arXiv subjects

Klaus Behrndt

Publications and source records attributed to Klaus Behrndt.

At least 55 records · Page 3Linked to original sources

arXiv1998

AdS_3 Gravity and Conformal Field Theories

We present a detailed analysis of $AdS_3$ gravity, the BTZ black hole and the associated conformal field theories (CFTs). In particular we focus on the non-extreme six-dimensional string solution with background metric $AdS_3 \times S^3$ near the horizon. In addition we introduce momentum modes along the string, corresponding to a BTZ black hole, and a Taub-NUT soliton in the transverse Euclidean space. We show that the $AdS_3$ space-time of this configuration has the spatial geometry of an annulus with a Liouville model at the outer boundary and a two-dimensional black hole at the inner boundary. These CFTs provide the dynamical degrees of freedom of the three-dimensional effective model and, together with the CFT corresponding to $S^3$, provide a statistical interpretation of the corresponding Bekenstein-Hawking entropy. We test the proposed exact black hole entropy, which should hold to all orders in $α^\prime$, by an independent field theoretical analysis including higher-order curvature corrections. We find consistent results that yield a renormalization of the classical parameters, only. In addition we find a logarithmic subleading black hole entropy coming from gravitational fivebrane instantons in a special limit in moduli space.

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arXiv1998

Higher-Order Black-Hole Solutions in N=2 Supergravity and Calabi-Yau String Backgrounds

Based on special geometry, we consider corrections to N=2 extremal black-hole solutions and their entropies originating from higher-order derivative terms in N=2 supergravity. These corrections are described by a holomorphic function, and the higher-order black-hole solutions can be expressed in terms of symplectic Sp(2$n$+2) vectors. We apply the formalism to N=2 type-IIA Calabi-Yau string compactifications and compare our results to recent related results in the literature.

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arXiv1998

Entropy and Conformal Field Theories of AdS_3 Models

We present a derivation of the Bekenstein-Hawking entropy from conformal field theories. In particular we consider a six-dimensional string configuration with background metric AdS_3 * S^3 near the horizon. In addition we introduce momentum modes along the string, corresponding to a Banados-Teitelboim-Zanelli (BTZ) black hole in the anti-de Sitter (AdS) space-time, and a Taub-NUT soliton in the transverse Euclidean space, projecting out a discrete subgroub of S^3. This spherical part is described by a SU(2)/Z(m) Wess-Zumino-Witten (WZW) model. The AdS_3 space-time, on the other hand, is determined by two conformal field theories living at the two boundaries: One SL(2,R)/U(1) WZW model on the horizon of the BTZ black hole and one Liouville model at infinity. The extremal BTZ black hole interpolates between these two conformal field theories. Moreover, we argue that the sum of the three conformal field theories yields the correct microscopic state-counting including all alpha' corrections.

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arXiv1998

Branes in N=2,D=4 sugra and the conformal field theory limit

In this article we summarise the brane solutions (instantons, black holes and strings) in 4 dimensions when embedded in N=2 supergravity. Like in 10 dimensions these solutions are related by duality transformations (T-duality, c-map). For the case that the graviphoton has no magnetic charge, we discuss the conformal field theory description of the near-horizon geometry. The decoupling of the massless modes in the matrix limit of the M-theory compactified on a Calabi-Yau threefold is discussed.

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arXiv1997

The entropy of near-extreme N=2 black holes

We give an explicit form of the classical entropy for four-dimensional static near-BPS-saturated black holes of generic N=2 superstring vacua. The expression is obtained by determining the leading corrections in the non-extremality parameter to the corresponding BPS-saturated black hole solutions. These classical results are quantitatively compared with the microscopic leading order corrections to the microscopic result of Maldacena Strominger and Witten for N=2 BPS-saturated black holes.

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arXiv1997

Entropy of bound states in the matrix description of M5-branes

Like the M-theory itself also the worldvolume theory of the M5-brane contains brane excitations, which can be extracted from the supersymmetry algebra. Bound states (intersecting branes) of the worldvolume can be translated into bound states of {11-d} SUGRA. In this paper, we discuss the matrix description for these bound states and their entropy (=degeneracy). In order to decouple the worldvolume field theory from the bulk gravity we have especially to assume that all charges are large, which gives a nice agreement with the Bekenstein-Hawking entropy of black holes.

