arXiv subjects

Klaus Behrndt

Publications and source records attributed to Klaus Behrndt.

At least 37 records · Page 2Linked to original sources

arXiv2002

Vacua of N=2 gauged supergravity derived from non-homogeneous quaternionic spaces

We discuss a class of 4-dimensional non-homogeneous quaternionic spaces, which become the two known homogeneous spaces (EAdS_4$ and SU(2,1)/U(2)) in certain limits. These moduli spaces have two regions where the metric is positive definite, separated by a non-physical region where the metric has timelike directions and which contains a curvature singularity. They admit four isometries and we consider their general Abelian gauging. The critical points of the resulting superpotential and hence the possible domain wall solutions differ significantly in the two regions. On one side one can construct only singular walls, whereas in the other we found a smooth domain wall interpolating between two infra-red critical points located exactly on the boundary of the physical allowed parameter region.

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arXiv2002

Bent BPS domain walls of D=5 N=2 gauged supergravity coupled to hypermultiplets

Within D=5 N=2 gauged supergravity coupled to hypermultiplets we derive consistency conditions for BPS domain walls with constant negative curvature on the wall. For such wall solutions to exist, the covariant derivative of the projector, governing the constraint on the Killing spinor, has to be non-zero and proportional to the cosmological constant on the domain walls. We also prove that in this case solutions of the Killing spinor equations are solutions of the equations of motion. We present explicit, analytically solved examples of such domain walls, employing the universal hypermultiplet fields. These examples involve the running of two scalar fields and the space-time in the transverse direction that is cut off at a critical distance, governed by the magnitude of the negative cosmological constant on the wall.

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arXiv2001

Gauging of N=2 Supergravity Hypermultiplet and Novel Renormalization Group Flows

We provide the explicit gauging of all the SU(2,1) isometries of one N=2 supergravity hypermultiplet, which spans SU(2,1)/U(2) coset space parameterized in terms of two complex projective coordinate fields z_1 and z_2. We derive the full, explicit Killing prepotential that specifies the most general superpotential. As an application we consider the supersymmetric flow (renormalization group) equations for: (i) the flow from a null singularity to the flat, supersymmetric space-time and (ii) the flow that violates c-theorem with the superpotential crossing zero.

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arXiv2001

Domain walls and flow equations in supergravity

Domain wall solutions have attracted much attention due to their relevance for brane world scenarios and the holographic RG flow. In this talk I discuss the following aspects for these applications: (i) derivation of the first order flow equations as Bogomol'nyi bound; (ii) different types of critical points of the superpotential; (iii) the superpotential needed to localize gravity; (iv) the constraints imposed by supersymmetry including an example for an $N$=1 flow and finally (v) sources and exponential trapping of gravity.

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arXiv2001

Curved BPS domain wall solutions in four-dimensional N=2 supergravity

We construct four-dimensional domain wall solutions of N=2 gauged supergravity coupled to vector and to hypermultiplets. The gauged supergravity theories that we consider are obtained by performing two types of Abelian gauging. In both cases we find that the behaviour of the scalar fields belonging to the vector multiplets is governed by the so-called attractor equations known from the study of BPS black hole solutions in ungauged N=2 supergravity theories. The scalar fields belonging to the hypermultiplets, on the other hand, are either constant or exhibit a run-away behaviour. These domain wall solutions preserve 1/2 of supersymmetry and they are, in general, curved. We briefly comment on the amount of supersymmetry preserved by domain wall solutions in gauged supergravity theories obtained by more general gaugings.

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arXiv2001

Domain Walls, Black Holes, and Supersymmetric Quantum Mechanics

Supersymmetric solutions, such as BPS domain walls or black holes, in four- and five-dimensional supergravity theories with eight supercharges can be described by effective quantum mechanics with a potential term. We show how properties of the latter theory can help us to learn about the physics of supersymmetric vacua and BPS solutions in these supergravity theories. The general approach is illustrated in a number of specific examples where scalar fields of matter multiplets take values in symmetric coset spaces.

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arXiv2000

Domain walls in five dimensional supergravity with non-trivial hypermultiplets

We study BPS domain wall solutions of 5-dimensional N=2 supergravity where isometries of the hypermultiplet geometry have been gauged. We derive the corresponding supersymmetric flow equations and define an appropriate c-function. As an example we discuss a domain wall solution of Freedman, Gubser, Pilch and Warner which is related to a RG-flow in a dual superconformal field theory.

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arXiv2000

A non-singular infra-red flow from D=5 gauged supergravity

We discuss domain wall solutions of 5-dimensional supergravity corresponding to a cosine-superpotential, which is derived by a gauging of the two Abelian isometries of the scalar coset SU(2,1)/U(2). We argue that this potential can be obtained from M-theory compactification in the presence of G-fluxes and an M5-brane instanton gas. If we decouple the volume scalar of the internal space, the superpotential allows for two extrema, which are either ultra-violet or infra-red attractive. Asymptotically we approach therefore either the boundary or the Killing horizon of an anti-deSitter space or flat spacetime for a vanishing cosmological constant. If the volume scalar does not decouple, we obtain a run-away potential corresponding to dilatonic domain walls, which always run towards a vanishing cosmological constant.

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arXiv2000

Infra-red fixed points at the boundary

Gauged supergravities (in four and five dimensions) with eight supercharges and with vector supermultiplets have a unique ultra-violet (UV) fixed point on a given physical domain \cal M of the space of the scalar fields. We show that in these models the infra-red (IR) fixed points are located on the boundary of \cal M, where the space-time metric becomes singular.

