Quantum Gravity and String Theory


On the Riemann Hypothesis and Tachyons in Dual String Scattering Amplitudes

Authors: Carlos Castro

It is the purpose of this work to pursue a novel physical interpretation of the nontrivial Riemann zeta zeros and prove why the location of these zeros zn = 1/2+iλn corresponds physically to tachyonic-resonances/tachyonic-condensates, originating from the scattering of two on-shell tachyons in bosonic string theory. Namely, we prove that if there were nontrivial zeta zeros (violating the Riemann hypothesis) outside the critical line Real z = 1/2 (but inside the critical strip), these putative zeros do not correspond to any poles of the bosonic open string scattering (Veneziano) amplitude A(s, t, u). The physical relevance of tachyonic-resonances/tachyonic-condensates in bosonic string theory, establishes an important connection between string theory and the Riemann Hypothesis. In addition, one has also a geometrical interpretation of the zeta zeros in the critical line in terms of very special (degenerate) triangular configurations in the upper-part of the complex plane.

Comments: 13 pages, This article appeared in the International Journal of Geometric Methods in Modern Physics (IJGMMP) vol 3, no. 2 (2006) 187-199.

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[v1] 24 Aug 2009

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