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arXiv1997

On central charges and the entropy in matrix theory

The Bekenstein-Hawking entropy of BPS black holes can be obtained as the minimum of the mass (= largest central charge). In this letter we investigate the analog procedure for the matrix model of M-theory. Especially we discuss the configurations: (i) $2 \times 2 \times 2$ corresponding to the 5-d black hole and (ii) the $5 \times 5 \times 5$ configuration yielding the 5-d string. After getting their matrix-entropy, we discuss a way of counting of microstates in matrix theory. As Yang Mills field theory we propose the gauged world volume theory of the 11-d KK monopole.

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arXiv1997

From Type IIA Black Holes to T-dual Type IIB D-Instantons in N=2, D=4 Supergravity

We discuss the T-duality between the solutions of type IIA versus IIB superstrings compactified on Calabi-Yau threefolds. Within the context of the N=2, D=4 supergravity effective Lagrangian, the T-duality transformation is equivalently described by the c-map, which relates the special Kahler moduli space of the IIA N=2 vector multiplets to the quaternionic moduli space of the N=2 hyper multiplets on the type IIB side (and vice versa). Hence the T-duality, or c-map respectively, transforms the IIA black hole solutions, originating from even dimensional IIA branes, of the special Kahler effective action, into IIB D-instanton solutions of the IIB quaternionic sigma-model action, where the D-instantons can be obtained by compactifying odd IIB D-branes on the internal Calabi-Yau space. We construct via this mapping a broad class of D-instanton solutions in four dimensions which are determinded by a set of harmonic functions plus the underlying topological Calabi-Yau data.

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arXiv1997

Stationary solutions of N=2 supergravity

We discuss general bosonic stationary configurations of N=2, D=4 supergravity coupled to vector multiplets. The requirement of unbroken supersymmetries imposes constraints on the holomorphic symplectic section of the underlying special Kähler manifold. The corresponding solutions of the field equations are completely determined by a set of harmonic functions. As examples we discuss rotating black holes, Taub-NUT and Eguchi-Hanson like instantons for the STU model. In addition, we discuss, in the static limit, worldsheet instanton corrections to the STU black hole solution, in the neighbourhood of a vanishing 4-cycle of the Calabi-Yau manifold. Our procedure is quite general and includes all known black hole solutions that can be embedded into N=2 supergravity.

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arXiv1997

Instanton effects in string cosmology

We consider the gauge dyonic string solution of the K3 compactified heterotic string theory in a four dimensional cosmological context. Since for this solution Green-Schwarz as well as Chern-Simons corrections have been taken into account it contains both world sheet and string loop corrections. The cosmological picture is obtained by rotating the world volume of the gauge dyonic string into two space like dimensions and compactifying those dimensions on a two torus. We compare the result with gauge neutral extreme and non-extreme cosmologies and find that the non-trivial Yang Mills background leads to a solution without any singularities whereas for trivial Yang-Mills backgrounds some of the fields become always singular at the big bang.

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arXiv1997

Moving Moduli, Calabi-Yau Phase Transitions and Massless BPS Configurations in Type II Superstrings

In this paper we discuss compactifications of type II superstrings where the moduli of the internal Calabi-Yau space vary over four-dimensional space time. The corresponding solutions of four-dimensional N=2 supergravity are given by charged, extremal BPS black hole configurations with non-constant scalar field values. In particular we investigate the behaviour of our solutions near those points in the Calabi-Yau moduli space where some internal cycles collapse and topology change (flop transitions, conifold transitions) can take place. The singular loci in the internal space are related to special points in the uncompactified space. The phase transition can happen either at spatial infinity (for positive charges) or on spheres (with at least one negative charge). The corresponding BPS configuration has zero ADM mass and can be regarded as a domain wall that separates topologically different vacua of the theory.

