Mathematical Underpinnings of Fundamental Gauge Theories

Who: Nicolai Sandal Banke (CP3-Origins)
When: Monday, May 30, 2016

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This thesis investigates the properties of potentials with a Lorentzian symmetry, that is, symmetries with symmetry group SO(N,M). Such a symmetry yields a direction in field space where the potential vanishes, and in the massless case this direction turns out to be the minimum of the potential. Such a symmetry is then convenient for Coleman–Weinberg symmetry breaking to occur, since no constraints on the coupling need to be imposed. Coleman–Weinberg symmetry breaking is investigated for a toy model with an SO(1,1) symmetry, and with two quartic couplings and one portal coupling.
Next, the phase structure is studied. The β functions are calculated for a theory with N flavors of the fields with coupling λ0 and M flavors of the fields with coupling λ1. In the case where M = N and λ0 = λ1, the flow diagram, at the 1-loop level, exhibits a phase where the potential is stable at all energy scales and a phase where instability occurs in the infrared. The 2-loop phase diagrams appear to qualitatively support this phase structure.