Realistic Type IIB supersymmetric Minkowski flux vacua

We show that there exist supersymmetric Minkowski vacua on Type IIB toroidal orientifold with general flux compactifications where the RR tadpole cancellation conditions can be relaxed elegantly. Then we present a realistic Pati–Salam like model. At the string scale, the gauge symmetry can be broken down to the Standard Model (SM) gauge symmetry, the gauge coupling unification can be achieved naturally, and all the extra chiral exotic particles can be decoupled so that we have the supersymmetric SMs with/without SM singlet(s) below the string scale. The observed SM fermion masses and mixings can also be obtained. In addition, the unified gauge coupling, the dilaton, the complex structure moduli, the real parts of the Kähler moduli and the sum of the imaginary parts of the Kähler moduli can be determined as functions of the four-dimensional dilaton and fluxes, and can be estimated as well.     

Flux compactifications in string theory: A comprehensive review

We present a pedagogical overview of flux compactifications in string theory, from the basic ideas to the most recent developments. We concentrate on closed-string fluxes in type-II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyze the resulting four-dimensional effective theories, as well as some of its perturbative and non-perturbative corrections, focusing on moduli stabilization. Finally, we briefly review statistical studies of flux backgrounds.     

The Low Energy Limit of String Theory and its Compactifications with Background Fluxes

String theory is consistently defined in ten dimensions. In order to extract any information about four-dimensional physics, we need to understand the properties of the six-dimensional compact manifold orthogonal to our four-dimensional universe. A possibility that is being very much explored lately is to look at manifolds on which background fluxes are turned on. In this article, we present an introduction to string theory, focusing on its massless sector. We then review traditional compactifications to four–dimensions, and finally motivate and describe the so-called flux compactifications. We interpret the allowed six-dimensional manifolds from the point of view of generalized complex geometry.     

De Sitter universes and the emerging landscape in string theory

We discuss a recent proposal to construct de Sitter vacua in string theory. It is based on flux compactifications in string theory where all the moduli are stabilised and supersymmetry is broken with control. The resulting picture is that of a complicated landscape with many vacua of widely varying values for the cosmological constant.     

Fermionic vacuum polarization in compactified cosmic string spacetime

We investigate the fermionic condensate and the vacuum expectation value (VEV) of the energy-momentum tensor for a charged massive fermionic field in the geometry of a cosmic string compactified along its axis. In addition, we assume the presence of two types of magnetic fluxes: a flux running along the cosmic string and another enclosed by the compact dimension. These fluxes give rise to Aharanov–Bohm-like effects on the VEVs. The VEVs are decomposed into two parts corresponding to the geometry of a straight cosmic string without compactification plus a topological part induced by the compactification of the string axis. Both contributions are even periodic functions of the magnetic fluxes with period equal to the flux quantum. The vacuum energy density is equal to the radial stress for the parts corresponding to the straight cosmic string and the topological one. Moreover, the axial stress is equal to the energy density for the parts corresponding to the straight cosmic string; however, for massive fermionic fields this does not occur for the topological contributions. With respect to the dependence on the magnetic fluxes, both the fermionic condensate and the vacuum energy density, can be either positive or negative. Moreover, for points near the string, the main contribution to the VEVs comes from the straight cosmic string part, whereas at large distances the topological ones dominate. In addition to the local characteristics of the vacuum state, we also evaluate the part in the topological Casimir energy induced by the string.     

Supersymmetry breaking with zero vacuum energy in M-theory flux compactifications

An attractive mechanism to break supersymmetry in vacua with zero vacuum energy arose in E(8) x E(8) heterotic models with hidden sector gaugino condensate. An H flux balances the exponentially small condensate on shell and fixes the complex structure moduli. At quantum level this balancing is, however, obstructed by the quantization of the H flux. We show that the warped flux compactification background in heterotic M theory can solve this problem through a warp-factor suppression of the integer flux relative to the condensate. We discuss the suppression mechanism both in the M theory and the four-dimensional effective theory and provide a derivation of the condensate's superpotential which is free of delta-function squared ambiguities.     

