Nikos Irges

Flavor Corrections in the Static Potential in Holographic QCD

We examine the static potential in the presence of flavors in the perturbative backreacted D4/D8 system from localized D8 branes, focusing in particular on the Sakai-Sugimoto model. For the case of long strings we find the flavor corrections to the static potential which are of exponential form. We then investigate shorter Wilson loops and express their energy analytically in terms of the lengths of two neighboring Wilson loops. Moreover, we find that the static force for all the cases in the backreacted background is reduced compared to one in the probe limit, as expected due to screening effects. We also compare the string world-sheets in the two backgrounds and find how they get modified by the backreaction. Our results are supported by numerical computations as well. Finally we discuss our results in comparison with the lattice data and comment on the issue of physical scales which seem to lie at the heart of the reason that obstructs our model at this level to fully describe QCD.

Mean-field gauge interactions in five dimensions II. The orbifold

Abstract We study Gauge–Higgs Unification in five dimensions on the lattice by means of the mean-field expansion. We formulate it for the case of an SU ( 2 ) pure gauge theory and orbifold boundary conditions along the extra dimension, which explicitly break the gauge symmetry to U ( 1 ) on the boundaries. Our main result is that the gauge boson mass computed from the static potential along four-dimensional hyperplanes is non-zero implying spontaneous symmetry breaking. This observation supports earlier data from Monte Carlo simulations in Irges and Knechtli (2007) [12] .

On the holographic width of flux tubes

A bstractWe investigate the width of the flux tube between heavy static quark charges. Using the gauge/gravity duality, we find the properties of the minimal connected surface related to the width of the bound state. We show that in the confining phase, the logarithmic broadening predicted by the effective string description and observed in lattice simulations is a generic property of all confining backgrounds. We also study the transverse fluctuations of the string connecting two static quarks in curved backgrounds. Our formalism is applied to AdS space where we compute the expectation value of the square of transverse deviations of the string, a quantity related to the width.

Higgs mechanism near the 5d bulk phase transition

Abstract We present a non-perturbative model of Gauge-Higgs Unification. We consider a five-dimensional pure SU ( 2 ) gauge theory with orbifold boundary conditions along the fifth dimension, such that the symmetry is reduced to U ( 1 ) at the fixed points of the orbifold action. The spectrum on the four-dimensional boundary hyperplanes includes, apart from the U ( 1 ) gauge boson, also a complex scalar, interpreted as a simplified version of the Standard Model Higgs field. The gauge theory is defined on a Euclidean lattice which is anisotropic in the extra dimension. Using the boundary Wilson Loop and the observable that represents the scalar and in the context of an expansion in fluctuations around a Mean-Field background, we show that a) near the bulk phase transition the model tends to reduce dimensionally to a four-dimensional gauge-scalar theory, b) the boundary U ( 1 ) gauge symmetry breaks spontaneously due to the broken translational invariance along the fifth dimension, c) it is possible to construct renormalized trajectories on the phase diagram along which the Higgs mass is constant as the lattice spacing is varied, d) by taking a continuum limit in the regime where the anisotropy parameter is small, it is possible to predict the existence of a Z ′ state with a mass around 1 TeV.

Non-perturbative gauge-Higgs unification: symmetries and order parameters

A bstractWe consider pure SU(N) gauge theories defined on an orbifold lattice, analogous to the S1/

Quantum phase transition of high dimensional Yang-Mills theories

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Reduction of N=1, E8 SYM over SU(3)/U(1)×U(1)×Z3 and its four-dimensional effective action

gauge theory orbifolds of the continuum, which according to the perturbative analysis do not have a Higgs phase. Non-perturbatively the conclusion for N even is the opposite, namely that spontaneous symmetry breaking does take place and some of the gauge bosons become massive. We interpret this new, non-perturbative phenomenon both mathematically and physically.

Renormalization of the Abelian–Higgs model in the R ξ and Unitary gauges and the physicality of its scalar potential

We determine the critical value of the coupling where the first order quantum phase transition takes place for lattice SU(2) Yang-Mills theories in dimensions higher than four. Within a Mean-Field approach we derive an approximate law valid for any dimension d and in the context of a Monte Carlo approach, in addition to the already known d=5 case, we look at d=6,7,8.

Five-Dimensional Gauge-Higgs Unification: A Standard Model-Like Spectrum

Abstract We propose an extension of the Standard Model inspired by the E 8 × E 8 Heterotic String. In order that a reasonable effective Lagrangian is presented we neglect everything else other than the ten-dimensional N = 1 supersymmetric Yang–Mills sector associated with one of the gauge factors and certain couplings necessary for anomaly cancellation. We consider a compactified space–time M 4 × B 0 / Z 3 , where B 0 is the nearly Kahler manifold SU ( 3 ) / U ( 1 ) × U ( 1 ) and Z 3 is a freely acting discrete group on B 0 . Then we reduce dimensionally the E 8 on this manifold and we employ the Wilson flux mechanism leading in four dimensions to an SU ( 3 ) 3 gauge theory with the spectrum of a N = 1 supersymmetric theory. We compute the effective four-dimensional Lagrangian and demonstrate that an extension of the Standard Model is obtained with interesting features including a conserved baryon number and fixed tree level Yukawa couplings and scalar potential. The spectrum contains new states such as right-handed neutrinos and heavy vector-like quarks.

Reduction of N=1, E_8 SYM over SU(3)/U(1) x U(1) x Z_3 and its four-dimensional effective action

Abstract We perform an old school, one-loop renormalization of the Abelian–Higgs model in the Unitary and R ξ gauges, focused on the scalar potential and the gauge boson mass. Our goal is to demonstrate in this simple context the validity of the Unitary gauge at the quantum level, which could open the way for an until now (mostly) avoided framework for loop computations. We indeed find that the Unitary gauge is consistent and equivalent to the R ξ gauge at the level of β-functions. Then we compare the renormalized, finite, one-loop Higgs potential in the two gauges and we again find equivalence. This equivalence needs not only a complete cancellation of the gauge fixing parameter ξ from the R ξ gauge potential but also requires its ξ-independent part to be equal to the Unitary gauge result. We follow the quantum behavior of the system by plotting Renormalization Group trajectories and Lines of Constant Physics, with the former the well known curves and with the latter, determined by the finite parts of the counter-terms, particularly well suited for a comparison with non-perturbative studies.