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Thomas Mohaupt

Publications and source records attributed to Thomas Mohaupt.

At least 37 records · Page 2Linked to original sources
arXiv2012

Developments in special geometry

We review the special geometry of N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we disucss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.

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arXiv2011

Conformal Aspects of Spinor-Vector Duality

We present a detailed study of various aspects of Spinor-Vector duality in Heterotic string compactifications and expose its origin in terms of the internal conformal field theory. In particular, we illustrate the main features of the duality map by using simple toroidal orbifolds preserving N_4 = 1 and N_4 = 2 spacetime supersymmetries in four dimensions. We explain how the duality map arises in this context by turning on special values of the Wilson lines around the compact cycles of the manifold. We argue that in models with N_4 = 2 spacetime supersymmetry, the interpolation between the Spinor-Vector dual vacua can be continuously realized. We trace the origin of the Spinor-Vector duality map to the presence of underlying N = (2, 2) and N = (4, 4) SCFTs, and explicitly show that the induced spectral-flow in the twisted sectors is responsible for the observed duality. The isomorphism between current algebra representations gives rise to a number of chiral character identities, reminiscent of the recently-discovered MSDS symmetry.

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arXiv2010

Euclidean Actions, Instantons, Solitons and Supersymmetry

Theories with axionic scalars admit three different Euclidean formulations, obtained by Wick rotation, Wick rotation combined with analytic continuation of the axionic scalars, and Wick rotation combined with Hodge dualization. We investigate the relation between these formulations for a class of theories which contains the sigma models of N=2 vector multiplets as a special case. It is shown that semi-classical amplitudes can be expressed equivalently using the two types of axionic actions, while the Hodge dualized version gives a different value for the instanton action unless the integration constants associated with the axion fields are chosen in a particular way. With this choice the instanton action is equal to the mass of the soliton or black hole obtained by dimensional lifting with respect to time. For supersymmetric models we use the Euclidean supersymmetry algebra to derive a Euclidean BPS condition, and we identify a geometrical criterion which distinguishes BPS from non-BPS extremal solutions.

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arXiv2009

Instantons, black holes and harmonic functions

We find a class of five-dimensional Einstein-Maxwell type Lagrangians which contains the bosonic Lagrangians of vector multiplets as a subclass, and preserves some features of supersymmetry, namely the existence of multi-centered black hole solutions and of attractor equations. Solutions can be expressed in terms of harmonic functions through a set of algebraic equations. The geometry underlying these Lagrangians is characterized by the existence of a Hesse potential and generalizes the very special real geometry of vector multiplets. Our construction proceeds by first obtaining instanton solutions for a class of four-dimensional Euclidean sigma models, which includes those occuring for four-dimensional Euclidean N=2 vector multiplets as a subclass.

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arXiv2009

Special Geometry of Euclidean Supersymmetry III: the local r-map, instantons and black holes

We define and study projective special para-Kahler manifolds and show that they appear as target manifolds when reducing five-dimensional vector multiplets coupled to supergravity with respect to time. The dimensional reductions with respect to time and space are carried out in a uniform way using an epsilon-complex notation. We explain the relation of our formalism to other formalisms of special geometry used in the literature. In the second part of the paper we investigate instanton solutions and their dimensional lifting to black holes. We show that the instanton action, which can be defined after dualising axions into tensor fields, agrees with the ADM mass of the corresponding black hole. The relation between actions via Wick rotation, Hodge dualisation and analytic continuation of axions is discussed.

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arXiv2008

From Special Geometry to Black Hole Partition Functions

These notes are based on lectures given at the Erwin-Schrodinger Insitut in Vienna in 2006/07 and at the 2007 School on Attractor Mechanism in Frascati. Lecture I: special geometry from the superconformal point of view. Lecture II: black hole attractor mechanism, its underlying variational principle, and black hole partition functions. Lecture III: large and small BPS black holes in N=4 supergravity. Lecture IV: state counting for N=4 string compactifications. Appendix A: special geometry from the mathematical point of view. Appendix B: review of modular forms. Contains four problems which allow the readers to develop some of the key concepts by themselves.

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arXiv2006

New developments in special geometry

We review recent developments in special geometry, emphasizing the role of real coordinates. In the first part we discuss the para-complex geometry of vector and hypermultiplets in rigid Euclidean N=2 supersymmetry. In the second part we study the variational principle governing the near horizon limit of BPS black holes in matter-coupled N=2 supergravity and observe that the black hole entropy is the Legendre transform of the Hesse potential encoding the geometry of the scalar fields.

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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

Domain Walls, Hitchin's Flow Equations and G_2-Manifolds

We construct BPS domain wall solutions of the effective action of type-IIA string theory compactified on a half-flat six-manifold. The flow equations for the vector and hypermultiplet scalars are shown to be equivalent to Hitchin's flow equations, implying that our domain walls can be lifted to solutions of ten-dimensional type-IIA supergravity. They take the form R^{1,2} x Y_7, where Y_7 is a G_2-holonomy manifold with boundaries.

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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

The Kahler Cone as Cosmic Censor

M-theory effects prevent five-dimensional domain-wall and black-hole solutions from developing curvature singularities. While so far this analysis was performed for particular models, we now present a model-independent proof that these solutions do not have naked singularities as long as the Kahler moduli take values inside the extended Kahler cone. As a by-product we obtain information on the regularity of the Kahler-cone metric at boundaries of the Kahler cone and derive relations between the geometry of moduli space and space-time.

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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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