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Klein, Remko; Malek, Emanuel; Roest, Diederik; Stefanyszyn, David (2018): No-go theorem for a gauge vector as a spacetime Goldstone mode. In: Physical Review D, Vol. 98, No. 6, 65001
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Scalars and fermions can arise as Goldstone modes of nonlinearly realized extensions of the Poincare group (with important implications for the soft limits of such theories): the Dirac-Born-Infeld scalar realizes 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 (ghost free) interacting U(1) gauge theories that nonlinearly realize space-time symmetries beyond gauge transformations. This implies that the structure of e.g., Born-Infeld theory is not fixed by symmetry.