IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

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We investigate several predictions about the properties of IIB flux vacua on Calabi-Yau orientifolds, by constructing and characterizing a very large set of vacua in a specific example, an orientifold of the Calabi-Yau hypersurface in WP1,1,1,1,44. We find support for the prediction of Ashok and Douglas that the density of vacua on moduli space is governed by det(-R - ω) where R and ω are curvature and Kähler forms on the moduli space. The conifold point ψ = 1 on moduli space therefore serves as an attractor, with a significant fraction of the flux vacua contained in a small neighborhood surrounding ψ = 1. We also study the functional dependence of the number of flux vacua on the D3 charge in the fluxes, finding simple power law growth. © SISSA/ISAS 2004.

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Journal of High Energy Physics

On the taxonomy of flux vacua

There are two known sources of nonperturbative superpotentials for Kähler moduli in type IIB orientifolds, or F-theory compactifications on Calabi-Yau fourfolds, with flux: euclidean brane instantons and low-energy dynamics in D7 brane gauge theories. The first class of effects, euclidean D3 branes which lift in M-theory to M5 branes wrapping divisors of arithmetic genus 1 in the fourfold, is relatively well understood. The second class has been less explored. In this paper, we consider the explicit example of F-theory on K3 × K3 with flux. The fluxes lift the D7 brane matter fields, and stabilize stacks of D7 branes at loci of enhanced gauge symmetry. The resulting theories exhibit gaugino condensation, and generate a nonperturbative superpotential for Kähler moduli. We describe how the relevant geometries in general contain cycles of arithmetic genus χ ≥ 1 (and how χ > 1 divisors can contribute to the superpotential, in the presence of flux). This second class of effects is likely to be important in finding even larger classes of models where the KKLT mechanism of moduli stabilization can be realized. We also address various claims about the situation for IIB models with a single Kähler modulus. © SISSA/ISAS 2005.

Gaugino condensation and nonperturbative superpotentials in flux compactifications

The presence of RR and NS three-form fluxes in type IIB string compactification on a Calabi-Yau orientifold gives rise to a nontrivial superpotential W for the dilaton and complex structure moduli. This superpotential is computable in terms of the period integrals of the Calabi-Yau manifold. In this paper, we present explicit examples of both supersymmetric and nonsupersymmetric solutions to the resulting 4d = 1 supersymmetric no-scale supergravity, including some nonsupersymmetric solutions with relatively small values of W. Our examples arise on orientifolds of the hypersurfaces in WP41,1,1,1,4 and WP41,1,2,2,6. They serve as explicit illustrations of several of the ingredients which have played a role in the recent proposals for constructing de Sitter vacua of string theory.

Flux Compactifications on Calabi-Yau Threefolds

We describe a new class of supersymmetric string compactifications to 4d Minkowski space. These solutions involve type II strings propagating on (orientifolds of) non Calabi-Yau spaces in the presence of background NS and RR fluxes. The simplest examples have descriptions as cosets, generalizing the three-dimensional nilmanifold. They can also be thought of as twisted tori. We derive a formula for the (super)potential governing the light fields, which is generated by the fluxes and certain "twists" in the geometry. Detailed consideration of an example also gives strong evidence that in some cases, these exotic geometries are related by smooth transitions to standard Calabi-Yau or G2 compactifications of M-theory. © SISSA/ISAS 2003.

New supersymmetric string compactifications

We study compactifications of type-IIB string theory on a K3 × T2/Z2 orientifold in the presence of RR and NS flux. We find the most general supersymmetry preserving, Poincare invariant, vacua in this model. All the complex structure moduli and some of the Kähler moduli are stabilised in these vacua. We obtain in an explicit fashion the restrictions imposed by supersymmetry on the flux, and the values of the fixed moduli. Some T-duals and Heterotic duals are also discussed, these are non-Calabi-Yau spaces. A superpotential is constructed describing these duals. Finally, we consider some susy breaking vacua where the flux gives rise to large extra dimensions with vanishing tree-level cosmological constant.