Topology, symmetry, and phase transitions in lattice gauge ... - tuprints

2 introduction
While waiting on experimental results from RHIC, LHC and the Compressed
Baryonic Experiment at FAIR [12], theorists perform their own experiments by
pushing and prodding QCD in various ways. There is much to be learned by changing
the number of colors or flavors of quarks, the number of spacetime dimensions,
and taking diametric extremes such as the limits of massless or infinitely heavy
quarks. By keeping track of the similarities and differences, one has a chance of
shaking out the most important qualitative features of QCD.
The long range correlations induced by strong interactions prompt one to consider
the large scale structure of the fields. Insight may be gained by identifying
the dynamically relevant configurations, and determining their fate as QCD and
QCD-like theories become weakly interacting at extreme temperatures and pressure.
Such fluctuations tend to be topological and permit a semi-classical interpretation.
They are objects such as vortices, monopoles, and instantons, which are
closely linked with the existence of global symmetries and whether they are realized
or spontaneously broken in various thermodynamic phases [13].
Such themes tie together the work presented in this thesis. 1 Lattice field theory is
employed throughout as a non-perturbative tool. Not only does it allow for quantitative
calculations with well controlled approximations, but its formulation as a
statistical system highlights the parallels between gauge theories and spin systems.
Global center symmetry, which is obtained in the limit of static quarks, is of special
interest. It allows one to relate the finite temperature deconfinement transition
to the spontaneous magnetization of a spin system. For pure SU(3) gauge theory
in 3 + 1 d, the transition is weakly first order, so an effective description in terms
of spins breaks down at some scale. In Chapter 3 we instead study SU(N) gauge
theories in 2 + 1 d, which have second order transitions for N < 4. The goal is to
see how far the correspondence with spin systems can take us, and to gain further
insight into the universal aspects of the deconfinement transition. Here we are
confronted by the Kramers-Wannier duality of N-state Potts models, which are all
self-dual in 2d. This allows for a precision study of the gauge theories, and emphasizes
the topological link between of the effective degrees of freedom at criticality:
color electric fluxes and the confining fluctuations which are interfaces between
between different center sectors of the theory.
In Chapter 4 we take a detour via magnetic monopoles in grand unified theories.
In particular, we search for boundary conditions that allow for a non-perturbative
lattice study of ’t Hooft-Polyakov monopoles in SU(N) gauge theories with an
adjoint Higgs field. We find that suitably twisted C-periodic boundary conditions
make this possible, but only for even N. Confinement is not a focus here, but is nevertheless
related. The center vortex mechanism of confinement in SU(N) gauge theories
has been paralleled by the monopole scenario, which attributes confinement
to a dual Meissner effect from a condensate of abelian monopoles. Interpreting the
monopole inducing boundary conditions in terms of center vortices highlights their
close relationship.
1 The work presented in Chapter 3 was obtained in collaboration with Lorenz von Smekal, and has
appeared elsewhere in Refs. [14] and [15], and also with Nils Strodthoff in Refs. [16, 17]. The results
in Chapter 4 have appeared in Ref. [18], also in collaboration with Dhagash Mehta and Arttu Rajantie.
Several of the results in Chapter 5 have been published in Ref. [19, 20] with Andre Sternbeck, and
others stem from a collaboration with Jeff Greensite and Kurt Langfeld.