Flux vacua statistics for two‐parameter Calabi‐Yau's

We study the number of flux vacua for type IIB string theory on an orientifold of the Calabi‐Yau expressed as a hypersurface in WCP ⁴[1,1,2,2,6] by evaluating a suitable integral over the complex‐structure moduli space as per the conjecture of Douglas and Ashok. We show that away from the singular conifold locus, one gets a power law, and that the (neighborhood) of the conifold locus indeed acts as an attractor in the (complex structure) moduli space. In the process, we evaluate the periods near the conifold locus. We also study (non)supersymmetric solutions near the conifold locus, and show that supersymmetric solutions near the conifold locus do not support fluxes.     

Mirror symmetry and the web of Landau-Ginzburg string vacua

We present some mathematical aspects of Landau-Ginzburg string vacua in terms of toric geometry. The one-to-one correspondence between toric divisors and some of the (−1, 1) states in the Landau-Ginzburg model is presented for superpotentials of typical types. The Landau-Ginzburg interpretation of non-toric divisors is also presented. Using this interpretation, we propose a method to solve the so-called “twisted sector problem” by orbifold construction. Moreover, this construction shows that the moduli spaces of the original Landau-Ginzburg string vacua and their orbifolds are connected. By considering the mirror map of the Landau-Ginzburg models, we obtain the relation between Mori vectors and the twist operators of our orbifoldization. This consideration enables us to argue the embedding of the Seiberg-Witten curve in the defining equation of the Calabi-Yau manifolds on which the type II string gets compactified. Related topics concerning the Calabi-Yau fourfolds and the extremal transition are discussed.     

The energy of the analytic lump solution in SFT

Journal of High Energy Physics - We study $ \mathcal{N} = 1 $ Minkowski vacua in compactifications of type II string theory in the language of exceptional generalized geometry (EGG). We find the...     

Heterotic strings on homogeneous spaces

We construct heterotic string backgrounds corresponding to families of homogeneous spaces as exact conformal field theories. They contain left cosets of compact groups by their maximal tori supported by NS‐NS 2‐forms and gauge field fluxes. We give the general formalism and modular‐invariant partition functions, then we consider some examples such as SU (2)/U (1) ~ S² (already described in a previous paper) and the SU (3)/U(1)² flag space. As an application we construct new supersymmetric string vacua with magnetic fluxes and a linear dilaton.     

Statistics in the landscape of intersecting brane models

An approach towards a statistical survey of four-dimensional supersymmetric vacua in the string theory landscape is described and illustrated with three examples of ensembles of intersecting D-brane models. The question whether it is conceivable to make predictions based on statistical distributions is discussed. Especially interesting in this context are possible correlations between low energy observables. As an example we look at correlations between properties of the gauge sector of intersecting D-brane models and Gepner model constructions. Based on a talk presented at “The 15th International Conference on Supersymmetry and the Unification of Fundamental Interactions”, July 26–August 1, 2007, Karlsruhe, Germany.     

Four-dimensional N = 2 superstring constructions and their (non-) perturbative duality connections

We investigate the connections between four-dimensional, N = 2 M-theory vacua constructed as orbifolds of type II, heterotic, and type I strings. All these models have the same massless spectrum, which contains an equal number of vector multiplets and hypermultiplets, with a gauge group of the maximal rank allowed in a perturbative heterotic string construction. We find evidence for duality between two type I compactifications recently proposed and a new heterotic construction that we present here. This duality allows us to gain insight into the non-perturbative properties of these models. In particular we consider gravitational corrections to the effective action.     

