrary spin

TL;DR

This paper introduces a new coset construction method to generate effective actions for particles of arbitrary spin, including fermions, by breaking Poincaré symmetry, and explores novel inverse Higgs constraints and spin-orbital couplings.

Contribution

It develops a partial coset construction for systems breaking Poincaré symmetry, enabling the description of diverse Goldstone excitations, including fermionic and extended particles.

Findings

Recovered known supersymmetry gauge symmetries for spin s particles.

Discovered a novel inverse Higgs constraint for massless particles.

Derived a new action describing particles with intrinsic spin and finite size.

Abstract

When a Poincar\'e-invariant system spontaneously breaks continuous internal symmetries, Goldstones's theorem demands the existence of massless, spin-zero excitations in a one-to-one correspondence with the broken symmetry generators. When a system spontaneously breaks Poincar\'e symmetry, however, the kinds of excitations that satisfy Goldstone's theorem can be quite unusual. In particular, they may have any spin and need not be particles or even quasiparticles. The standard coset construction used to formulate effective actions of Goldstones, however, is rather restrictive and is incapable of generating the full spectrum of possibilities allowed by Goldstone's theorem. We propose a (partial) remedy to this problem by postulating a novel coset construction for systems that spontaneously break Poincar\'e symmetry. This new construction is capable of generating effective actions with a wide range of Goldstone excitations---including fermionic degrees of freedom---even when all symmetries are bosonic. To demonstrate it's utility, we focus on constructing effective actions for point particles of various spins. We recover the known result that a particle of spin $s$ requires an $\mathcal N=2s$ supersymmetric worldline reparameterization gauge symmetry, which we implement at the level of the coset construction. In the process, we discover that massless particles require a novel kind of inverse Higgs constraint that bears some resemblance to the dynamical inverse Higgs constraints that appear in certain fermi liquid effective field theories. We then consider particles that, in addition to quantum spin, have finite spatial extent and are free to rotate. We derive a novel action for such particles and find a `spin-orbital' coupling between the intrinsic quantum spin and the physical-rotation degrees of freedom.