Abstract
We discuss the issue of complementarity between the confining phase and the Higgs phase for gauge theories in which there are no light particles below the scale of confinement or spontaneous symmetry breaking. We show with a number of examples that even though the low energy effective theories are the same (and trivial), discontinuous changes in the structure of heavy stable particles can signal a phase transition and thus we can sometimes argue that two phases which have different structures of heavy particles that cannot be continuously connected and thus the phases cannot be complementary. We discuss what this means and suggest that such “stability conditions” can be a useful physical check for complementarity.
Highlights
This note is an attempt to understand better the classic papers by Fradkin and Shenker [1], Banks and Rabinovici [2], ’t Hooft [3] and Dimopoulos, Raby and Susskind [4,5] related to complementarity between the Higgs and confining phases in gauge theories.1 In model building, this is important because it sometimes happens that one takes a Higgsed theory that is perturbatively calculable for small couplings and pushes it into regions in which perturbation theory is questionable
If the Higgs phase and confining phase are complementary, that is if there is no phase transition separating the Higgs phase and confining phase, one may hope that this will give a picture of the physics that is qualitatively correct even if it is not quantitatively reliable
The Higgs phase and the confining phase are distinguished in spite of the fact that there is nothing in the low energy theory in either case, because the stable heavy particle sectors have different global U (1) charges
Summary
This note is an attempt to understand better the classic papers by Fradkin and Shenker [1], Banks and Rabinovici [2], ’t Hooft [3] and Dimopoulos, Raby and Susskind [4,5] related to complementarity between the Higgs and confining phases in gauge theories.1 In model building, this is important because it sometimes happens that one takes a Higgsed theory that is perturbatively calculable for small couplings and pushes it into regions in which perturbation theory is questionable. In the Higgs phase, all the triality and duality zero gauge singlet combinations like 3 (3, 1)2 scalars or 6 (3, 2)1 massive vector bosons all have U (1) charges which are multiples of 6.
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