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Frank Saueressig

Publications and source records attributed to Frank Saueressig.

104 records · Page 6Linked to original sources
arXiv2006

Off-shell N=2 tensor supermultiplets

A multiplet calculus is presented for an arbitrary number n of N=2 tensor supermultiplets. For rigid supersymmetry the known couplings are reproduced. In the superconformal case the target spaces parametrized by the scalar fields are cones over (3n-1)-dimensional spaces encoded in homogeneous SU(2) invariant potentials, subject to certain constraints. The coupling to conformal supergravity enables the derivation of a large class of supergravity Lagrangians with vector and tensor multiplets and hypermultiplets. Dualizing the tensor fields into scalars leads to hypermultiplets with hyperkahler or quaternion-Kahler target spaces with at least n abelian isometries. It is demonstrated how to use the calculus for the construction of Lagrangians containing higher-derivative couplings of tensor multiplets. For the application of the c-map between vector and tensor supermultiplets to Lagrangians with higher-order derivatives, an off-shell version of this map is proposed. Various other implications of the results are discussed. As an example an elegant derivation of the classification of 4-dimensional quaternion-Kahler manifolds with two commuting isometries is given.

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arXiv2006

String loop corrected hypermultiplet moduli spaces

Using constraints from supersymmetry and string perturbation theory, we determine the string loop corrections to the hypermultiplet moduli space of type II strings compactified on a generic Calabi-Yau threefold. The corresponding quaternion-Kahler manifolds are completely encoded in terms of a single function. The latter receives a one-loop correction and, using superspace techniques, we argue for the existence of a non-renormalization theorem excluding higher loop contributions.

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arXiv2005

Membrane Instantons and de Sitter Vacua

We investigate membrane instanton effects in type IIA strings compactified on rigid Calabi-Yau manifolds. These effects contribute to the low-energy effective action of the universal hypermultiplet. In the absence of additional fivebrane instantons, the quaternionic geometry of this hypermultiplet is determined by solutions of the three-dimensional Toda equation. We construct solutions describing membrane instantons, and find perfect agreement with the string theory prediction. In the context of flux compactifications we discuss how membrane instantons contribute to the scalar potential and the stabilization of moduli. Finally, we demonstrate the existence of meta-stable de Sitter vacua.

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arXiv2005

On de Sitter Vacua in Type IIA Orientifold Compactifications

This letter discusses the orientifold projection of the quantum corrections to type IIA strings compactified on rigid Calabi-Yau threefolds. It is shown that N=2 membrane instanton effects give a holomorphic contribution to the superpotential, while the perturbative corrections enter into the Kahler potential. At the level of the scalar potential the corrections to the Kahler potential give rise to a positive energy contribution similar to adding anti-D3-branes in the KKLT scenario. This provides a natural mechanism to lift an AdS vacuum to a meta-stable dS vacuum.

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arXiv2005

Special geometry of Euclidean supersymmetry II: hypermultiplets and the c-map

We construct two new versions of the c-map which allow us to obtain the target manifolds of hypermultiplets in Euclidean theories with rigid N =2 supersymmetry. While the Minkowskian para-c-map is obtained by dimensional reduction of the Minkowskian vector multiplet lagrangian over time, the Euclidean para-c-map corresponds to the dimensional reduction of the Euclidean vector multiplet lagrangian. In both cases the resulting hypermultiplet target spaces are para-hyper-Kahler manifolds. We review and prove the relevant results of para-complex and para-hypercomplex geometry. In particular, we give a second, purely geometrical construction of both c-maps, by proving that the cotangent bundle N=T^*M of any affine special (para-)Kahler manifold M is para-hyper-Kahler.

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arXiv2004

Effective Supergravity Actions for Conifold Transitions

We construct gauged supergravity actions which describe the dynamics of M-theory on a Calabi-Yau threefold in the vicinity of a conifold transition. The actions explicitly include N charged hypermultiplets descending from wrapped M2-branes which become massless at the conifold point. While the vector multiplet sector can be treated exactly, we approximate the hypermultiplet sector by the non-compact Wolf spaces X(1+N). The effective action is then uniquely determined by the charges of the wrapped M2-branes.

