A cosmotopological relation for a unified field theory

I present an argument, based on the topology of the universe, why there are three generations of fermions. The argument implies a preferred unified gauge group of SU(5), but with SO(10) representations of the fermions. The breaking pattern $SU(5) \to SU(3) \times SU(2) \times U(1)$ is preferred over the pattern $SU(5) \to SU(4) \times U(1)$. On the basis of the argument one expects an asymmetry in the microwave data, which might have been detected already.Comment: 6 page

Massive Hyper-Kahler Sigma Models and BPS Domain Walls

With the non-Abelian Hyper-Kahler quotient by U(M) and SU(M) gauge groups, we give the massive Hyper-Kahler sigma models that are not toric in the N=1 superfield formalism. The U(M) quotient gives N!/[M! (N-M)!] (N is a number of flavors) discrete vacua that may allow various types of domain walls, whereas the SU(M) quotient gives no discrete vacua. We derive BPS domain wall solution in the case of N=2 and M=1 in the U(M) quotient model.Comment: 16 pages, 1 figure, contribution to the Proceedings of the International Conference on "Symmetry Methods in Physics (SYM-PHYS10)" held at Yerevan, Armenia, 13-19 Aug. 200

Membrane solitons in eight-dimensional hyper-Kaehler backgrounds

We derive the BPS equations satisfied by lump solitons in $(2+1)$-dimensional sigma models with toric 8-dimensional hyper-K\"ahler (${HK}_8$) target spaces and check they preserve 1/2 of the supersymmetry. We show how these solitons are realised in M theory as M2-branes wrapping holomorphic 2-cycles in the \bE^{1,2}\times {HK}_8 background. Using the $\kappa$-symmetry of a probe M2-brane in this background we determine the supersymmetry they preserve, and note that there is a discrepancy in the fraction of supersymmetry preserved by these solitons as viewed from the low energy effective sigma model description of the M2-brane dynamics or the full M theory. Toric ${HK}_8$ manifolds are dual to a Hanany-Witten setup of D3-branes suspended between 5-branes. In this picture the lumps correspond to vortices of the three dimensional ${\mathcal N}=3$ or ${\mathcal N}=4$ theory.Comment: 12+1 pages. LaTex. v2: Typos corrected and references adde

A Modular Invariant Partition Function for the Fivebrane

We compute an SL(6,Z) invariant partition function for the chiral two-form of the M theory fivebrane compactified on the six-torus. From a manifestly SL(5,Z) invariant formalism, we prove that the partition function has an additional SL(2,Z) symmetry. The combination of these two symmetries ensures SL(6,Z) invariance. Thus, whether or not a fully covariant Lagrangian is available, the fivebrane on the six-torus has a consistent quantum theory.Comment: 27 pages. References added. To appear in Nuclear Physics

D=2, N=2, Supersymmetric theories on Non(anti)commutative Superspace

The classical action of a two dimensional N=2 supersymmetric theory, characterized by a general K\"{a}hler potential, is written down on a non(anti)commutative superspace. The action has a power series expansion in terms of the determinant of the non(anti)commutativity parameter $C^{\alpha\beta}$. The theory is explicitly shown to preserve half of the N=2 supersymmetry, to all orders in (det C)^n. The results are further generalized to include arbitrary superpotentials as well.Comment: 32 pages, Latex; v2:minor typos corrected and a reference adde

Probing grain boundaries in ceramic scintillators using x-ray radioluminescence microscopy

