4 research outputs found
Searching for a continuum 4D field theory arising from a 5D non-abelian gauge theory
The anisotropic 5D SU(2) Yang-Mills model has been widely investigated on the
lattice during the last decade. In the case where all dimensions are large in
size, it was previously claimed that there is a new phase in the phase diagram,
called the Layer phase. In this phase, the gauge fields would be localized on
4D layers. Previous works claim that the phase transition to the Layer phase is
of second order, which would allow a continuum limit to be taken. We present
the extension of the previous work to large lattices, for which we found a
first order phase transition. This leaves the scenario that this 5D theory can
be dimensionally reduced to a continuum 4D field theory, doubtful.Comment: 6 pages, 2 figures - talk presented at the 31st International
Symposium on Lattice Field Theory - Lattice 2013, Mainz, German
Phase structure of five-dimensional anisotropic lattice gauge theories
The idea that we live in a higher-dimensional space was first introduced almost
100 years ago. In the past two decades many extra-dimensional models have been
proposed in order to solve fundamental problems of nature such as the hierarchy
problem. Most of them need exploration via non-perturbative approaches and
Lattice Gauge Theory provides a tool for doing this.
In this thesis, we make attempts to find a non-perturbative way to localize gauge
fields that arise from five-dimensional SU(2) gauge theories on 3-branes. In 1984,
it was proposed that the phase diagram of anisotropic extra-dimensional lattice
gauge theories inherits a new phase, called the "layered" phase, where the gauge
fields behave as four-dimensional ones. This was shown for the abelian case,
but the existence of this new phase for the simplest non-abelian group, SU(2),
was still in doubt. We investigated this system in large volumes using Monte
Carlo simulations and we could not find a second order phase transition from a
five-dimensional to a continuous four-dimensional theory when all directions were
kept large. This made the model unattractive for further exploration as nothing
suggests that a non-trivial fixed point could exist.
The above investigation was done in a flat background metric. We extended the
previous work by putting our theory into a slice of AdS5 space, usually called the
warped background. The motivation for this is that our SU(2) theory looks like
the gauge-sector of the Randall-Sundrum model, which does not have a concrete
solution to the problem of localization of the gauge fields on a 3-brane. We
carried out our investigation using the Mean-Field Approach and we present
novel results for the phase diagram and measurements of important observables.
In our implementation we have a finite extent of the extra dimension and one
layer (or 3-brane) on each extra-dimensional coordinate. At weak coupling, we
observed that each layer decouples one at a time in the transition to the fully
layered phase of the system, forming a mixed phase, whereas there is a strong and
sharp transition between the fully layered and the strong-coupling phase. Within
the mixed phase, close to the transition into the layered phase, we found evidence
that the system is four-dimensional acquiring a Yukawa mass and resembling a
Higgs-like phase. The mixed phase grows as the curvature increases suggesting
that for an infinite extra dimension the entire weak-coupling phase is mixed
The transition to a layered phase in the anisotropic five-dimensional SU(2) Yang-Mills theory
We extend to large lattices the work of a previous investigation of the phase
diagram of the anisotropic five-dimensional SU(2) Yang-Mills model using Monte
Carlo simulations in the regime where the lattice spacing in the fifth
dimension is larger than in the other four dimensions. We find a first order
phase transition between the confining and deconfining phase at the anisotropic
parameter point which was previously claimed to be the critical
point at which the order of the transition changes from first to second. We
conclude that large lattices are required to establish the first order nature
of this line of transitions and consequently that the scenario of dimensional
reduction of the five-dimensional theory to a continuum four-dimensional theory
via the existence of the so-called "layer phase" is unpromising.Comment: 5 pages, 1 table, 6 figure