Simple constraints on the proton-decay lifetime are derived in SO(10) grand unified theory for major descents to the standard group SU(3)cXSU(2)L XU(l)y. It is shown that the only unambiguous pattern of symmetry breaking that predicts a longer proton lifetime [than SU (5)] goes through the Pati-Salam group SU(4)XSU(2)L XSU(2)R and distinguishes quarks from leptons [i.e., SU(4) breaks down to SU(3)c x U (~)~-~] before parity is broken [i.e., SU(2)R is broken]. The lifetime depends on MR [the mass scale associated with SU(2)R breaking] but neither on the other intermediate mass scales nor on sinZew in the limit where Higgs-boson contributions are neglected.
We generalize the formula by Elitzur and Nair on the global-anomaly coefficients in even (D =2n)-dimensional space and analyze global anomalies for Sp(2M, SO(M, and SU(M groups. In particular, we show that any irreducible representation of any Sp(M and SU(2) group has no global anomalies in D = 8k dimensions. In D = 8k +4 dimensions, SU(2) has 2,-type global anomalies only if the spin J of an irreducible representation has the form J = f ( 1 +41) = i, $, P,. . . . For any SU(M group in D =2n, the global-anomaly coefficients can be expressed in terms of so-called unstable James numbers of Stiefel manifold SU(n +l)/SU(n -k) and generalized Dynkin indices Q. +,(a) for SU(n + 1).
Exotic fermions, i.e., fermions with quantum numbers in the standard group [SU(3)cXSU(2)L XU( l)y] different from those of quarks and leptons and/or spin +, are possible candidates for new particles likely to be observed at or above 100 GeV. Two phenomenological lists of exotic fermions are produced, one based on the interaction of the hypothesized exotics with ordinary quarks and leptons via gauge bosons associated with the standard group and the other arising from gauge bosons associated with the enlarged group [SU(4)c X SU( 2 )L X SU(2)R] which contains B -L as a generator. An independent list of exotic fermions in the form of three-preon composites, possessing relatively low masses and special modes of decay, is predicted by the chiral E6c3S0 ( 10) preon model. The connection between the phenomenological and preon-generated exotic fermions is discussed, as is the experimental signatures of these exotics.
A complete analysis is done for the classical Kaluza-Klein cosmology with a torus space, a cosmological constant, and matter. We show that only a negative cosmological constant with the extra dimension greater than one can provide an inflation and the entropy production in our space.
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