Jerome P. Gauntlett

Overlapping branes in M theory

We construct new supersymmetric solutions of D = 11 supergravity describing n orthogonally “overlapping” membranes and fivebranes for n = 2,…,8. Overlapping branes arise after separating intersecting branes in a direction transverse to all of the branes. The solutions, which generalize known intersecting brane solutions, preserve at least 2−n of the supersymmetry. Each pairwise overlap involves a membrane overlapping a membrane in a 0-brane, a fivebrane overlapping a fivebrane in a 3-brane or a membrane overlapping a fivebrane in a string. After reducing n overlapping membranes to obtain n overlapping D-2-branes in D = 10, T-duality generates new overlapping D-brane solutions in type IIA and type IIB string theory. Uplifting certain type IIA solutions leads to the D = 11 solutions. Some of the new solutions reduce to dilaton black holes in D = 4. Additionally, we present a D = 10 solution that describes two D-5-branes overlapping in a string. T-duality then generates further D = 10 solutions and uplifting one of the type IIA solutions gives a new D = 11 solution describing two fivebranes overlapping in a string.

STRINGS AS SOLITONS& BLACK HOLES AS STRINGS

Abstract Supersymmetric closed string theories contain an infinite tower of BPS-saturated, oscillating, macroscopic strings in the perturbative spectrum. When these theories have dual formulations, this tower of states must exist nonperturbatively as solitons in the dual theories. We present a general class of exact solutions of low-energy supergravity that corresponds to all these states. After dimensional reduction they can be interpreted as supersymmetric black holes with a degeneracy related to the degeneracy of the string states. For example, in four dimensions we obtain a point-like solution which is asymptotic to a stationary, rotating, electrically-charged black hole with Regge-bounded angular momentum and with the usual ring-singularity replaced by a string source. This further supports the idea that the entropy of supersymmetric black holes can be understood in terms of counting of string states. We also discuss some applications of these solutions to string duality.

Pair creation of extremal black holes and Kaluza-Klein monopoles.

Classical solutions describing charged dilaton black holes accelerating in a background magnetic field have recently been found. They include the Ernst metric of the Einstein-Maxwell theory as a special case. We study the extremal limit of these solutions in detail, both at the classical and quantum levels. It is shown that near the event horizon the extremal solutions reduce precisely to the static extremal black hole solutions. For a particular value of the dilaton coupling, these extremal black holes are five-dimensional Kaluza-Klein monopoles. The Euclidean sections of these solutions can be interpreted as instantons describing the pair creation of extremal black holes and/or Kaluza-Klein monopoles in a magnetic field. The action of these instantons is calculated and found to agree with the Schwinger result in the weak-field limit. For the Euclidean Ernst solution, the action for the extremal solution differs from that of the previously discussed wormhole instanton by the Bekenstein-Hawking entropy. However, in many cases quantum corrections become large in the vicinity of the black hole, and the precise description of the creation process is unknown.

Magnetic monopoles in string theory

Abstract Magnetic monopole solutions to heterotic string theory are discussed in toroidal compactifications to four spacetime dimensions. Particular emphasis is placed on the relation to previously studied five-brane solutions in ten dimensions and on the possibility of constructing exact monopole solutions related to symmetric five-branes.

Dyons and S-duality in N = 4 supersymmetric gauge theory

Abstract We analyze the spectrum of dyons in N = 4 supersymmetric Yang-Mills theory with gauge group SU (3) spintaneously broken down to U (1) × U (1). The Higgs fields select a natural basis of simple roots. Acting with S -duality on the W -boson states corresponding to simplr roots leads to an orbit of BPS dyon states that are magnetically charged with respect to one of the U (1)s. The corresponding monopole solutions can be obtained by embedding SU (2) monopoles into SU (3) and the S -duality predictions reduce to the SU (2) case. Acting with S -duality on the W -boson corresponding to a nonsimple root leads to an infinite set of new S -duality predictions. The simplest of these corresponds to the existence of a harmonic form on the moduli space of SU (3) monopoles that have magnetic charge (1,1) with respect to the two U (1)s. We argue that the moduli space is given by R 3 × (R 1 x M)/ |Z , where M is Euclidean Taub-NUT space, and that the latter admits the appropriate normalizable harmonic two-form. We briefly discuss the generalizations to other gauge groups.

Low-energy dynamics of N = 2 supersymmetric monopoles

Abstract It is argued that the low-energy dynamics of k-monopoles in N = 2 supersymmetric Yang-Mills theory are determined by an N = 4 supersymmetric quantum mechanics based on the moduli space of k static monople solutions. This generalises Mantons “geodesic approximation” for studying the low-energy dynamics of (bosonic) BPS monopoles. We discuss some aspects of the quantisation and in particular argue that Dolbeault cohomology classes of the moduli space are related to bound states of the full quantum field theory.

S-duality and the dyon spectrum in N = 2 super Yang-Mills theory

Abstract We study the dyon spectrum in N = 2 super Yang-Mills theory with gauge group SU (2) coupled to N f matter multiplets in the fundamental representation. For magnetic charge one and two we determine the spectrum explicitly and show that it is in agreement with the duality predictions of Seiberg and Witten. We briefly discuss the extension to higher charge monopoles for the self-dual N f = 4 case and argue that the conjectured spectrum of dyons predicts the existence of certain harmonic spinors on the moduli space of higher charge monopoles.

A ϰ-symmetry calculus for superparticles☆

Abstract We develop a ϰ -symmetry calculus for the d = 2 and d = 3, N = 2 massive superparticles, which enables us to construct higher order ϰ -invariant actions. The method relies on a reformulation of these models as supersymmetric sigma models that are invariant under local worldline superconformal transformations. We show that the ϰ -symmetry is embedded in the superconformal symmetry so that a calculus for the ϰ -symmetry is equivalent to a tensor calculus for the latter. We develop such a calculus without the introduction of a worldline supergravity multiplet.

Scattering of macroscopic heterotic strings

Abstract We show that macroscopic heterotic strings, formulated as strings which wind around a compact direction of finite but macroscopic extent, exhibit non-trivial scattering at low energies. This occurs at order velocity squared and may thus be described as geodesic motion on a moduli space with a non-trivial metric which we construct. Our result is in agreement with a direct calculation of the string scattering amplitude.