INTERPLAY OF MATHEMATICS AND PHYSICS: ATIYAH—SINGER INDEX THEORY AND GAUGE THEORIES OF PARTICLE PHYSICS: Atiyah—Singer Index Theory, which relates the solution space of certain types of partial differential equations (PDEs) to topological data of the PDE, is a highlight of modern mathematics. It also has major physical consequences in gauge theories of particle physics where it implies a connec...

We study unification in the Randall-Sundrum scenario for solving the hierarchy problem, with gauge fields and fermions in the bulk. We calculate the one-loop corrected low-energy effective gauge couplings in a unified theory, broken at the scale MGUT in the bulk. We find that, although this scenario has an extra dimension, there is a robust (calculable in the effective field theory) logarithmic...

We study unification in the Randall-Sundrum scenario for solving the hierarchy problem, with gauge fields and fermions in the bulk. We calculate the one-loop corrected low-energy effective gauge couplings in a unified theory, broken at the scale MGUT in the bulk. We find that, although this scenario has an extra dimension, there is a robust (calculable in the effective field theory) logarithmic...

Grand gauge-Higgs unification of five dimensional SU(6) gauge theory on an orbifold $S^1/Z_2$ with localized kinetic terms is discussed. The Standard model (SM) fermions the boundaries and some massive bulk coupling to SM boundary are introduced. Taking power-law running contributions from fields into account, perturbative shown be realized at around $10^{14}$ GeV, which a few order smaller tha...

We systematically study the unification of gauge couplings in the presence of (one or more) effective dimension-5 operators cHG G =4Mpl, induced into the grand unified theory by gravitational interactions at the Planck scale. These operators alter the usual condition for gauge-coupling unification, which can, depending on the Higgs content H and vacuum expectation value, result in unification a...

From the quantum field theory point of view, matter and gauge fields are generally expected to be localised around branes or topological defects occurring in extra dimensions. Here I discuss a simple scenario where, by starting with a five dimensional SU(3) gauge theory, we end up with several 4-D parallel branes with localised “chiral” fermions and gauge fields to them. I will show that it is ...

We show that more than two generations of quarks and leptons are required to have an anomaly free discrete R symmetry larger than R parity, provided that the supersymmetric standard model can be minimally embedded into a grand unified theory. This connects an explanation for the number of generations with seemingly unrelated problems such as supersymmetry breaking, proton decay, the μ problem, ...

We study the connection between N = 2 supersymmetry and a topological bound in a two-Higgsdoublet system having an SU(2) × U(1)Y × U(1)Y ′ gauge group. We derive Bogomol’nyi equations from supersymmetry considerations showing that they hold provided certain conditions on the coupling constants, which are a consequence of the huge symmetry of the theory, are satisfied. Supersymmetric Grand Unifi...

We examine the consequences of leptoquark explanation of HERA anomaly in the context of R parity conserving supersymmetric gauge unified theory with the gauge unification scale at ∼ 10 16 GeV. We pointed out the difficulty of constructing a grandunified theory. However gauge unification is still possible at ∼ 10 16 GeV when additional multiplets are introduced. We determine the mass spectrum of...

We construct a minimal supersymmetric SO(10) grand unified model in 5 dimensions. The extra dimension is compactified on an S/(Z2 × Z ′ 2) orbifold which has two inequivalent fixed points. These are flat 4-dimensional Minkowski spaces: the visible and the hidden branes. By orbifolding, the gauge symmetry on the hidden brane is reduced down to the Pati–Salam gauge symmetry SU(4)×SU(2)L×SU(2)R. O...