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arXiv1997

BPS-Saturated Bound States of Tilted P-Branes in Type II String Theory

We found BPS-saturated solutions of M-theory and Type II string theory which correspond to (non-marginally) bound states of p-branes intersecting at angles different from pi/2. These solutions are obtained by starting with a BPS marginally bound (orthogonally) intersecting configurations of two p-branes (e.g, two four-branes of Type II string theory), performing a boost transformation at an angle with respect to the world-volume of the configuration, performing T-duality transformation along the boost-direction, S-duality transformation, and T- transformations along the direction perpendicular to the boost transformation. The resulting configuration is non-marginally bound BPS-saturated solution whose static metric possesses the off-diagonal term which cannot be removed by a coordinate transformation, and thus signifies an angle (different from pi/2) between the resulting intersecting p-branes. Additional new p-branes are bound to this configuration, in order to ensure the stability of such a static, tilted configuration.

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arXiv1997

Quantum corrections for D=4 black holes and D=5 strings

In recent times quantum corrections for N=2 black holes in 4 dimensions have been addressed in the framework of double extreme black hole solutions, which are characterised by constant scalar fields. In this paper we generalize these solutions to non-constant scalar fields. This enables us to discuss quantum corrections for massless black holes and for configurations that are classically singular. We also discuss the relation to the 5-dimensional magnetic string solution.

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arXiv1997

Subleading contributions from instanton corrections in N = 2 supersymmetric black hole entropy

We present subleading corrections to the N=2 supersymmetric black hole entropy. These subleading contributions correspond to instanton corrections of the Type II string theory. In particular we consider an axion free black hole solution of low-energy effective Type II string theory. We present a procedure to include successively all instanton corrections. Expanding these corrections at particular points in moduli space yields polynomial and logarithmic instanton corrections to the classical black hole entropy. We comment on a microscopic interpretation of these instanton corrections and find that the logarithmic corrections correspond to subleading terms in the degeneracy of the spectrum of an underlying quantum theory.

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arXiv1996

Entropy of N=2 black holes and their M-brane description

In this paper we discuss the M-brane description for a N=2 black hole. This solution is a result of the compactification of M-5-brane configurations over a Calabi-Yau threefold with arbitrary intersection numbers $C_{ABC}$. In analogy to the D-brane description where one counts open string states we count here open 2-branes which end on the M-5-brane.

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arXiv1996

Decompactification near the horizon and non-vanishing entropy

Intersecting D-brane configurations are related to black holes in D=4. Using the standard way of compactification only the Reissner-Nordstrøm black hole is non-singular. In this paper we argue, that also the other black holes are non-singular if i) we compactify over a periodic array and ii) we allow the string metric after reaching a critical curvature to choose the dual geometry. Effectively this means that near the horizon the solution completely decompactifies and chooses a non-singular D-brane configuration.

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arXiv1996

Intersecting D-Branes in ten and six dimensions

We show how, via $T$-duality, intersecting $D$-Brane configurations in ten (six) dimensions can be obtained from the elementary $D$-Brane configurations by embedding a Type IIB $D$-Brane into a Type IIB Nine-Brane (Five-Brane) and give a classification of such configurations. We show that only a very specific subclass of these configurations can be realized as (supersymmetric) solutions to the equations of motion of IIA/IIB supergravity. Whereas the elementary $D$-brane solutions in $d=10$ are characterized by a single harmonic function, those in $d=6$ contain two independent harmonic functions and may be viewed as the intersection of two $d=10$ elementary $D$-branes. Using string/string/string triality in six dimensions we show that the heterotic version of the elementary $d=6$ $D$-Brane solutions correspond in ten dimensions to intersecting Neveu-Schwarz/Neveu-Schwarz (NS/NS) strings or five-branes and their $T$-duals. We comment on the implications of our results in other than ten and six dimensions.

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arXiv1996

STU Black Holes and String Triality

We find double-extreme black holes associated with the special geometry of the Calabi-Yau moduli space with the prepotential F=STU. The area formula is STU-moduli independent and has ${[SL(2,Z)]}^3$ symmetry in space of charges. The dual version of this theory without prepotential treats the dilaton S asymmetric versus T,U-moduli. We display the dual relation between new (STU) black holes and stringy (S|TU) black holes using particular Sp(8, Z) transformation. The area formula of one theory equals that of the dual theory when expressed in terms of dual charges. We analyse the relation between (STU) black holes to string triality of black holes: (S|TU), (T|US), (U|ST) solutions. In the democratic STU-symmetric version we find that all three S and T and U duality symmetries are non-perturbative and mix electric and magnetic charges.

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