Abstract
We present a lattice study of the equation of state in Yang-Mills theory based on the exceptional G(2) gauge group. As is well-known, at zero temperature this theory shares many qualitative features with real-world QCD, including the absence of colored states in the spectrum and dynamical string breaking at large distances. In agreement with previous works, we show that at finite temperature this theory features a first-order deconfining phase transition, whose nature can be studied by a semi-classical computation. We also show that the equilibrium thermodynamic observables in the deconfined phase bear striking quantitative similarities with those found in SU(N) gauge theories: in particular, these quantities exhibit nearly perfect proportionality to the number of gluon degrees of freedom, and the trace anomaly reveals a characteristic quadratic dependence on the temperature, also observed in SU(N) Yang-Mills theories (both in four and in three spacetime dimensions). We compare our lattice data with analytical predictions from effective models, and discuss their implications for the deconfinement mechanism and high-temperature properties of strongly interacting, non-supersymmetric gauge theories. Our results give strong evidence for the conjecture that the thermal deconfining transition is governed by a universal mechanism, common to all simple gauge groups.
Highlights
JHEP03(2015)057 transition temperature, as well as of the QGP bulk thermodynamic properties is settled [49,50,51] and accurate results are being obtained for various parameters describing fluctuations, for the QGP response to strong magnetic fields, et c. [52]
We present a lattice study of the equation of state in Yang-Mills theory based on the exceptional G2 gauge group
While this is consistent with the interpretation of confinement in non-supersymmetric gauge theories as a phenomenon due to condensation of center vortices [70, 71], it begs the question, what happens in a theory based on a non-Abelian gauge group with trivial center? In this respect, it is interesting to consider the G2 gauge theory: since this exceptional group is the smallest connected group with a trivial center, it is an ideal toy model to be studied on the lattice
Summary
JHEP03(2015) transition temperature, as well as of the QGP bulk thermodynamic properties (at vanishing quark chemical potential μ) is settled [49,50,51] and accurate results are being obtained for various parameters describing fluctuations, for the QGP response to strong magnetic fields, et c. [52]. As the system is heated up, these theories will interpolate between two distinct limits: one that can be modeled as a gas of massive, non-interacting hadrons (glueballs) at low temperature, and one that is described by a gas of free massless gluons at (infinitely) high temperature These limits are separated by a finite-temperature region, in which deconfinement takes place. If one defines confinement as the existence of an asymptotically linear potential between static color sources, the infrared dynamics of G2 Yang-Mills theory could rather be described as “screening”. Previous lattice studies indicate that, at zero and low temperatures, the G2 Yang-Mills theory has a confining phase, in which static color sources in the smallest fundamental irreducible representation 7 are confined by string-like objects, up to intermediate distances. This is a straightforward consequence of representation theory (and, of the lack of a non-trivial N -ality for this group): as eq (A.15) in the appendix A shows, the representation 7 appears in the decomposition of the product of three adjoint representations 14, a fundamental G2 quark can be screened by three gluons
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