Vacua In String Theory Research Articles

Flux-induced SUSY-breaking soft terms

We describe the computation of SUSY-breaking terms on a D3-brane in a quite general type IIB supergravity background. We apply it to study the SUSY-breaking induced on the D3-brane worldvolume by the presence of NSNS and RR 3-form fluxes. We provide explicit general formulae for the SUSY-breaking soft terms valid for the different types of fluxes, leading to different patterns of soft terms. Imaginary anti-self-dual fluxes with G3 a pure (3,0)-form lead to soft terms corresponding to dilaton-dominated SUSY-breaking. More general SUSY-breaking patterns are discussed, arising from more general fluxes, or from distant anti-D3-branes. The known finiteness properties of dilaton-dominated soft terms are understood in terms of holography. The above results are interpreted in the context of the 4d effective supergravity theory, where flux components correspond to auxiliary fields of, e.g., the 4d dilaton and overall volume modulus. We present semirealistic type IIB orientifold examples with (meta)stable vacua leading to non-vanishing soft terms of the dilaton-domination type. Such models have many of the ingredients of the recent construction of de Sitter vacua in string theory. We finally explore possible phenomenological applications of this form of SUSY-breaking, where we show that soft terms are of order Ms2/Mp. Thus a string scale of order Ms=1010 GeV, and compactification scale three orders of magnitude smaller could explain the smallness of the weak scale versus the Planck mass.

Counting Flux Vacua

We develop a technique for computing expected numbers of vacua in Gaussian ensembles of supergravity theories, and apply it to derive an asymptotic formula for the index counting all flux supersymmetric vacua with signs in Calabi-Yau compactification of type IIb string theory, which becomes exact in the limit of a large number of fluxes. This should give a reasonable estimate for actual numbers of vacua in string theory, for CY's with small b_3.

Scalar field theory and the definition of momentum in curvedspace

String propagation in ten-dimensionalMinkowski space or the direct product ofMinkowski space and a six-dimensionalKähler manifold or orbifold might beregarded as an approximation to a theorywhich allows for the local curvature ofspacetime by the energy-momenta of thecomponent fields. String scattering in theinteraction region might then be based onquantum field theory in a local region witha curved geometry. Special emphasis isgiven to field theory in anti-de Sitterspace, as it represents a maximallysymmetric spacetime of constant curvaturewhich could arise in the description ofmatter interactions in local regions ofspacetime. Curvature shifts in themomentum and squared mass are evaluatedfor scalar fields in anti-de Sitter space,and it is shown that the shift in p2 + m2 compensates the ground-statecontribution to the bosonic stringHamiltonian, implying the consistency ofcomputing the scattering entirely in flatspace. Dual space rules for evaluatingFeynman diagrams in Euclideananti-de Sitter space are initially definedusing eigenfunctions based on generalizedplane waves. Loop integrals can beevaluated even more easily using momentumspace rules in conformally flatcoordinates for anti-de Sitter space,which admits flat three-dimensionalsections that are analytic continuationsof horospheres in hyperbolic space H4.An additional argument in favour of themodel of string propagation described inthis paper is based on the removal ofreflective boundary conditions on quantumfields interacting in a locallyanti-de Sitter region without spatialinfinity, implying the existence of aone-parameter family of O(3,2)-invariantvacua in this region consistent with thedegree of freedom in defining the stringtheory vacuum.

String universality

If there is a single underlying "theory of everything" which in some limits of its "moduli space" reduces to the five weakly coupled string theories in 10D, and 11D SUGRA, then it is possible that all six of them have some common domain of validity and that they are in the same universality class, in the sense that the 4D low energy physics of the different theories is the same. We call this notion String Universality. This suggests that the true vacuum of string theory is in a region of moduli space equally far (in some sense) from all perturbative theories, most likely around the self-dual point with respect to duality symmetries connecting them. We estimate stringy non-perturbative effects from wrapped brane instantons in each perturbative theory, show how they are related by dualities, and argue that they are likely to lead to moduli stabilization only around the self-dual point. We argue that moduli stabilization should occur near the string scale, and SUSY breaking should occur at a much lower intermediate scale, and that it originates from different sources. We discuss the problems of moduli stabilization and SUSY breaking in currently popular scenarios, explain why these problems are generic, and discuss how our scenario can evade them. We show that String Universality is not inconsistent with phenomenology but that it is in conflict with some popular versions of brane world scenarios.

Linear dilatons, NS5-branes and holography

We argue that vacua of string theory which asymptote at weak coupling to linear dilaton backgrounds are holographic. The full string theory in such vacua is ``dual'' to a theory without gravity in fewer dimensions. The dual theory is generically not a local quantum field theory. Excitations of the string vacuum, which can be studied in the weak coupling region using worldsheet methods, give rise to observables in the dual theory. An interesting example is string theory in the near-horizon background of parallel NS5-branes, the CHS model, which is dual to the decoupled NS5-brane theory (``little string theory''). This duality can be used to study some of the observables in this theory and some of their correlation functions. Another interesting example is the ``old'' matrix model, which gives a holographic description of two dimensional string theory.

Comments on Gepner models and type I vacua in string theory

We construct open descendants of Gepner models, concentrating mainly on the six-dimensional case, where they give type I vacua with rich patterns of Chan-Paton symmetry breaking and various numbers of tensor multiplets, including zero. We also relate the models in D < 10 without open sectors, recently found by other authors, to the generalized Klein-bottle projections allowed by the crosscap constraint.

Gauged supergravity vacua in string theory

We present a first instance of an exact supersymmetric string vacuum in curved space-time. It corresponds to the Freedman-Gibbons electrovac solution to one version of N=4 supergravity, with N=2 space-tme supersymmetry. The conformal theory includes a Wess-Zumino-Witten model on the SU (1,1) group manifold.