Flux Compactification

We review recent work in which compactifications of string and M theory are constructed in which all scalar fields (moduli) are massive, and supersymmetry is broken with a small positive cosmological constant, features needed to reproduce real world physics. We explain how this work implies that there is a ``landscape'' of string/M theory vacua, perhaps containing many candidates for describing real world physics, and present the arguments for and against this idea. We discuss statistical surveys of the landscape, and the prospects for testable consequences of this picture, such as observable effects of moduli, constraints on early cosmology, and predictions for the scale of supersymmetry breaking.Comment: 66 pages, 3 figures, Latex with revtex4 macros. v3: version to appear in RM

Physics of String Flux Compactifications

We provide a qualitative review of flux compactifications of string theory, focusing on broad physical implications and statistical methods of analysis.Comment: 39 pages, Latex ar2e.cl

Gravitational backreaction of anti-D branes in the warped compactification

We derive a low-energy effective theory for gravity with anti-D branes, which are essential to get de Sitter solutions in the type IIB string warped compactification, by taking account of gravitational backreactions of anti-D branes. In order to see the effects of the self-gravity of anti-D branes, a simplified model is studied where a 5-dimensional anti-de Sitter ({\it AdS}) spacetime is realized by the bulk cosmological constant and the 5-form flux, and anti-D branes are coupled to the 5-form field by Chern-Simon terms. The {\it AdS} spacetime is truncated by introducing UV and IR cut-off branes like the Randall-Sundrum model. We derive an effective theory for gravity on the UV brane and reproduce the familiar result that the tensions of the anti-D branes give potentials suppressed by the forth-power of the warp factor at the location of the anti-D branes. However, in this simplified model, the potential energy never inflates the UV brane, although the anti-D-branes are inflating. The UV brane is dominated by dark radiation coming from the projection of the 5-dimensional Weyl tensor, unless the moduli fields for the anti-D branes are stabilized. We comment on the possibility of avoiding this problem in a realistic string theory compactification.Comment: typos corrected, 11 pages, 3 figure

The Scaling of the No Scale Potential and de Sitter Model Building

We propose a variant of the KKLT (A)dS flux vacuum construction which does not require an antibrane to source the volume modulus. The strategy is to find nonzero local minima of the no-scale potential in the complex structure and dilaton directions in moduli space. The corresponding no-scale potential expanded about this point sources the volume modulus in the same way as does the antibrane of the KKLT construction. We exhibit explicit examples of such nonzero local minima of the no-scale potential in a simple toroidal orientifold model.Comment: 11 pages, harvmac big. v2: trivial typos fixe

Compactification Effects in D-brane Inflation

We determine the scalar potential for a D3-brane in a warped conifold background subject to general ultraviolet perturbations. Incorporating the effects of imaginary anti-self-dual (IASD) fluxes and four-dimensional curvature at the nonlinear level, we compute the leading terms in the D3-brane potential. We then provide strong cross-checks of our results by reproducing them in the dual gauge theory. Finally, we observe that the D3-brane potential induced by nonperturbative effects on D7-branes can be represented by a ten-dimensional supergravity solution containing suitable IASD fluxes. Our method allows for the systematic inclusion of compactification effects and serves to constrain the D3-brane effective action in a large class of stabilized compactifications.Comment: 4 pages; v2: minor correction

Aspects of brane-antibrane inflation

I describe a dynamical mechanism for solving the fine-tuning problem of brane-antibrane inflation. By inflating with stacks of branes and antibranes, the branes can naturally be trapped at a metastable minimum of the potential. As branes tunnel out of this minimum, the shape of the potential changes to make the minimum shallower. Eventually the minimum disappears and the remaining branes roll slowly because the potential is nearly flat. I show that even with a small number of branes, there is a good chance of getting enough inflation. Running of the spectral index is correlated with the tilt in such a way as to provide a test of the model by future CMB experiments.Comment: 6 pages, 5 figures; proceedings of Theory Canada 1 conference, 2-5 June 2005, UBC, Vancouve

On the Taxonomy of Flux Vacua

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 $WP^{4}_{1,1,1,1,4}$. We find support for the prediction of Ashok and Douglas that the density of vacua on moduli space is governed by ${\rm det}(-R - \omega)$ where $R$ and $\omega$ are curvature and K\"ahler forms on the moduli space. The conifold point $\psi=1$ on moduli space therefore serves as an attractor, with a significant fraction of the flux vacua contained in a small neighborhood surrounding $\psi=1$. We also study the functional dependence of the number of flux vacua on the D3 charge in the fluxes, finding simple power law growth.Comment: 22 pages, harvmac; v2 typos corrected, refs added; v3 minor error correcte

Rapid Tunneling and Percolation in the Landscape

Motivated by the possibility of a string landscape, we reexamine tunneling of a scalar field across single/multiple barriers. Recent investigations have suggested modifications to the usual picture of false vacuum decay that lead to efficient and rapid tunneling in the landscape when certain conditions are met. This can be due to stringy effects (e.g. tunneling via the DBI action), or by effects arising due to the presence of multiple vacua (e.g. resonance tunneling). In this paper we discuss both DBI tunneling and resonance tunneling. We provide a QFT treatment of resonance tunneling using the Schr\"odinger functional approach. We also show how DBI tunneling for supercritical barriers can naturally lead to conditions suitable for resonance tunneling. We argue using basic ideas from percolation theory that tunneling can be rapid in a landscape where a typical vacuum has multiple decay channels and discuss various cosmological implications. This rapidity vacuum decay can happen even if there are no resonance/DBI tunneling enhancements, solely due to the presence of a large number of decay channels. Finally, we consider various ways of circumventing a recent no-go theorem for resonance tunneling in quantum field theory.Comment: 47 pages, 16 figures. Acknowledgements adde

Multi-Throat Brane Inflation

We present a scenario where brane inflation arises more generically. We start with D3 and anti-D3-branes at the infrared ends of two different throats. This setup is a natural consequence of the assumption that in the beginning we have a multi-throat string compactification with many wandering anti-D3-branes. A long period of inflation is triggered when D3-branes slowly exit the highly warped infrared region, under a potential generically arising from the moduli stabilization. In this scenario, the usual slow-roll conditions are not required, and a large warping is allowed to incorporate the Randall-Sundrum model.Comment: 11 pages; v3: minor revision, PRD versio