Andre Lukas

The Universe as a domain wall

It is shown that the effective five-dimensional theory of the strongly coupled heterotic string is a gauged version of N=1 five-dimensional supergravity with four-dimensional boundaries. For the universal supermultiplets, this theory is explicitly constructed by a generalized dimensional reduction procedure on a Calabi-Yau manifold. A crucial ingredient in the reduction is the retention of a {open_quotes}non-zero mode{close_quotes} of the four-form field strength, leading to the gauging of the universal hypermultiplet by the graviphoton. We show that this theory has an exact three-brane domain wall solution which reduces to Witten{close_quote}s {open_quotes}deformed{close_quotes} Calabi-Yau background upon linearization. This solution consists of two parallel three-branes with sources provided by the four-dimensional boundary theories and constitutes the appropriate background for a reduction to four dimensions. Four-dimensional space-time is then identified with the three-brane world volume. {copyright} {ital 1999} {ital The American Physical Society}

Heterotic M-theory in five dimensions

Abstract We derive the five-dimensional effective action of strongly coupled heterotic string theory for the complete (1,1) sector of the theory by performing a reduction, on a Calabi-Yau three-fold, of M-theory on S 1 / Z 2 . A crucial ingredient for a consistent truncation is a non-zero-mode of the antisymmetric tensor field strength which arises due to magnetic sources on the orbifold planes. The correct effective theory is a gauged version of five-dimensional N = 1 supergravity coupled to Abelian vector multiplets, the universal hypermultiplet and four-dimensional boundary theories with gauge and gauge matter fields, The gauging is such that the dual of the four-form field strength in the universal multiplet is charged under a particular linear combination of the Abelian vector fields. In addition, the theory has potential terms for the moduli in the bulk as well as on the boundary. Because of these potential terms, the supersymmetric ground state of the theory is a multi-charged BPS three-brane domain wall, which we construct in general. We show that the five-dimensional theory together with this solution provides the correct starting point for particle phenomenology as well as early universe cosmology. As an application, we compute the four-dimensional N = 1 supergravity theory for the complete (1, 1) sector to leading non-trivial order by a reduction on the domain wall background. We find a correction to the matter field Kahler potential and threshold corrections to the gauge kinetic functions.

On the four-dimensional effective action of strongly coupled heterotic string theory

We derive the ten-dimensional effective action of the strongly coupled heterotic string as the low energy limit of M-theory on S^1/Z_2. In contrast to a conventional dimensional reduction, it is necessary to integrate out nontrivial heavy modes which arise from the sources located on the orbifold fixed hyperplanes. This procedure, characteristic of theories with dynamical boundaries, is illustrated by a simple example. Using this method, we determine a complete set of R^4, F^2R^2, and F^4 terms and the corresponding Chern-Simons and Green-Schwarz terms in ten dimensions. As required by anomaly cancelation and supersymmetry, these terms are found to exactly coincide with their weakly coupled one-loop counterparts.

Nonstandard embedding and five-branes in heterotic M theory

We construct vacua of M theory on S{sup 1}/Z{sub 2} associated with Calabi-Yau threefolds. These vacua are appropriate for compactification to N=1 supersymmetry theories in both four and five dimensions. We allow for general E{sub 8}{times}E{sub 8} gauge bundles and for the presence of five-branes. The five-branes span the four-dimensional uncompactified space and are wrapped on holomorphic curves in the Calabi-Yau manifold. Properties of these vacua, as well as of the resulting low-energy theories, are discussed. We find that the low-energy gauge group is enlarged by gauge fields that originate on the five-brane world-volumes. In addition, the five-branes increase the types of new E{sub 8}{times}E{sub 8} breaking patterns allowed by the non-standard embedding. Characteristic features of the low-energy theory, such as the threshold corrections to the gauge kinetic functions, are significantly modified due to the presence of the five-branes, as compared to the case of standard or non-standard embeddings without five-branes. thinsp {copyright} {ital 1999} {ital The American Physical Society}

