Deconfining temperatures in SO(N) and SU(N) gauge theories

The Dark Sector and the Standard Model from a Local Generalisation of Extra Dimensions

“…Similarly we are employing the term 'hadron' in 'dark hadron' in a generic sense bearing in mind the translation of the original Greek hadros as 'bulky'. The analogy between SO(m) gauge theory and QCD was noted in subsection 2.1 with reference to [14,15]. This structure with SO(m) acting upon elementary scalar states, while considered an unphysical model in [14], is here physically realised through table 2 as a natural basis for a dark matter candidate.…”

“…Such gauge groups have been studied in analogy with, and to help elucidate the properties of, standard QCD itself [14,15]. Connections have been established between the gauge theories of the closely related gauge groups SO(6) and SU(4) ( [15] equation 4.4) as well as for SO(m) and SU(n) for m = 2n in the large n limit for which some simplifications apply while keeping essential features ([15] equations 1.1 and 4.6; the links in particular involve the deconfining temperatures of the respective theories).…”

“…Such gauge groups have been studied in analogy with, and to help elucidate the properties of, standard QCD itself [14,15]. Connections have been established between the gauge theories of the closely related gauge groups SO(6) and SU(4) ( [15] equation 4.4) as well as for SO(m) and SU(n) for m = 2n in the large n limit for which some simplifications apply while keeping essential features ([15] equations 1.1 and 4.6; the links in particular involve the deconfining temperatures of the respective theories). The coupling of the gauge group SO(m) to a real scalar field has also been studied ( [14] with the Lagrangian of equation 1 therein), although with such a model there considered non-physical since there is no known empirical correlate of such a theory.…”

“…In subsection 2.1 (with reference to [15]) we alluded to the close relationship between the gauge group SO(6) and its double cover SU(4), which share the same Lie algebra structure. In the present theory the internal G = SU(3) c × U(1) Q symmetry in table 1, identified at the E 6 and E 7 levels for equation 11, forms a subgroup of an SU( 4) ⊂ E 6 ⊂ E 7 that is equivalent to an SO(6) action on the six real components underlying the set of scalar 'u L '-quark states (and similarly for the scalar 'u R '-quarks) in table 1 (see discussion in [57] from equation 62 to the end of subsection 4.2).…”