On the 4D effective theory in warped compactifications with fluxes and branes

We present a systematic way to derive the four-dimensional effective theories for warped compactifications with fluxes and branes in the ten-dimensional type IIB supergravity. The ten-dimensional equations of motion are solved using the gradient expansion method and the effective four-dimensional equations of motions are derived by imposing the consistency condition that the total derivative terms with respect to the six-dimensional internal coordinates vanish when integrated over the internal manifold. By solving the effective four-dimensional equations, we can find the gravitational backreaction to the warped geometry due to the dynamics of moduli fields, branes and fluxes.     

N = 4 Supersymmetric (Dyonic) Hypermultiplets in String Theory

In four-dimensional N = 4 supersymmetric gauge theory, we obtain an exact metric on the moduli space of quantum vacua and analyze the spectra of BPS states in weak as well as in strong coupling regions. Identifying the hypermultiplet of the dyonic state as a string stretched between D₃-brane probe and a 7-brane, we demonstrate that the two hypermultiplets, which become massless at two singularities in supersymmetric theory, correspond to open strings beginning on the D₃-brane and ending on the respective 7-brane.     

Why there is something rather than nothing: cosmological constant from summing over everything in lorentzian quantum gravity

The density matrix of the Universe for the microcanonical ensemble in quantum cosmology describes an equipartition in the physical phase space of the theory (sum over everything), but in terms of the observable spacetime geometry this ensemble is peaked about the set of recently obtained cosmological instantons limited to a bounded range of the cosmological constant. This suggests the mechanism of constraining the landscape of string vacua and a possible solution to the dark energy problem in the form of the quasiequilibrium decay of the microcanonical state of the Universe.     

Critical Points and Supersymmetric Vacua, III: String/M Models

A fundamental problem in contemporary string/M theory is to count the number of inequivalent vacua satisfying constraints in a string theory model. This article contains the first rigorous results on the number and distribution of supersymmetric vacua of type IIb string theories compactified on a Calabi-Yau 3-fold X with flux. In particular, complete proofs of the counting formulas in Ashok-Douglas [AD] and Denef-Douglas [DD1] are given, together with van der Corput style remainder estimates.Supersymmetric vacua are critical points of certain holomorphic sections (flux superpotentials) of a line bundle over the moduli space of complex structures on X × T ² with respect to the Weil-Petersson connection. Flux superpotentials form a lattice of full rank in a 2 b ₃(X)-dimensional real subspace . We show that the density of critical points in for this lattice of sections is well approximated by Gaussian measures of the kind studied in [DSZ1,DSZ2,AD,DD1].Research partially supported by DOE grant DE-FG02-96ER40959 (first author) and NSF grants DMS-0100474 (second author) and DMS-0302518 (third author).     

Gravitational waves as string vacua II

Classical propagation of (super)strings through gravitational shock waves is analyzed. The exact classical solutions are used for quantization and for the identification of the exact quantumS-matrix describing string scattering by the wave. ThisS-matrix coincides with theS-matrix of the string-string scattering in theflat space-time for particular profile of the shock wave! This is interpreted as the generation of curved geometry from the flat space-time string theory. The quantum consistence of (super)string motion in gravitational plane wave backgrounds is then studied. It turns out that for the standard dimensionsD=26 (D=10) the vanishing of the Ricci tensor for the plane wave is sufficient condition for vanishing of the Weyl (superWeyl) anomaly. Thus, plane wave solutions of the Einstein equations are automatically the classical (super)string vacua. For particular plane waves the anomaly can be evaluated even nonperturbatively.This is the second part of the review based on the PhD thesis of the author defended in 1989 at SISSA, Trieste.     

The Flux‐Scaling scenario: De sitter uplift and axion inflation

Non‐geometric flux‐scaling vacua provide promising starting points to realize axion monodromy inflation via the F‐term scalar potential. We show that these vacua can be uplifted to Minkowski and de Sitter by adding an ‐brane or a D‐term containing geometric and non‐geometric fluxes. These uplifted non‐supersymmetric models are analyzed with respect to their potential to realize axion monodromy inflation self‐consistently. Admitting rational values of the fluxes, we construct examples with the required hierarchy of mass scales.