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--><!-- Mariana Kirchbach1and Cliffor B. Compean21Instituto de Fsica, UASLP, Zona Universitaria, San Luis Potos, Mexico2Facultad de Ciencias, UASLP, Privadas del Pedregal, San Luis Potos, Mexico Part of the book: Future Relativity, Gravitation, Cosmology Abstract Conformal symmetry and color confinement in the infrared regime of QCD are interpreted by means of a conjectured deSitter dS4 geometry of the internal space-time of hadrons, an assumption inspired by the hypothesis on deSitter special relativity. Within such a scenario, the interactions involving the virtual gluon- and constituent quark degrees of freedom of hadrons are deduced from the Green functions of Laplace operators on the dS4 geodesics. Then the conformal symmetry of QCD emerges as a direct consequence of the conformal symmetry of the dS4 space-time, while the color confinement, understood as colorlessness of hadrons, appears as a consequence of the inevitable charge neutrality of the unique closed space-like manifold, the three dimensional hyper-sphere S 3 , on whose geodesics the hadrons constituents are conjectured to reside when near rest frame. Mesons are now modelled as quarkish color-anticolor dipoles, whose free quantum motions on the aforementioned S 3 geodesics are perturbed by a potential generated by a gluonanti-gluon color dipole. The potential predicted presents itself as the color charge analogue to the curved Coulomb potential, i.e. to the electric potential that defines a consistent electrostatic theory on a hyper-spherical surface. The advantage of this method is that it allows to establish a direct relationship of the potential parameters to the fundamental constants of QCD. We apply the model to the description of the spectra of the a1 and f1 mesons, and the pion electric charge form factor, finding fair agreement with data. Keywords: deSitter special relativity, conformal symmetry, color confinement, unflavored mesons, strong coupling constant References [1] K. A. Olive et al. ( Particle Data Group), Review of Particle Physics, Chinese PhysicsC 38 090001 (2014) and 2015 update.[2] Fayyazuddin and Riazuddin, A Modern Introduction to Particle Physics, 2nd edition(World Scientific, Singapore, 2000)[3] A. Chodos, R. L. Jaffe, K. Johnson, and C. B. Thron, Phys. Rev. D 10 (1974) 2599.[4] D. Kharzeev, E. Levin, and K. Tuchin, Phys. Rev. D 70 (2004) 054005 .[5] M. Kirchbach and C. B. Compean, Eur. Phys. J. A 52 (2016) 210.[6] R. Aldrovandi, J. P. Beltran Almeida, and J. G. Pereira, Class. Quant. Grav. 24 (2007) 1385.[7] O. D. Kelogg, Foundations of Potential Theory (Dover, New York, 1953).[8] M. Kirchbach and C. B. Compean, Eur. Phys. J. A 53 (2017) 65.[9] A. O. Barut and R. Wilson, Phys. Lett. A 110 (1983) 351.[10] M. Kirchbach and C. B. Compean, Nucl. Phys. A 980 (2018) 32.[11] Slava Rychkov, EPFL Lectures on Conformal Field Theory in D 3 dimensions,E-print arXiv:1601.05000[hep-th].[12] Yoonbai Kim, Chae Young Oh, and Namil Park, J. Korean Phys. Soc. 42 (2003) 573 .[13] Andrew Pressley, Elementary Differential Geometry (Springer, London DordrechtHeidelberg New York, 2012).[14] F. Cooper, A. Khare, and U. P. Sukhatme, Supersymmetry in Quantum Mechanics(World Scientific, Singapore, 2001).[15] D. Cevik, M. Gadella, S. Kuru, and J. Negro, Phys. Lett. A 380 (2016) 1600.[16] H. Bateman, Proc. London Math. Soc. (ser. 2) 7 (1909) 70.[17] L. D. Landau and E. M. Lifschitz, The Classical Theory of Fields, Vol. 2 of A Courseof Theoretical Physics, 3d edition (Pergamon Press 1971) p.335.[18] Pouria Pedram, Am. J. Phys. 78 (2010) 403.[19] S. Fubini, A. J. Hanson, and R. Jackiw, Phys. Rev. D 7 (1972) 1732.[20] B. Alertz, Ann. Inst. Henri Poincare, 53 (1990) 319.[21] Kerson Huang, Quarks, Leptons and Gauge Fields (World Scientific, Singapore, 1982).[22] J.-M. Gaillol and M. Trulsson, J. Chem. Phys. 141 (2014) 124111.[23] A. V. Belitsky, A. S. Gorsky, and G. P. Korchglemsky, Nucl. Phys. B 67 (2003) 3.[24] A. Deur, V. Burkert, J. P. Chen, and W. Korsch, Phys. Lett. 665 (2008) 349.[25] Dipankar Chakrabart, Chandan Mondal, Eur. Phys. J. C 73 (2013) 2671.[26] S. R. Amendolia et al., Nucl. Phys. B 277 (1986) 168.
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