Annales Henri Poincaré - Volume 4 - Supplements by Vincent Rivasseau (Chief Editor)

By Vincent Rivasseau (Chief Editor)

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Success of this analysis raises hope that perhaps the tachyon in (25+1) dimensional bosonic string theory may also be understood in a similar manner. Vol. 4, 2003 Tachyons in String Theory S41 References [1] A. Sen, JHEP 9808, 012 (1998) [arXiv:hep-th/9805170]. [2] A. Sen, JHEP 9912, 027 (1999) [arXiv:hep-th/9911116]. [3] A. Sen, JHEP 9808, 010 (1998) [arXiv:hep-th/9805019]. [4] A. Sen, JHEP 9809, 023 (1998) [arXiv:hep-th/9808141]. [5] E. Witten, JHEP 9812, 019 (1998) [arXiv:hep-th/9810188]. [6] A.

5] E. Witten, JHEP 9812, 019 (1998) [arXiv:hep-th/9810188]. [6] A. Sen, JHEP 9812, 021 (1998) [arXiv:hep-th/9812031]. [7] P. Horava, Adv. Theor. Math. Phys. 2, 1373 (1999) [arXiv:hep-th/9812135]. [8] A. Sen, arXiv:hep-th/9904207. [9] A. Sen, JHEP 0204, 048 (2002) [arXiv:hep-th/0203211]. [10] A. Sen, JHEP 0207, 065 (2002) [arXiv:hep-th/0203265]. [11] A. Sen, Mod. Phys. Lett. A 17, 1797 (2002) [arXiv:hep-th/0204143]. [12] M. R. Garousi, Nucl. Phys. B 584, 284 (2000) [arXiv:hep-th/0003122]; Nucl.

A possible difficulty is that one is used to expect that large splittings correspond to small mixings because normally only close-by states are strongly mixed. In a 2 by 2 matrix context the requirement of large splitting and large mixings leads to a condition of vanishing determinant. For example the matrix m∝ x2 x x 1 . (15) has eigenvalues 0 and 1 + x2 and for x of 0(1) the mixing is large. Thus in the limit of neglecting small mass terms of order m1,2 the demands of large atmospheric neutrino mixing and dominance of m3 translate into the condition that the 2 by 2 subdeterminant 23 of the 3 by 3 mixing matrix approximately vanishes.

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