The Pacific Institute for the Mathematical Sciences, The University of British Columbia, Earth Sciences Building, 2207 Main Mall, Vancouver, BC V6T 1Z4, Canada

Department of Physics, Simon Fraser University, V5A 1S6 Burnaby B.C., Canada

E-mail Address: [email protected]

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https://doi.org/10.1142/S0219887821502273Cited by:4 (Source: Crossref)

Abstract

In this paper, we introduce a new geometric/topological approach to the emerging braneworld scenario in the context of D-branes using partially negative-dimensional product (PNDP) manifolds. The working hypothesis is based on the fact that the orientability of PNDP manifolds can be arbitrary, and starting from this, we propose that gravitational interaction can derive naturally from the non-orientability. According to this hypothesis, we show that topological defects can emerge from non-orientability and they can be identified as gravitational interaction at macroscopic level. In other words, the orientability of fundamental PNDPs can be related to the appearance of curvature at low-energy scales.

Keywords:

AMSC: 83E30, 53C25

References

1. J. Dai, R. G. Leigh and J. Polchinski , New connections between string theories, Mod. Phys. Lett. A 4(21) (1989) 2073–2083. Link, Web of Science, Google Scholar
2. P. Horava , Background duality of open-string models, Phys. Lett. B 231(3) (1989) 251–257. Crossref, Web of Science, Google Scholar
3. C. V. Johnson , D-Branes, Cambridge Monograph on Mathematical Physics, Vol. 29 (Cambridge University Press, Cambridge, England, 2005), p. 2041009. Google Scholar
4. S. Capozziello, G. Basini and M. De Laurentis , Deriving the mass of particles from extended theories of gravity in LHC era, Eur. Phys. J. C 71 (2011) 1679. Crossref, Web of Science, Google Scholar
5. G. Basini and S. Capozziello , A general covariant symplectic structure from conservation laws, Mod. Phys. Lett. A 20 (2005) 251. Link, Web of Science, Google Scholar
6. S. Capozziello and M. De Laurentis , Extended theories of gravity, Phys. Rept. 509 (2011) 167. Crossref, Web of Science, Google Scholar
7. A. Pigazzini, C. Özel, P. Linker and S. Jafari , On PNDP-manifold, Poincare J. Anal. Appl. 8(1) (2021) 111–125. Google Scholar
8. R. Pincak, A. Pigazzini, S. Jafari and C. Özel , The “emerging” reality from “hidden” spaces, Universe 7(3) (2021) 75. Crossref, Web of Science, Google Scholar
9. D. Joyce, Kuranishis and Symplectic Geometry, Vol. II, https://people.maths.ox.ac.uk/joyce/Kuranishi.html. Google Scholar
10. R. Casalbuoni , Conformal symmetry for relativistic point particles, Phys. Rev. D 90 (2014) 026001. Crossref, Web of Science, Google Scholar
11. Y. Cao, N. Conan Leung , Orientability for gauge theories on Calabi? Yau manifolds, Adv. Math. 314 (2017) 48. Crossref, Web of Science, Google Scholar
12. M. J. Hadley , The orientability of space-time, Class. Quantum Grav. 19 (2002) 4565. Crossref, Web of Science, Google Scholar
13. F. Bajardi, D. Vernieri and S. Capozziello, Exact Solutions in Higher-Dimensional Lovelock and $A d S_{5}$ Chern-Simons Gravity, e-Print:2106.07396 [gr-qc]. Google Scholar
14. S. Capozziello, D. J. Cirilo-Lombardo and A. Dorokhov , Fermion interactions, cosmological constant and spacetime dimensionality in an unified approach based on affine geometry, Int. J. Theor. Phys. 53(11) (2014) 3882. Crossref, Web of Science, Google Scholar
15. N. Arkani-Hamed, A. G. Cohen and H. Georgi , (De)Constructing dimensions, Phys. Rev. Lett. 86 (2001) 4757. Crossref, Web of Science, Google Scholar
16. C. T. Hill, S. Pokorski and J. Wangi , Gauge invariant effective Lagrangian for Kaluza–Klein modes, Phys. Rev. D 64 (2001) 105005. Crossref, Web of Science, Google Scholar
17. H. C. Cheng, C. T. Hill, S. Pokorski and J. Wang , The standard model in the Latticized bulk, Phys. Rev. D 64 (2001) 065007. Crossref, Web of Science, Google Scholar
18. S. Capozziello, D. J. Cirilo-Lombardo and M. De Laurentis , The affine tructure of gravitational theories: Symplectic groups and geometry, Int. J. Geom. Methods Mod. Phys. 11(10) (2014) 1450081. Link, Web of Science, Google Scholar
19. R. C. Myers and V. Periwal , The orientability of random surfaces, Phys. Rev. D 42 (1990) 3600. Crossref, Web of Science, Google Scholar
20. E. Witten , String theory and non-commutative gauge theory, Class. Quantum Grav. 17 (2000) 1299. Crossref, Web of Science, Google Scholar
21. M. B. Green , World sheet dynamics of Bosonic string theory, Phys. Lett. B 193 (1987) 439. Crossref, Web of Science, Google Scholar
22. J. H. Schwarz , The future of string theory, J. Math. Phys. 42 (2001) 2889. Crossref, Web of Science, Google Scholar
23. H. Ooguri and C. Vafa , On the geometry of the string landscape and the swampland, Nucl. Phys. B 766 (2007) 21. Crossref, Web of Science, Google Scholar
24. M. Benetti, S. Capozziello and L. Lobato Graef , Swampland conjecture in f(R) gravity by Noether symmetry approach, Phys. Rev. D 100(8) (2019) 084013. Crossref, Web of Science, Google Scholar