Abstract
Scalars and fermions can arise as Goldstone modes of non-linearly realised extensions of the Poincare group (with important implications for the soft limits of such theories): the Dirac-Born-Infeld scalar realises a higher-dimensional Poincare symmetry, while the Volkov-Akulov fermion corresponds to super-Poincare. In this paper we classify extensions of the Poincare group which give rise to a vector Goldstone mode instead. Our main result is that there are no healthy interacting $U(1)$ gauge theories that non-linearly realise space-time symmetries beyond gauge transformations. This implies that the special soft limits of e.g. the Born-Infeld vector cannot be explained by space-time symmetries.
Highlights
Nonlinear realizations of spontaneously broken symmetries form an important and interesting part of quantum field theory
Scalars and fermions can arise as Goldstone modes of nonlinearly realized extensions of the Poincaregroup: the Dirac-Born-Infeld scalar realizes a higher-dimensional Poincaresymmetry, while the Volkov-Akulov fermion corresponds to superPoincare
The possible nonlinear realizations of space-time symmetries are always accompanied by enhanced soft limits, and vice versa
Summary
Nonlinear realizations of spontaneously broken symmetries form an important and interesting part of quantum field theory. Goldstone’s theorem does not apply to spontaneously broken space-time symmetries [7,8], for which there can be fewer Goldstone modes than broken generators: every spontaneously broken generator that commutes with translations into another such generator gives rise to an inessential Goldstone [8,9,10]. The latter can be removed from the low-energy effective field theory (EFT) by imposing inverse Higgs constraints [8].
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