Dileep P. Jatkar

Dyon spectrum in CHL models

We propose a formula for the degeneracy of quarter BPS dyons in a class of CHL models. The formula uses a modular form of a subgroup of the genus two modular group Sp(2, Z). Our proposal is S-duality invariant and reproduces correctly the entropy of a dyonic black hole to first non-leading order for large values of the charges.

On the cosmological relevance of the tachyon

Abstract We analyse of the effective action of the tachyon field on a D-brane, of both bosonic as well as superstring theory. We find that the non-standard kinetic term of the tachyon field requires a correction to the Born–Infeld type Lagrangian. The cosmological significance of the resulting dynamics is explored. We also examine if the rolling tachyon can provide an effective cosmological constant and contrast its behaviour with quintessence.

Product representation of dyon partition function in CHL models

A formula for the exact partition function of 1/4 BPS dyons in a class of CHL models has been proposed earlier. The formula involves inverse of Siegel modular forms of subgroups of Sp(2,). In this paper we propose product formulae for these modular forms. This generalizes the result of Borcherds and Gritsenko and Nikulin for the weight 10 cusp form of the full Sp(2,) group.

Dyon spectrum in generic N=4 supersymmetric Z(N) orbifolds

We find the exact spectrum of a class of quarter BPS dyons in a generic N=4 supersymmetric Z_N orbifold of type IIA string theory on K3\times T^2 or T^6. We also find the asymptotic expansion of the statistical entropy to first non-leading order in inverse power of charges and show that it agrees with the entropy of a black hole carrying same set of charges after taking into account the effect of the four derivative Gauss-Bonnet term in the effective action of the theory.

Gravitational couplings and Z2 orientifolds

The interplay between gravitational couplings on branes and the occurrence of fractional flux in low-dimensional orientifolds is examined. It is argued that gravitational couplings need to be assigned not only to D-branes but also to orientifold planes. The fractional charges of the orientifold d-planes can be understood in terms of flux quantization of the d − 3 form potential and modified Bianchi identities. Detailed results are presented for the case of the type IIB orientifold on T6/Z2, which is dual to F-theory on a complex 4-fold with terminal singularities.

Nielsen-Olesen vortices in noncommutative abelian Higgs model

We construct Nielsen-Olesen vortex solution in the noncommutative abelian Higgs model. We derive the quantized topological flux of the vortex solution. We find that the flux is integral by explicit computation in the large-θ limit as well as in the small-θ limit. In the context of a tachyon vortex on the brane-antibrane system we demonstrate that it is this topological charge that gives rise to the RR charge of the resulting BPS D-brane. We also consider the left-right-symmetric gauge theory which does not have a commutative limit and construct an exact vortex solution in it.

Dyon spectrum in Script N = 4 supersymmetric type II string theories

We compute the spectrum of quarter BPS dyons in freely acting Z 2 and Z 3 orbifolds of type II string theory compactified on a six dimensional torus. For large charges the result for statistical entropy computed from the degeneracy formula agrees with the corresponding black hole entropy to first non-leading order after taking into account corrections due to the curvature squared terms in the effective action. The result is significant since in these theories the entropy of a small black hole, computed using the curvature squared corrections to the effective action, fails to reproduce the statistical entropy associated with elementary string states.

Hybrid inflation and brane–antibrane system

We study a string theory inspired model for hybrid inflation in the context of a brane–antibrane system partially compactified on a compact submanifold of (a caricature of) a Calabi–Yau manifold. The interbrane distance acts as the inflaton, whereas the end of the inflationary epoch is brought about by the rapid rolling of the tachyon. The number of e-foldings is sufficiently large and is controlled by the initial conditions. The slow roll parameters, however, are essentially determined by the geometry and have little parametric dependence. Primordial density fluctuations can be made consistent with current data at the cost of reducing the string scale.

Dyon spectrum in generic = 4 supersymmetric ℤN orbifolds

We find the exact spectrum of a class of quarter BPS dyons in a generic N=4 supersymmetric Z_N orbifold of type IIA string theory on K3\times T^2 or T^6. We also find the asymptotic expansion of the statistical entropy to first non-leading order in inverse power of charges and show that it agrees with the entropy of a black hole carrying same set of charges after taking into account the effect of the four derivative Gauss-Bonnet term in the effective action of the theory.

Adding charges to N = 4 dyons

The spectrum of dyons in a class of N = 4 supersymmetric string theories has been found for a specific set of electric and magnetic charge vectors. We extend the analysis to more general charge vectors by considering various charge carrying collective excitations of the original system.