Shamit Kachru

De Sitter vacua in string theory

We outline the construction of metastable de Sitter vacua of type IIB string theory. Our starting point is highly warped IIB compactifications with nontrivial NS and RR three-form fluxes. By incorporating known corrections to the superpotential from Euclidean D-brane instantons or gaugino condensation, one can make models with all moduli fixed, yielding a supersymmetric AdS vacuum. Inclusion of a small number of {ovr D3} branes in the resulting warped geometry allows one to uplift the AdS minimum and make it a metastable de Sitter ground state. The lifetime of our metastable de Sitter vacua is much greater than the cosmological timescale of 10{sup 10} years. We also prove, under certain conditions, that the lifetime of dS space in string theory will always be shorter than the recurrence time.

Hierarchies from Fluxes in String Compactifications

Warped compactifications with significant warping provide one of the few known mechanisms for naturally generating large hierarchies of physical scales. We demonstrate that this mechanism is realizable in string theory, and give examples involving orientifold compactifications of IIB string theory and F-theory compactifications on Calabi-Yau four-folds. In each case, the hierarchy of scales is fixed by a choice of RR and NS fluxes in the compact manifold. Our solutions involve compactifications of the Klebanov-Strassler gravity dual to a confining N = 1 supersymmetric gauge theory, and the hierarchy reflects the small scale of chiral symmetry breaking in the dual gauge theory.

Towards Inflation in String Theory

We investigate the embedding of brane inflation into stable compactifications of string theory. At first sight a warped compactification geometry seems to produce a naturally flat inflaton potential, evading one well known difficulty of brane?antibrane scenarios. Careful consideration of the closed string moduli reveals a further obstacle: superpotential stabilization of the compactification volume typically modifies the inflaton potential and renders it too steep for inflation. We discuss the non-generic conditions under which this problem does not arise. We conclude that brane inflation models can only work if restrictive assumptions about the method of volume stabilization, the warping of the internal space, and the source of inflationary energy are satisfied. We argue that this may not be a real problem, given the large range of available fluxes and background geometries in string theory.

Gravity duals of Lifshitz-like fixed points

We find candidate macroscopic gravity duals for scale-invariant but non-Lorentz invariant fixed points, which do not have particle number as a conserved quantity. We compute two-point correlation functions which exhibit novel behavior relative to their AdS counterparts, and find holographic renormalization group flows to conformal field theories. Our theories are characterized by a dynamical critical exponent z, which governs the anisotropy between spatial and temporal scaling t {yields} {lambda}{sup z}t, x {yields} {lambda}x; we focus on the case with z = 2. Such theories describe multicritical points in certain magnetic materials and liquid crystals, and have been shown to arise at quantum critical points in toy models of the cuprate superconductors. This work can be considered a small step towards making useful dual descriptions of such critical points.

4D Conformal Field Theories and Strings on Orbifolds

We propose and test correspondences between 4D quantum field theories (QFTs) with N=2,thinsp1,thinsp0 (super)conformal invariance and type IIB string theory on various orbifolds of AdS{sub 5}{times} S{sup 5} . This allows us to translate the problem of finding stable nontrivial nonsupersymmetric string backgrounds into the problem of realizing nontrivial renormalization group (RG) fixed point QFTs on branes. RG fixed lines in this context correspond to string theories in which no vacuum energy is generated quantum mechanically. {copyright} {ital 1998} {ital The American Physical Society}

Geometric singularities and enhanced gauge symmetries

Abstract Using “Tates algorithm,” we identify loci in the moduli of F-theory compactifications corresponding to enhanced gauge symmetry. We apply this to test the proposed F-theory/heterotic dualities in six dimensions. We recover the perturbative gauge symmetry enhancements of the heterotic side and the physics of small SO (32) instantons, and discover new mixed perturbative/nonperturbative gauge symmetry enhancements. Upon further toroidal compactification to four dimensions, we derive the chain of Calabi-Yau threefolds dual to various Coulomb branches of heterotic strings.

Moduli stabilization from fluxes in a simple IIB orientifold

We study novel type IIB compactifications on the T{sup 6}/Z{sub 2} orientifold. This geometry arises in the T-dual description of Type I theory on T{sup 6}, and one normally introduces 16 space-filling D3-branes to cancel the RR tadpoles. Here, we cancel the RR tadpoles either partially or fully by turning on three-form flux in the compact geometry. The resulting (super)potential for moduli is calculable. We demonstrate that one can find many examples of {Nu} = 1 supersymmetric vacua with greatly reduced numbers of moduli in this system. A few examples with {Nu} > 1 supersymmetry or complete supersymmetry breaking are also discussed.

Type IIA moduli stabilization

We demonstrate that flux compactifications of type IIA string theory can classically stabilize all geometric moduli. For a particular orientifold background, we explicitly construct an infinite family of supersymmetric vacua with all moduli stabilized at arbitrarily large volume, weak coupling, and small negative cosmological constant. We obtain these solutions from both ten-dimensional and four-dimensional perspectives. For more general backgrounds, we study the equations for supersymmetric vacua coming from the effective superpotential and show that all geometric moduli can be stabilized by fluxes. We comment on the resulting picture of statistics on the landscape of vacua.

Exact results for N=2 compactifications of heterotic strings

We search for N = 2, d = 4 theories which can be realized both as heterotic string compactifications on K 3 × T 2 and as type II string compactifications on Calabi-Yau threefolds. In such cases, the exact non-perturbative superpotential of one string theory is given in terms of tree level computations in the other string theory. In particular we find concrete examples which provide the stringy realization of the results of Seiberg and Witten on N=2 Yang-Mills theory, corrected by gravitational/stringy effects. We also discuss some examples which shed light on how the moduli spaces of different N=2 heterotic vacua are connected (This contribution to the conference proceeding has already been published in Nucl. Phys. B 450 (1995) 69).

Holography of Charged Dilaton Black Holes

We study charged dilaton black branes in AdS4. Our system involves a dilaton ϕ coupled to a Maxwell field Fμν with dilaton-dependent gauge coupling,