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Spontaneous symmetry breaking: a view from derived geometry | | Elliott
; Chris
; Gwilliam
; Owen
; | | Date: |
8 Aug 2020 | | Abstract: | We examine symmetry breaking in field theory within the framework of derived
geometry, as applied to field theory via the Batalin-Vilkovisky formalism. Our
emphasis is on the standard examples of Ginzburg-Landau and Yang-Mills-Higgs
theories and is primarily interpretive. The rich, sophisticated language of
derived geometry captures the physical story elegantly, allowing for sharp
formulations of slogans (e.g., for the Higgs mechanism, that the unstable
ghosts eat the Goldstone modes). Rewriting these results in the BV formalism
provides, as one nice payoff, a reformulation of ’t Hooft’s family of
gauge-fixing conditions for spontaneously broken gauge theory that behaves well
in the $xi o infty$ limit. | | Source: | arXiv, 2008.03599 | | Services: | Forum | Review | PDF | Favorites | |
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