Abstract
Though not a part of mainstream physics, Salam’s theory of strong gravity remains a viable effective model for the description of strong interactions in the gauge singlet sector of QCD, capable of producing particle confinement and asymptotic freedom, but not of reproducing interactions involving SU(3) color charge. It may therefore be used to explore the stability and confinement of gauge singlet hadrons, though not to describe scattering processes that require color interactions. It is a two-tensor theory of both strong interactions and gravity, in which the strong tensor field is governed by equations formally identical to the Einstein equations, apart from the coupling parameter, which is of order 1~{mathrm{GeV}}^{-1}. We revisit the strong gravity theory and investigate the strong gravity field equations in the presence of a mixing term which induces an effective strong cosmological constant, Lambda _{f}. This introduces a strong de Sitter radius for strongly interacting fermions, producing a confining bubble, which allows us to identify Lambda _{f} with the ‘bag constant’ of the MIT bag model, B simeq 2 times 10^{14}~{mathrm{g}}~{mathrm{cm}}^{-3}. Assuming a static, spherically symmetric geometry, we derive the strong gravity TOV equation, which describes the equilibrium properties of compact hadronic objects. From this, we determine the generalized Buchdahl inequalities for a strong gravity ‘particle’, giving rise to upper and lower bounds on the mass/radius ratio of stable, compact, strongly interacting objects. We show, explicitly, that the existence of the lower mass bound is induced by the presence of Lambda _f, producing a mass gap, and that the upper bound corresponds to a deconfinement phase transition. The physical implications of our results for holographic duality in the context of the AdS/QCD and dS/QCD correspondences are also discussed.
Highlights
One of the most intriguing aspects of short-distance physics is that the strong interactions of hadrons in the infrared (IR)regime exhibit certain features bearing a close resemblance to gravity
It is important to note that the strength of the gravitational interaction increases with energy, the coupling being proportional to G E2, where E is the total energy of the particle and G is Newton’s constant
Gravitational interactions become more and menoerregyimexpcoeretadnstEat=heigch2e/r√eGnergi1e0s.18InGefVac, tt,heifgtrhaevitpaatriotincalel interaction is stronger than the electromagnetic interaction and, at energies of the order of 1019 GeV, it is as strong as the strong nuclear interaction
Summary
One of the most intriguing aspects of short-distance physics is that the strong interactions of hadrons in the infrared (IR). An alternative attempt to describe the physics of strong interactions using a geometric, general-relativity-inspired picture is the reformulation of Yang–Mills theory proposed in the so-called ‘chromogravity’ model [26,27] In this model, QCD in the IR region is approximated by the exchange of a dressed two-gluon phenomenological field Gμν(x) = Bμa Bνbηab, where ηab is a color-SU(3) metric, and Bμa is the dressed gluon field. Which implies the existence of a lower bound for the mass/radius ratio or, equivalently, the density of a stable, charge-neutral, gravitating compact object, i.e. Though the derivation of this condition is somewhat involved [44], its physical meaning is intuitively obvious.
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