Ashoke Sen

The sliding singlet mechanism in N = 1 supergravity gut

Abstract We show how the sliding singlet mechanism may be successfully incorporated in SU(6) grand unified theories coupled to N = 1 supergravity, to keep the weak doublet Higgs light, while its color triplet partner acquires a large mass.

On the conservation of electric charge around a monopole of finite size

In monopole-fermion dynamics, the boundary condition which is responsible for baryon number non-conservation also violates electric and color hypercharge conservation. We show by detailed calculations that actually the latter conservation laws are dynamically restored. It is shown that for a finite size monopole, there is a small but finite amplitude for the monopole ground state to make a virtual transition into a state containing a dyon and some fermions carrying equal and opposite charge as that of the dyon. But the amplitude for this state to make a virtual transition to a state carrying a net total charge is identically zero. The monopole ground state, as a result, is an eigenstate of electric charge even in the presence of massless fermions. We also calculate the four-body charge and chirality conserving but baryon number violating condensates, which exist independently of the existence of the anomaly and hence persist even in the presence of more generations of massless fermions.

Monopole-induced baryon number violation due to weak anomally

Abstract Magnetic monopoles may catalyze baryon number violation due to the weak t Hooft anomaly, even if the boundary conditions at the monopole core conserve baryon number. We show, by analyzing a simple toy model, that this effect is unsuppressed by any power of the monopole size, weak symmetry breaking scale, or coupling constant, provided the radius of the monopole core is smaller than Eg2/mw2, E being the energy of the external fermions, g the coupling constant of the SU(2)weak group, and mw the SU(2)weak breaking scale. It is argued that this is a general feature of all monopoles (not necessarily t Hooft-Polyakov monopoles). Possible suppression factors due to the presence of higher generation fermions are discussed.

Cancellation of Sudakov Effects in the Drell-Yan Process

We show, by a direct examination of Feynman graphs, that lowest-order Sudakov effects factorize from Glauber-region gluons in quark-hadron scattering. We then find that the Sudakov double logarithms cancel. This result is consistent with order-by-order factorization in perturbation theory for the Drell-Yan process.

Baryon Number Violation Induced by the Monopoles of the Pati-Salam Model

We study the possible baryon-number violating effects induced by the monopoles that are formed due to the spontaneous breakdown of the Pati-Salam [SU(2) L ×SU(2) R ×SU(4)]. This effect is due to the weak t Hooft anomaly. Although the baryon-number violating condensates involving only the first and the second generation fermions are suppressed by powers of mixing angles, we show that all the relevant mixing angles may be large, while still being consistent with the smallness of the Kobayashi-Maskawa mixing angles. Hence the baryon-number violating effects caused by such monopoles need not be suppressed.

Heterotic String Theory on Calabi-Yau Manifolds in the Green-Schwarz Formalism*

The σ-model describing the propagation of the heterotic string in a Calabi-Yau background is written down in the Green-Schwarz formulation. This model has manifest N=1 space-time supersymmetry, however only the SO(2) subgroup of the four-dimensional Lorentz group is realized linearly. The criteria for the existence of the full SO(3, 1) Lorentz symmetry in this model are studied. These requirements turn out to be identical to those obtained by demanding the existence of space-time supersymmetry in the Neveu-Schwarz-Ramond formulation of the theory, where the SO(3, 1) Lorentz symmetry is manifest, but space-time supersymmetry is not. The analysis is easily generalized to more general backgrounds, which give rise to (2, 0) superconformal field theories on the world sheet. Finally it is shown that if the requirements which give unbroken N=1 space-time supersymmetry and full SO(3, 1) Lorentz invariance are satisfied, then the unbroken gauge group after the compactification of the E 8 ×E 8 heterotic string theory on Calabi-Yau spaces is E 8 ×E 6 .

Conservation Laws in the Monopole-Fermion System

It is shown that the monopole induced baryon number non-conservation is a necessary consequence of the exact conservation laws of the full four dimensional fermion-gauge field-Higgs system and properties of the J = 0 partial wave fermions.