Cosmological solutions of Hořava-Witten theory

We discuss cosmological solutions of Ho{hacek r}ava-Witten theory describing the strongly coupled heterotic string. At energies below the grand-unified scale, the effective theory is five, not four, dimensional, where the additional coordinate parametrizes an S{sup 1}/Z{sub 2} orbifold. Furthermore, it admits no homogeneous solutions. Rather, the static vacuum state, appropriate for a reduction to four-dimensional N=1 supersymmetric models, is a BPS domain wall pair. Relevant cosmological solutions are those associated with this BPS state. In particular, such solutions must be inhomogeneous, depending on the orbifold coordinate as well as on time. We present two examples of this new type of cosmological solution, obtained by separation of variables rather than by exchange of the time and radius coordinates of a brane solution, as in previous work. The first example represents the analogue of a rolling radii solution with the radii specifying the geometry of the domain wall pair. This is generalized in the second example to include a nontrivial {open_quotes}Ramond-Ramond{close_quotes} scalar. {copyright} {ital 1999} {ital The American Physical Society}

Gaugino condensation in M theory on s**1 / Z(2)

In the low energy limit of M theory on S{sup 1}/Z{sub 2}, we calculate the gaugino condensate potential in four dimensions using the background solutions due to Ho{hacek r}ava. We show that this potential is free of delta-function singularities and has the same form as the potential in the weakly coupled heterotic string. A general flux quantization rule for the three-form field of M theory on S{sup 1}/Z{sub 2} is given and checked in certain limiting cases. This rule is used to fix the free parameter in the potential originating from a zero mode of the form field. Finally, we calculate soft supersymmetry breaking terms. We find that corrections to the K{umlt a}hler potential and the gauge kinetic function, which can be large in the strongly coupled region, contribute significantly to certain soft terms. In particular, for supersymmetry breaking in the T-modulus direction, the small values of gaugino masses and trilinear couplings that occur in the weakly coupled, large radius regime are enhanced to order m{sub 3/2} in M theory. The scalar soft masses remain small even, in the strong coupling M-theory limit. {copyright} {ital 1998} {ital The American Physical Society}

String and M theory cosmological solutions with Ramond forms

Abstract A general framework for studying a large class of cosmological solutions of the low-energy limit of type II string theory and of M-theory, with non-trivial Ramond form fields excited, is presented. The framework is applicable to space-times decomposable into a set of flat or, more generally, maximally symmetric spatial subspaces, with multiple non-trivial form fields spanning one or more of the subspaces. It is shown that the corresponding low-energy equations of motion are equivalent to those describing a particle moving in a moduli space consisting of the scale factors of the subspaces together with the dilaton. The choice of which form fields are excited controls the potential term in the particle equations. Two classes of exact solutions are given, those corresponding to exciting only a single form and those with multiple forms excited which correspond to Toda theories. Although typically these solutions begin or end in a curvature singularity, there is a subclass with positive spatial curvature which appears to be singularity free. Elements of this class are directly related to certain black p-brane solutions.

Cosmological solutions of type II string theory

Abstract We study cosmological solutions of type II string theory with a metric of the Kaluza-Klein type and nontrivial Ramond-Ramond forms. It is shown that models with only one form excited can be integrated in general. Moreover, some interesting cases with two nontrivial forms can be solved completely since they correspond to Toda models. We find two types of solutions corresponding to a negative time superinflating phase and a positive time subluminal expanding phase. The two branches are separated by a curvature singularity. Within each branch the effect of the forms is to interpolate between different solutions of pure Kaluza-Klein theory.

Stabilizing dilaton and moduli vacua in string and M-theory cosmology

We show how non-trivial form fields can induce an effective potential for the dilaton and metric moduli in compactifications of type II string theory and M-theory. For particular configurations, the potential can have a stable minimum. In cosmological compactifications of type II theories, we demonstrate that, if the metric moduli become fixed, this mechanism can then lead to the stabilization of the dilaton vacuum. Furthermore, we show that for certain cosmological M-theory solutions, non-trivial forms lead to the stabilization of moduli. We present a number of examples, including cosmological solutions with two solitonic forms and examples corresponding to the infinite throat of certain p-branes.

Soliton solutions of M-theory on an orbifold

Abstract We explicitly construct soliton solutions in the low energy description of M-theory on S 1 / Z 2 . It is shown that the 11-dimensional membrane is a BPS solution of this theory if stretched between the Z 2 hyperplanes. A similar statement holds for the 11-dimensional 5-brane oriented parallel to the hyperplanes. The parallel membrane and the orthogonal 5-brane, though solutions, break all supersymmetries. Furthermore, we construct the analog of the gauge 5-brane with gauge instantons on the hyperplanes. This solution varies nontrivially along the orbifold direction due to the gauge anomalies located on the orbifold hyperplanes. Its zero mode part is identical to the weakly coupled 10-dimensional gauge 5-brane.