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Soft theorems and spontaneous symmetry breaking
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The soft photon and soft graviton theorems of Weinberg are known to derive from conservation laws associated with asymptotic symmetries. Within the corresponding classical theories, one often speaks of spontaneous symmetry breaking and vacuum degeneracy, but a genuine quantum description of this phenomenon has largely been lacking. Here we establish spontaneous breaking of asymptotic symmetries and the existence of Goldstone `particles' using exclusively the language of quantum field theory. This is made possible through the reformulation of massless scattering theory in terms of carrollian conformal field theory, and the observation that soft theorems correspond to Ward identities of broken symmetries. A suitable version of Goldstone theorem shows that there must exist zero-momentum particles described by conformal fields on the celestial sphere, in agreement with the common lore. More specifically, these belong to unitary representations in the discrete series of the Lorentz group, and are therefore naturally equipped with logarithmic two-point functions. We discuss the relevance of these observations to the problem of infrared divergences that scattering amplitudes suffer from.
Forward citations
Cited by 4 Pith papers
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Carrollian Dictionary for Massive Particles at Null Infinity
Massive one-particle states are encoded on null infinity by projecting their momenta onto null frames, giving an isometric map into the complete Carrollian representation.
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Dressed States Call for Logarithmic Asymptotic Symmetries
Dressed particles with soft-boson clouds are irreducible unitary representations of asymptotic symmetry groups only after adding logarithmic 'dual' symmetries, which supply the needed Heisenberg central extension.
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A Soft Theorem from vertex-like operators in BFSS Theory
In the large-distance effective theory of BFSS, graviton-like vertex operators are shown to have correlators that factorize in the soft limit at leading and subleading order, matching the predicted BFSS soft theorem.
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Lectures on Carrollian Holography
Massless scattering amplitudes, including gravitons, can be recast as correlators of a carrollian conformal field theory on null infinity, but the non-perturbative bootstrap program remains incomplete.
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