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arXiv2004

Dynamical Conifold Transitions and Moduli Trapping in M-Theory Cosmology

We study five-dimensional Kasner cosmologies in the vicinity of a conifold locus occurring in a time-dependent Calabi-Yau compactification of M-theory. The dynamics of M2-brane winding modes, which become light in this region, is taken into account using a suitable gauged supergravity action. We find cosmological solutions which interpolate between the two branches of the transition, establishing that conifold transitions can be realized dynamically. However, generic solutions do not correspond to transitions, but to the moduli getting trapped close to the conifold locus. This effect results from an interplay between the scalar potential and Hubble friction. We show that the dynamics does not depend on the details of the potential, but only on its overall shape.

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arXiv2004

Phase Space Analysis of Quintessence Cosmologies with a Double Exponential Potential

We use phase space methods to investigate closed, flat, and open Friedmann-Robertson-Walker cosmologies with a scalar potential given by the sum of two exponential terms. The form of the potential is motivated by the dimensional reduction of M-theory with non-trivial four-form flux on a maximally symmetric internal space. To describe the asymptotic features of run-away solutions we introduce the concept of a `quasi fixed point.' We give the complete classification of solutions according to their late-time behavior (accelerating, decelerating, crunch) and the number of periods of accelerated expansion.

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arXiv2003

Space-Time Singularities and the Kahler Cone

We review recent results on the interplay between the five-dimensional space-time and the internal manifold in Calabi-Yau compactifications of M-theory. Black string, black hole and domain wall solutions as well as Kasner type cosmologies cannot develop a naked singularity as long as the moduli take values inside the Kahler cone.

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arXiv2003

Special Geometry of Euclidean Supersymmetry I: Vector Multiplets

We construct the general action for Abelian vector multiplets in rigid 4-dimensional Euclidean (instead of Minkowskian) N=2 supersymmetry, i.e., over space-times with a positive definite instead of a Lorentzian metric. The target manifolds for the scalar fields turn out to be para-complex manifolds endowed with a particular kind of special geometry, which we call affine special para-Kahler geometry. We give a precise definition and develop the mathematical theory of such manifolds. The relation to the affine special Kahler manifolds appearing in Minkowskian N=2 supersymmetry is discussed. Starting from the general 5-dimensional vector multiplet action we consider dimensional reduction over time and space in parallel, providing a dictionary between the resulting Euclidean and Minkowskian theories. Then we reanalyze supersymmetry in four dimensions and find that any (para-)holomorphic prepotential defines a supersymmetric Lagrangian, provided that we add a specific four-fermion term, which cannot be obtained by dimensional reduction. We show that the Euclidean action and supersymmetry transformations, when written in terms of para-holomorphic coordinates, take exactly the same form as their Minkowskian counterparts. The appearance of a para-complex and complex structure in the Euclidean and Minkowskian theory, respectively, is traced back to properties of the underlying R-symmetry groups. Finally, we indicate how our work will be extended to other types of multiplets and to supergravity in the future and explain the relevance of this project for the study of instantons, solitons and cosmological solutions in supergravity and M-theory.

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arXiv2003

Singular compactifications and cosmology

We summarize our recent results of studying five-dimensional Kasner cosmologies in a time-dependent Calabi-Yau compactification of M-theory undergoing a topological flop transition. The dynamics of the additional states, which become massless at the transition point and give rise to a scalar potential, helps to stabilize the moduli and triggers short periods of accelerated cosmological expansion.

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arXiv2003

M-theory cosmologies from singular Calabi-Yau compactifications

We study five-dimensional Kasner cosmologies in a time-dependent Calabi-Yau compactification of M-theory undergoing a flop transition. The dynamics of the additional states, which become massless at the transition point and give rise to a scalar potential, are taken into account using a recently constructed gauged supergravity action. Due to the dynamics of these states the moduli do not show the usual run-away behavior but oscillate around the transition region. Moreover, the solutions typically exhibit short periods of accelerated expansion. We also analyze the interplay between the geometries of moduli space and space-time.

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arXiv2003

Effective Supergravity Actions for Flop Transitions

We construct a family of five-dimensional gauged supergravity actions which describe flop transitions of M-theory compactified on Calabi-Yau threefolds. While the vector multiplet sector can be treated exactly, we use the Wolf spaces X(1+N) = U(1+N,2)/(U(1+N) x U(2)) to model the universal hypermultiplet together with N charged hypermultiplets corresponding to winding states of the M2-brane. The metric, the Killing vectors and the moment maps of these spaces are obtained explicitly by using the superconformal quotient construction of quaternion-Kahler manifolds. The inclusion of the extra hypermultiplets gives rise to a non-trivial scalar potential which is uniquely fixed by M-theory physics.

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