Spontaneously Broken Gauge Theories and the Coset Construction

Abstract

The methods of non-linear realizations have proven to be powerful in studying the low energy physics resulting from spontaneously broken internal and spacetime symmetries. In this paper, we reconsider how these techniques may be applied to the case of spontaneously broken gauge theories, concentrating on Yang-Mills theories. We find that coset methods faithfully reproduce the description of low energy physics in terms of massive gauge bosons and discover that the Stückelberg replacement commonly employed when treating massive gauge theories arises in a natural manner. Uses of the methods are considered in various contexts, including generalizations to $p$-form gauge fields. We briefly discuss potential applications of the techniques to theories of massive gravity and their possible interpretation as a Higgs phase of general relativity.

28 pages. v2: added references

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• Resummation of Massive Gravity
• Counting rule for Nambu-Goldstone modes in nonrelativistic systems
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• Generalized Galileon Duality
• Nonlinear realizations of symmetries and unphysical Goldstone bosons
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Cited by in corpus (7)

• Dispersion relations of Nambu-Goldstone modes at finite temperature and density
• Counting Nambu-Goldstone modes of higher-form global symmetries
• Effective field theories for gapless phases with fractons via a coset construction
• Large Charge Sector of 3d Parity-Violating CFTs
• Gauged Galileons
• The coset construction for particles of arbitrary spin
• Spontaneous Breaking of (2+1)-dimensional Lorentz Symmetry by an antisymmetric tensor