Dimensional reduction and confinement from five dimensions

Knechtli, Francesco; Irges, Nikos; Rago, Antonio

doi:10.22323/1.105.0059

Cited by 1 publication

(1 citation statement)

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“…We computed the static potential V (r) along spatial directions orthogonal to the extra dimension (and averaged over the extra dimension). In the deconfined phase (where the Polyakov loops are broken) it is a five-dimensional Coulomb potential [43]. Here we choose parameters which correspond to bulk phase transition points and we put ourselves approximately in the middle of the hysteresis curve.…”

Section: The Static Potentialmentioning

confidence: 99%

On the phase structure of five-dimensional SU(2) gauge theories with anisotropic couplings

2012

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The phase diagram of five-dimensional SU(2) gauge theories is explored using Monte Carlo simulations of the theory discretized on a Euclidean lattice using the Wilson plaquette action and periodic boundary conditions. We simulate anisotropic gauge couplings which correspond to different lattice spacings a 4 in the four dimensions and a 5 along the extra dimension. In particular we study the case where a 5 > a 4 . We identify a line of first order phase transitions which separate the confined from the deconfined phase. We perform simulations in large volume at the bulk phase transition staying in the confined vacuum. The static potential measured in the hyperplanes orthogonal to the extra dimension hint at dimensional reduction. We also locate and analyze second order phase transitions related to breaking of the center along one direction.Our interest in studying five-dimensional gauge theories comes from extensions of the Standard Model called Gauge-Higgs unification. The idea is to identify the Higgs boson with (some of) the extra dimensional components of the gauge field. Since five-dimensional gauge theories are non-renormalizable 1 an ultra-violet cut-off is mandatory. The lattice regularization provides such a gauge-invariant cut-off (the inverse lattice spacing) and is therefore a natural setup to study these theories.Here we consider the five-dimensional pure SU(2) gauge theory and investigate its non-perturbative phase diagram through Monte Carlo simulations. The theory is discretized on a Euclidean space-time lattice. The seminal work done by Creutz [1] using the Wilson plaquette gauge action [2] demonstrated the existence of (at least) two bulk phases in the non-perturbative phase diagram of the theory in infinite volume. There is a confined phase at large values of the gauge coupling and a deconfined phase when the gauge coupling is small.The question we are after is where dimensional reduction from five to four dimensions occurs. Possible mechanisms, which have been proposed are compactification or localization. In compactification models the size of the extra dimension is small and the system is described by an effective four-dimensional low energy theory valid for energies much below the inverse compactification radius. The existence of a minimal physical size of the extra dimension, below which the theory becomes four-dimensional has been suggested by lattice simulations in [3]. The extra dimension can even "disappear" when the correlation length of the fourdimensional theory grows exponentially fast with the size of the extra dimension. This is the mechanism of D-theory [4,5], which relies on the existence of the Coulomb phase and has been recently studied on the lattice [6].The most prominent of localization models in flat space 2 is the domain wall construction for fermions [7], which has been shown to be equivalent to an orbifold construction [8]. A possible localization mechanism for gauge field has been proposed in [9] and relies on a mechanism that confines the theory in the bulk and deconfi...

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Section: The Static Potentialmentioning

confidence: 99%