X-ray radioluminescence microscopy (XRLM), a novel fluorescence microscopy technique under focused x-ray excitation, was used to characterize micro-scale luminescence of Eu:Y2O3 and Ce:YAG transparent ceramics and bicrystals. The diffusion length of a known semiconductor measured by XRLM was found to be in agreement with previously measured values, illustrating its use for characterizing charge carrier transport. Emission intensity was found to drop at the boundaries in both Eu:Y2O3 and Ce:YAG ceramics and bicrystals. The depletion in emission at grain boundaries was ultimately found to be related to charge carrier depletion (through either deep trapping or non-radiative recombination). A charge carrier diffusion model was used to understand the effect of grain boundaries on charge carrier transport in these scintillators. The diffusion model was found to accurately predict the spatial distribution of emission in a Ce:YAG single-crystal as a function of x-ray excitation energy. Structural and chemical characterization of grain boundaries in an Eu:Y2O3 ceramic using transmission electron microscopy and secondary ion mass spectrometry mapping showed an ordered boundary region and no detectable segregation of impurities or Eu, justifying the use of an abrupt boundary condition to determine boundary recombination velocities in these materials. The boundary recombination velocities were then used to show that, for ceramics with grain sizes \u3e similar to 20 mu m, there would be a minimal effect from the detected charge carrier depletion at grain boundaries on their bulk x-ray radioluminescence intensity. Ultimately, this study illustrates how this new XRLM technique can be used to measure charge carrier diffusion properties and how it may be coupled with microstructural and micro-scale chemical analyses to fully investigate the effect of grain boundaries on scintillator properties

Sigma-model soliton intersections from exceptional calibrations

A first-order `BPS' equation is obtained for 1/8 supersymmetric intersections of soliton-membranes (lumps) of supersymmetric (4+1)-dimensional massless sigma models, and a special non-singular solution is found that preserves 1/4 supersymmetry. For 4-dimensional hyper-K\"ahler target spaces ($HK_4$) the BPS equation is shown to be the low-energy limit of the equation for a Cayley-calibrated 4-surface in \bE^4\times HK_4. Similar first-order equations are found for stationary intersections of Q-lump-membranes of the massive sigma model, but now generic solutions preserve either 1/8 supersymmetry or no supersymmetry, depending on the time orientation.Comment: 21 pages. Version 3: Minor corrections and one further reference: version published in JHE

Comments on Supersymmetric Vector and Matrix Models

Some results in random matrices are generalized to supermatrices, in particular supermatrix integration is reduced to an integration over the eigenvalues and the resulting volume element is shown to be equivalent to a one dimensional Coulomb gas of both positive and negative charges.It is shown that,for polynomial potentials, after removing the instability due to the annihilation of opposite charges, supermatrix models are indistinguishable from ordinary matrix models, in agreement with a recent result by Alvarez-Gaume and Manes. It is pointed out however that this may not be true for more general potentials such as for instance the supersymmetric generalization of the Penner model.Comment: 6 page

A geometric bound on F-term inflation

We discuss a general bound on the possibility to realise inflation in any minimal supergravity with F-terms. The derivation crucially depends on the sGoldstini, the scalar field directions that are singled out by spontaneous supersymmetry breaking. The resulting bound involves both slow-roll parameters and the geometry of the K\"ahler manifold of the chiral scalars. We analyse the inflationary implications of this bound, and in particular discuss to what extent the requirements of single field and slow-roll can both be met in F-term inflation.Comment: 14 pages, improved analysis, references added, matches published versio

Riemannian Geometry of Noncommutative Surfaces

A Riemannian geometry of noncommutative n-dimensional surfaces is developed as a first step towards the construction of a consistent noncommutative gravitational theory. Historically, as well, Riemannian geometry was recognized to be the underlying structure of Einstein's theory of general relativity and led to further developments of the latter. The notions of metric and connections on such noncommutative surfaces are introduced and it is shown that the connections are metric-compatible, giving rise to the corresponding Riemann curvature. The latter also satisfies the noncommutative analogue of the first and second Bianchi identities. As examples, noncommutative analogues of the sphere, torus and hyperboloid are studied in detail. The problem of covariance under appropriately defined general coordinate transformations is also discussed and commented on as compared with other treatments.Comment: 28 pages, some clarifications, examples and references added, version to appear in J. Math. Phy