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arXiv2000

Domain Walls and Superpotentials from M Theory on Calabi-Yau Three-Folds

Compactification of M theory in the presence of G-fluxes yields N=2 five-dimensional gauged supergravity with a potential that lifts all supersymmetric vacua. We derive the effective superpotential directly from the Kaluza-Klein reduction of the eleven-dimensional action on a Calabi-Yau three-fold and compare it with the superpotential obtained by means of calibrations. We discuss an explicit domain wall solution, which represents five-branes wrapped over holomorphic cycles. This solution has a ``running volume'' and we comment on the possibility that quantum corrections provide a lower bound allowing for an AdS_5 vacuum of the 5-dimensional supergravity.

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arXiv2000

Domain walls of D=5 supergravity and fixed points of N=1 Super Yang Mills

Employing the AdS/CFT correspondence, we give an explicit supergravity picture for the renormalization group flow of couplings 4-d super Yang Mills with four supercharges. The solution represents a domain wall of 5-d, N=2 supergravity, that interpolates between two (different) AdS_5 vacua and is obtained by gauging a U(1) subgroup of the SU(2) R-symmetry. On the supergravity side the domain wall couples only to scalar fields from vector mulitplets, but not to scalars from hyper multiplets. We discuss the c-theorem, the beta-functions and consider two examples: one is the sugra solution related to Z_k orbifolds (corresponding to N=2 SYM) and the other is an orientifold construction for an elliptically fibered CY with F_1 basis (corresponding to N=1 SYM).

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arXiv2000

Anti-deSitter Vacua of Gauged Supergravities with 8 Supercharges

We investigate supersymmetric extrema of Abelian gauged supergravity theories with non-trivial vector multiplets and 8 supercharges in four and five dimensions. The scalar fields of these models parameterize a manifold consisting of disconnected branches and restricting to the case where this manifold has a non-singular metric we show that on every branch there can be at most one extremum, which is a local maximum (for W>0) or a minimum (for W<0) of the superpotential W. Therefore, these supergravity models do not allow for regular domain wall solutions interpolating between different extrema of the superpotential and the space-time transverse to the wall asymptotically always approaches the boundary of AdS (UV-fixed points in a dual field theory).

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arXiv1999

Supersymmetric Domain-Wall World from D=5 Simple Gauged Supergravity

We address a supersymmetric embedding of domain walls with asymptotically anti-deSitter (AdS) space-times in five-dimensional simple, N=2 U(1) gauged supergravity theory constructed by Gunaydin, Townsend and Sierra. These conformally flat solutions interpolate between supersymmetric AdS vacua, satisfy the Killing spinor (first order) differential equations, and the four-dimensional world on the domain wall is a flat world with N=1 supersymmetry. Regular solutions in this class have the energy density related to the cosmological constants of the supersymmetric AdS vacua. An analysis of such solutions is given for the example of one (real, neutral) vector supermultiplet with the most general form of the prepotential. There are at most two supersymmetric AdS vacua that are in general separated by a singularity in the potential. Nevertheless the supersymmetric domain wall solution exists with the scalar field interpolating continuously across the singular region.

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arXiv1999

On Domain-Wall/QFT Dualities in Various Dimensions

We investigate domain-wall/quantum field theory correspondences in various dimensions. Our general analysis does not only cover the well-studied cases in ten and eleven dimensions but also enables us to discuss new cases like a Type I/Heterotic 6-brane in ten dimensions and domain wall dualities in lower than ten dimensions. The examples we discuss include `d-branes' in six dimensions preserving 8 supersymmetries and extreme black holes in various dimensions. In the latter case we construct the quantum mechanics Hamiltonian and discuss several limits.

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arXiv1999

Branes, Waves and AdS Orbifolds

The embedding of a Taub-NUT space in the directions transverse to the world volume of branes describes branes at (spherical) orbifold singularities. Similarly, the embedding of a pp-wave in the brane world volume yields an AdS orbifold. In case of the D1-D5--brane system, the AdS3 orbifolds yields a BTZ black hole; as we will show, the same holds for D3-branes corresponding to AdS5. In addition we will show that the AdS orbifolds and the spherical orbifolds are U-dual to each other. However in contrast to spherical orbifolds the AdS orbifolds lead to a running coupling, which is in the IR inverse to the coupling of the spherical orbifold. A discussion of the general pp-wave solution in AdS space is added.

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arXiv1998

Orbifolds of AdS(3) and fixpoints of the CFT

The 3-d BTZ black hole represents an orbifold of $AdS_3$ gravity. The UV as well as the IR region of the CFT is governed by a gauged SL(2, R) WZW model. In the UV it corresponds to a light-cone gauging (Liouville model) whereas in the IR it is a space-like gauging (2-d black hole).

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arXiv1998

Classical and quantum aspects of 4 dimensional black holes

In this talk I address some aspects in the recent developments for N=2 black holes in 4 dimensions. I restrict myself on axion-free solutions that can classically be related to intersections of isotropic $D$- or $M$-branes. After reviewing of some classical properties I include corrections coming from a general cubic prepotential. On the heterotic side these are quantum corrections for these black hole solutions. Finally, I discuss a microscopic interpretation of the entropy for the extremal as well as near-extremal black hole.

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arXiv1998

AdS gravity and field theories at fixpoints

The renormalization group flow of the worldvolume theory depends very much from the number of unbroken supersymmetries. In the dual $AdS$ picture we break supersymmetry by adding different types of BPS black holes. We argue, that this BPS black hole causes a non-trivial renormalization group flow in the worldvolume field theory and especially a regular horizon translates into a non-trivial IR fixpoint. For this interpretation we have to rewrite the $AdS$ models into a flat space description with a linear dilaton vacuum. The dual models (linear dilaton and the $AdS$ vacuum) can be seen as the different sides of a domain wall. We discuss the cases of $AdS_3$ and $AdS_5$.

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