Renata Kallosh

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.

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.

Black holes and critical points in moduli space

We study the stabilization of scalars near a supersymmetric black hole horizon using the equation of motion of a particle moving in a potential and background metric. When the relevant 4-dimensional theory is described by special geometry, the generic properties of the critical points of this potential can be studied. We find that the extremal value of the central charge provides the minimal value of the BPS mass and of the potential under the condition that the moduli space metric is positive at the critical point. This is a property of a regular special geometry. We also study the critical points in all N ⩾ 2 supersymmetric theories. We relate these ideas to the Weinhold and Ruppeiner metrics introduced in the geometric approach to thermodynamics and used for the study of critical phenomena.

Universality of supersymmetric attractors

The macroscopic entropy-area formula for supersymmetric black holes in {ital N}=2,4,8 theories is found to be universal: in {ital d}=4 it is always given by the square of the largest of the central charges extremized in moduli space. The proof of universality is based on the fact that the doubling of unbroken supersymmetry near the black hole horizon requires that all central charges other than {ital Z}={ital M} vanish at the attractor point for {ital N}=4,8. The ADM mass at the extremum can be computed in terms of duality symmetric quartic invariants which are moduli independent. The extension of these results for {ital d}=5, {ital N}=1,2,4 is also reported. A duality symmetric expression for the energy of the ground state with spontaneous breaking of supersymmetry is provided by the power 1/2 (2/3) of the black hole area of the horizon in {ital d}=4 ({ital d}=5). It is suggested that the universal duality symmetric formula for the energy of the ground state in supersymmetric gravity is given by the modulus of the maximal central charge at the attractor point in any supersymmetric theory in any dimension. {copyright} {ital 1996 The American Physical Society.}

De Sitter string vacua from supersymmetric D-terms

We propose a new mechanism for obtaining de Sitter vacua in type-IIB string theory compactified on (orientifolded) Calabi-Yau manifolds similar to those recently studied by Kachru, Kallosh, Linde and Trivedi (KKLT). dS vacuum appears in KKLT model after uplifting an AdS vacuum by adding an anti-D3-brane, which explicitly breaks supersymmetry. We accomplish the same goal by adding fluxes of gauge fields within the D7-branes, which induce a D-term potential in the effective 4D action. In this way we obtain dS space as a spontaneously broken vacuum from a purely supersymmetric 4D action. We argue that our approach can be directly extended to heterotic string vacua, with the dilaton potential obtained from a combination of gaugino condensation and the D-terms generated by anomalous U(1) gauge groups.

κ-symmetry, supersymmetry and intersecting branes

We present a new form of κ-symmetry transformations for D-branes in which the dependence on the Born-Infeld field strength is expressed as a relative rotation on the left- and right-moving fields with opposite parameters. Then, we apply this result to investigate the supersymmetry preserved by certain intersecting brane configurations at arbitrary angles and with non-vanishing constant Born-Infeld fields. We also comment on the covariant quantization of the D-brane actions.

Superconformal inflationary α -attractors

A bstractRecently a broad class of superconformal inflationary models was found leading to a universal observational prediction

Minimal Supergravity Models of Inflation

{n_s}=1-\frac{2}{N}

Landscape, the scale of SUSY breaking, and inflation

and

Universality class in conformal inflation

r=\frac{12 }{{{N^2}}}