## Arts & Sciences Electronic Theses and Dissertations

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#### Title

Phase Structure of Gauge Theories on R3 X S1

Summer 8-15-2012

#### Author's School

Graduate School of Arts and Sciences

Physics

#### Degree Name

Doctor of Philosophy (PhD)

Dissertation

#### Abstract

We review recent work on confining gauge theories on $R^3 \times S^1$. $SU(N)$ gauge theories with either adjoint fermions with periodic boundary condition on $S^1$ or particular deformation potentials can lead to a restoration of center symmetry and confinement for sufficiently small $L$ of $S^1$. At small $L$, we can reliably use perturbation theory to compute the effective potential in terms of the Polyakov loop, which is an order parameter for confinement. When center symmetry is restored, the gauge field in the compact direction, $A_0$, acquires an expectation value and acts like a Higgs field, breaking the symmetry as $SU(N) \rightarrow U(1)^{N-1}$. Consequently, there are nontrivial solutions of $N-1$ usual BPS monopoles and one Kaluza-Klein monopole. A condensation of the monopoles gives rise to a linear potential between two charges and thus realizes the dual Meissner effect as a confinement mechanism. Moreover, the string tension and mass gap can be calculated analytically in these models. In the case of adjoint fermions, we show a connection between the large-$L$ and small-$L$ confined phases by developing a phenomenological model called PNJL. Also we show that the extension of deformed gauge theories with scalar fields allows us to study the relationship between the Higgs and confined phases. Having the confining theories under analytical control, we are able to explore the phase structure of gauge theories on $R^3 \times S^1$.

English (en)

#### Chair and Committee

Michael C Ogilvie

#### Committee Members

Michael Ogilvie, Mark Alford, Claude Bernard, Brian Blank, Francesc Ferrer