Chiral symmetry and spectral properties of the Dirac operator inG₂Yang-Mills theory

Abstract

We study spontaneous chiral symmetry breaking and the spectral properties of the staggered lattice Dirac operator using quenched gauge configurations for the exceptional group G 2 , which has a trivial center. In particular we study the system below and above the finite temperature transition and use the temporal boundary conditions of the fermions to probe the system. We evaluate several observables: The spectral density at the origin, the spectral gap, the chiral condensate and the recently proposed dual chiral condensate. We show that chiral symmetry is broken at low temperatures and is restored at high temperatures at the thermodynamic phase transition. Concerning the role of the boundary conditions we establish that in all respects the spectral quantities behave for G 2 in exactly the same way as for SU(N ), when for the latter group the gauge ensemble above T c is restricted to the sector of configurations with real Polyakov loop.

Gauge bosons at zero and finite temperature

“…However, even for theories which do not possess a non-trivial center, the Polyakov loop is an acceptable order parameter [398][399][400][401], and can therefore be expected to remain so also for the standard model. It is then, however, no longer related to a symmetry-breaking transition, and is also not strictly zero in either phase [460], though to a very good approximation it turns out to be so [400,401,460]. There are further arguments concerning the product-group structure of the standard model suggesting its usefulness [454].…”

Phase diagram of the latticeG2Higgs model

“…The smallest simple and simply connected Lie group with a trivial center is the 14 dimensional exceptional Lie group G 2 . This is one reason why G 2 gauge theory with and without Higgsfields has been investigated in series of papers [6][7][8][9][10][11]. Although there is no symmetry * bjoern.wellegehausen@uni-jena.de, wipf@tpi.uni-jena.de and Christian.Wozar@uni-jena.de reason for a deconfinement phase transition in G 2 gluodynamics it has been conjectured that a first order deconfinement transition without order parameter exists.…”

Topology and θ dependence in finite temperature G 2 lattice gauge theory

“…What is probably surprising is that the results of these analysis gave a picture much similar to that of standard SU(N ) theory: the spectrum of the G 2 theory at zero temperature is composed only of color neutral objects [11,12,15], the string tension at intermediate distances (i.e. before string breaking [20]) satisfies Casimir scaling [13,18,20], a first order deconfinement transition is present [14,16,22], (quenched) chiral symmetry is broken in the low temperature phase and restored above the critical temperature [19], the topological susceptibility is suppressed above deconfinement [21], propagators [17] and thermodynamical observables (like e.g. pressure and trace anomaly) [22] do not show any qualitative difference with respect to the SU(N ) case.…”

“…Bearing all this in mind, it is not surprising that the G 2 lattice gauge theory was actively investigated in the past, both at zero and finite temperature [11][12][13][14][15][16][17][18][19][20][21][22]. What is probably surprising is that the results of these analysis gave a picture much similar to that of standard SU(N ) theory: the spectrum of the G 2 theory at zero temperature is composed only of color neutral objects [11,12,15], the string tension at intermediate distances (i.e.…”