Particle theory

Abstract:

We review the spectral cover formalism for constructing both U(n) and SU(n) holomorphic vector bundles on elliptically fibered Calabi-Yau three-folds which admit a section. We discuss the allowed bases of these three-folds and show that physical constraints eliminate Enriques surfaces from consideration. Relevant properties of the remaining del Pezzo and Hirzebruch surfaces are presented. Restricting the structure group to SU(n), we derive, in detail, a set of rules for the construction of three-family particle physics theories with phenomenologically relevant gauge groups. We show that anomaly cancellation generically requires the existence of non-perturbative vacua containing five-branes. We illustrate these ideas by constructing four explicit three-family non-perturbative vacua.

Abstract:

In this letter, we introduce a general theory for the construction of particle physics theories, with three families and realistic gauge groups, within the context of heterotic M-theory. This is achieved using semi-stable holomorphic gauge bundles over elliptically fibered Calabi-Yau three-folds. Construction of realistic theories is facilitated by the appearance of non-perturbative five-branes in the vacuum. The complete moduli space of these five-branes is computed and their worldvolume gauge theory discussed. In the context of holomorphic gauge bundles, it is shown how grand unified gauge groups can be spontaneously broken to the gauge group of the standard model. These ideas are illustrated in an explicit SU(5) three-family example.

Abstract:

We calculate the mass spectra and string tensions of SU(2), SU(3), SU(4) and SU(5) gauge theories in 2+1 dimensions. We do so by simulating the corresponding lattice theories and then extrapolating dimensionless mass ratios to the continuum limit. We find that such mass ratios are, to a first approximation, independent of the number of colors, Nc, and that the remaining dependence can be accurately reproduced by a simple O(1/Nc2) correction. This provides us with a prediction of these mass ratios for all SU(Nc) theories in 2+1 dimensions and demonstrates that these theories are already "close" to Nc=∞ for Nc≥2. We find that the theory retains a non-zero confining string tension as Nc→∞ and that the dimensionful coupling g2 is proportional to 1/Nc at large Nc, when expressed in units of the dynamical length scale of the theory. During the course of these calculations we study in detail the effects of including over-relaxation in the Monte Carlo calculation, of using a mean-field improved coupling to extrapolate to the continuum limit, and the use of space-time asymmetric lattice actions to resolve heavy glueball correlators. ©1998 The American Physical Society.

Abstract:

Models of leptogenesis often invoke the out-of-equilibrium decays of heavy right-handed neutrinos in order to create a baryon asymmetry of the universe through the electroweak phase transition. Their presumed existence argues strongly for the presence of an SU(2)R gauge symmetry. We study the equilibrating effects of the resulting additional right-handed interactions and find that successful leptogenesis requires that mN≳1016 GeV if mN>mWR, and mWRR≳2× 105 GeV(mN/102 GeV)3//4 if mNmwR. We show also that the mN>mwR option is excluded in a supersymmetric theory with gravitinos. © 1999 Published by Elsevier Science B.V. All rights reserved.

Abstract:

We investigate the contribution of instantons to the eigenvalue spectrum of the Dirac operator in quenched QCD. The instanton configurations that we use have been derived, elsewhere, from cooled SU(3) lattice gauge fields and, for comparison, we also analyze a random “gas” of instantons. Using a set of simplifying approximations, we find a non-zero chiral condensate. However, we also find that the spectral density diverges for small eigenvalues, so that the chiral condensate, at zero quark mass, diverges in quenched QCD. The degree of divergence decreases with the instanton density, so that it is negligible for the smallest number of cooling sweeps but becomes substantial for larger number of cools. We show that the spectral density scales, that finite volume corrections are small and we see evidence for the screening of topological charges. However, we also find that the spectral density and chiral condensate vary rapidly with the number of cooling sweeps — unlike, for example, the topological susceptibility. Whether the problem lies with the cooling or with the identification of the topological charges is an open question. This problem needs to be resolved before one can determine how important the divergence we have found is for quenched QCD. © 1999 The American Physical Society.