https://doi.org/10.1140/epjc/s10052-017-5381-9
Regular Article - Theoretical Physics
The QCD mass gap and quark deconfinement scales as mass bounds in strong gravity
1
High Energy Physics Theory Group, Department of Physics, Faculty of Science, Chulalongkorn University, Phyathai Rd., Bangkok, 10330, Thailand
2
Department of Physics, Babes-Bolyai University, Kogalniceanu Street, 400084, Cluj-Napoca, Romania
3
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK
4
School of Physics, Sun Yat-Sen University, Guangzhou, 510275, China
5
School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore
6
The Institute for Fundamental Study, “The Tah Poe Academia Institute”, Naresuan University, Phitsanulok, 65000, Thailand
7
Thailand Center of Excellence in Physics, Ministry of Education, Bangkok, 10400, Thailand
* e-mail: piyabut@gmail.com
Received:
2
June
2017
Accepted:
10
November
2017
Published online:
24
November
2017
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 
. 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, 
. This introduces a strong de Sitter radius for strongly interacting fermions, producing a confining bubble, which allows us to identify with the ‘bag constant’ of the MIT bag model, 
. 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 
, 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.
© The Author(s), 2017
