Mass Generation for an Ultralight Axion

If a global chiral symmetry is explicitly broken by anomalies in nonabelian gauge theories, a pseudo Nambu-Goldstone boson (axion) associated with a spontaneous breakdown of such a global symmetry acquires a mass through nonperturbative instanton effects. We calculate the axion mass assuming a supersymmetric SU(2) gauge theory and show that the axion obtains an extremely small mass when the SU(2) gauge symmetry is broken down at very high energy, say at the Planck scale. We identify the axion with a hypothetical ultralight boson field proposed to account for a small but nonzero cosmological constant suggested from recent cosmological observations.Comment: 11 pages, Late

A Solution to the Doublet-Triplet Splitting Problem in the Type IIB Supergravity

The doublet--triplet mass splitting problem is one of the most serious problems in supersymmetric grand unified theories (GUTs). A class of models based on a product gauge group, such as the SU(5)_{GUT} times U(3)_H or the SU(5)_{GUT} times U(2)_H, realize naturally the desired mass splitting that is protected by an unbroken R symmetry. It has been pointed out that various features in the models suggest that these product-group unification models are embedded in a supersymmetric brane world. We show an explicit construction of those models in the supersymmetric brane world based on the Type IIB supergravity in ten dimensions. We consider T^6/(Z_{12} times Z_2) orientifold for the compactified six extra dimensions. We find that all of the particles needed for the GUT-symmetry-breaking sector are obtained from the D-brane fluctuations. The three families of quarks and leptons are introduced at an orbifold singularity, although their origin remains unexplained. This paper includes extensive discussion on anomaly cancellation in a given orbifold geometry. Relation to the Type IIB string theory, realization of R symmetry as a rotation of extra-dimensional space, and effective superpotential at low energies are also discussed.Comment: 61 page