Deconfinement and Duality of (super) Yang-Mills on Toroidially-Compactified Spacetimes for all Gauge Groups
Year: 2015
Type: dissertation
Abstract: I study gauge theories for any gauge group G, in particular Yang-Mills (YM) theories including super Yang-Mills (SYM) and mass deformed super Yang-Mills (SYM*), on toroidially compactified spacetimes. Each compact direction introduces r=rank(G) massive scalar fields into the theory and results in an effective potential added to the Lagrangian of the theory. The mathematics of such potentials is interesting, however important applications begin with special simple cases. The first case studied here is finite temperature super Yang-Mills where a thermal circle of size 1/T is introduced and the temperature dependence of phases of the theory can be studied including the deconfinement phase transition. Further compactification on a spatial circle of size L is useful. For small such L we are in a regime where semiclassical calculations can be performed at weak coupling. The transition is found to be mediated by the competition between non-perturbative objects including monopole-instantons and 'exotic' topological molecules: neutral and magnetic bions composed of BPS and KK monopole constituents, with charges in the co-root lattice of the gauge group G, as well as electrically charged W-bosons (and wino superpartners in the case of SYM) with charges in the root lattice of G.\\ The second case is super Yang-Mills on circle compactified spacetimes, but with softly broken supersymmetry with a small mass m for the adjoint fermion. This is interesting as there is a conjectured continuity relating this theory, and its quantum deconfining phase transition at some critical mass for the gluino, to pure Yang-Mills with a thermal deconfinement transition at some critical temperature. Furthermore, on torus compactified spacetimes, I determine a duality for all G to a 2D Coulomb gas of bions of different charges of their monopole constituents, and W-bosons of both scalar and electric charges. Aharonov-Bohm interactions exist between magnetic bions and W-bosons. New scalar interactions of W-bosons and neutral bions exist which attract like charges, as opposed to the magnetic and electric charges where like charges repel. I then propose a dual lattice 'affine' XY-model with symmetry-breaking perturbations coupled to the scalar field, for SU(2), and show results of lattice studies to determine the nature of the deconfinement phase transition and propose generalizations for other groups.
Source: TSpace (University of Toronto)
Author: Brett Teeple
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2603555537