Topological order in the color-flavor locked phase of (3+1)-dimensional U ( N ) gauge-Higgs system Ryo Yokokura (KEK) 2019. 8. 19 Strings and Fields 2019 @ YITP Based on Y. Hidaka, Y Hirono, M. Nitta, Y. Tanizaki, RY, 1903.06389
v v v <latexit sha1_base64="hnMbFVtNdRtDXPqv/E2K32Tz5A=">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</latexit> Overview of this talk = exp 2 π ik 3 k + 1 ∈ Z 3 k +1 (for N = 3 ) Color-flavor locked phase of a U ( N ) gauge theory with N -Higgs fields is topologically ordered if the Higgs fields have non-trivial U (1) charge k . • Non-Abelian vortex and Wilson loop have a Z Nk +1 fractional linking phase. • There are Z Nk +1 1- and 2-form symmetries , and both of them are spontaneously broken.
1 Introduction 2 Topological order in Abelian Higgs model 3 Topological order in CFL phase of U ( N ) gauge-Higgs system
Higgs phase of gauge theories • Massive gauge fields • Some Nambu–Goldstone (NG) bosons are eaten • Admitting extended objects e.g. vortex • Vortex in many contexts: • magnetic vortex in superconductor (SC), • (local) cosmic strings in cosmology Higgs phases can be further classified by “topological order”
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Topological order & p -form symmetry [ Banks & Seiberg ’10; Kapustin & Seiberg ’14; Gaiotto et al. 14 ] Topologically ordered phase can be characterized by 1. p -form symmetry and their breaking 2. Fractional linking phases between non-local operators In this talk, we consider the possibility of topologicaly ordered phase in 3 + 1 dim. non-Abelian gauge theories in order to understand phases of non-Abelian gauge theories.
Topological order in Abelian Higgs model Review based on Hansson, et al. 04,; Banks & Seiberg ’10; Seiberg & Kapustin ’14; Gaiotto, et al. ’14
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