Abstract
We explore the confinement-deconfinement phase transition (PT) of the first order (FO) arising in SU(N) pure Yang-Mills theory, based on Polyakov loop models (PLMs), in light of the induced gravitational wave (GW) spectra. We demonstrate that the PLMs with the Haar measure term, involving models successful in QCD with N = 3, are potentially incompatible with the large N scaling for the thermodynamic quantities and the latent heat at around the criticality of the FOPT reported from the lattice simulations. We then propose a couple of models of polynomial form, which we call the 4-6 PLM (with four- and six-point interactions among the basic PL fields which have center charge 1) and 4-8 PLM (with four- and eight-point interactions), and discuss how such models can naturally arise in the presence of a heavy PL with charge 2. We show that those models give the consistent thermodynamic and large N properties at around the criticality. The predicted GW spectra are shown to have high enough sensitivity to be probed in the future prospected interferometers such as BBO and DECIGO.
Highlights
We demonstrate that the Polyakov loop models (PLMs) with the Haar measure term, involving models successful in QCD with N = 3, are potentially incompatible with the large N scaling for the thermodynamic quantities and the latent heat at around the criticality of the FOPT reported from the lattice simulations
A pure SU(N ) Yang-Mills (PYM) sector, for instance, predicted by the string theory, may be an active part of particle physics beyond the standard model (SM). Maybe, such a PYM sector is completely secluded to the SM sector, and we should peek into this dark sector by means of its gravitational wave (GW) signals, which are generated during the first-order (FO) confinement-deconfinement phase transition (PT)
A proper effective model based on L, namely the Polyakov loop model (PLM)
Summary
The PL plays a center role in understanding the confinement-deconfinement PT in the PYM theory [24]. To keep the PYM action gauge invariant, they are just required to satisfy the twisted boundary condition (the center twisted gauge transformations): V (x, β) = zkV (x, 0), where zk = ei2kπ/N with k = 1, · · · , N belonging to the discrete group ZN ; the transformation. Under the action of Vk(x4), l is not invariant and changes as l → zkl the Euclidean action is invariant In this sense, l is charged under the global center ZN. PLs with different ZN charges can be introduced [38, 40]. We introduce traced PLs in a different representation R under SU(N ), normalized by the dimension dR. PLs in the representations of dR,± = (N 2 ± N )/2 have charge 2. The higher-ZN charged PLs are assumed to be heavy and can be integrated out, which leads to the polynomial potential that we will use in section 2 (See eqs. (2.28) and (2.29), and discussions around there.)
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