Light Cone Black Holes

When probed with conformally invariant matter fields, light cones in Minkowski spacetime satisfy thermodynamical relations which are the analog of those satisfied by stationary black holes coupled to standard matter fields. These properties stem from the fact that light cones are conformal Killing horizons stationary with respect to observers following the radial conformal Killing fields in flat spacetime. The four laws of light cone thermodynamics relate notions such as (conformal) temperature, (conformal) surface gravity, (conformal) energy and a conformally invariant notion related to area change. These quantities do not admit a direct physical interpretation in flat spacetime. However, they become the usual thermodynamical quantities when Minkowski is mapped, via a Weyl transformation, to a target spacetime where the conformal Killing field becomes a proper Killing field. In this paper we study the properties of such spacetimes. The simplest realisation turns out to be the Bertotti-Robinson solution, which is known to encode the near horizon geometry of near extremal and extremal charged black holes. The analogy between light cones in flat space and black hole horizons is therefore strengthened. The construction works in arbitrary dimensions; in two dimensions one recovers the Jackiv-Teitelboim black hole of dilaton gravity. Other interesting realisations are also presented.Comment: 23 pages, 7 figures; v2: typos corrected, matches published versio

Superconformal hypermultiplets

We present theories of N=2 hypermultiplets in four spacetime dimensions that are invariant under rigid or local superconformal symmetries. The target spaces of theories with rigid superconformal invariance are (4n)-dimensional {\it special} hyper-K\"ahler manifolds. Such manifolds can be described as cones over tri-Sasakian metrics and are locally the product of a flat four-dimensional space and a quaternionic manifold. The latter manifolds appear in the coupling of hypermultiplets to N=2 supergravity. We employ local sections of an Sp$(n)\times{\rm Sp}(1)$ bundle in the formulation of the Lagrangian and transformation rules, thus allowing for arbitrary coordinatizations of the hyper-K\"ahler and quaternionic manifolds

Higher Grading Generalisations of the Toda Systems

In the present paper we obtain some integrable generalisations of the Toda system generated by flat connection forms taking values in higher ${\bf Z}$--grading subspaces of a simple Lie algebra, and construct their general solutions. One may think of our systems as describing some new fields of the matter type coupled to the standard Toda systems. This is of special interest in nonabelian Toda theories where the latter involve black hole target space metrics. We also give a derivation of our conformal system on the base of the Hamiltonian reduction of the WZNW model; and discuss a relation between abelian and nonabelian systems generated by a gauge transformation that maps the first grading description to the second. The latter involves grades larger than one.Comment: 24 pages, latex, no figures; Expanded version accepted for publication in Nuclear Physics

Extended supersymmetric sigma models in AdS_4 from projective superspace

There exist two superspace approaches to describe N=2 supersymmetric nonlinear sigma models in four-dimensional anti-de Sitter (AdS_4) space: (i) in terms of N=1 AdS chiral superfields, as developed in arXiv:1105.3111 and arXiv:1108.5290; and (ii) in terms of N=2 polar supermultiplets using the AdS projective-superspace techniques developed in arXiv:0807.3368. The virtue of the approach (i) is that it makes manifest the geometric properties of the N=2 supersymmetric sigma-models in AdS_4. The target space must be a non-compact hyperkahler manifold endowed with a Killing vector field which generates an SO(2) group of rotations on the two-sphere of complex structures. The power of the approach (ii) is that it allows us, in principle, to generate hyperkahler metrics as well as to address the problem of deformations of such metrics. Here we show how to relate the formulation (ii) to (i) by integrating out an infinite number of N=1 AdS auxiliary superfields and performing a superfield duality transformation. We also develop a novel description of the most general N=2 supersymmetric nonlinear sigma-model in AdS_4 in terms of chiral superfields on three-dimensional N=2 flat superspace without central charge. This superspace naturally originates from a conformally flat realization for the four-dimensional N=2 AdS superspace that makes use of Poincare coordinates for AdS_4. This novel formulation allows us to uncover several interesting geometric results.Comment: 88 pages; v3: typos corrected, version published in JHE

Superconformal Hypermultiplets

We present theories of N=2 hypermultiplets in four spacetime dimensions that are invariant under rigid or local superconformal symmetries. The target spaces of theories with rigid superconformal invariance are (4n)-dimensional {\it special} hyper-Kähler manifolds. Such manifolds can be described as cones over tri-Sasakian metrics and are locally the product of a flat four-dimensional space and a quaternionic manifold. The latter manifolds appear in the coupling of hypermultiplets to N=2 supergravity. We employ local sections of an Sp$(n)\times{\rm Sp}(1)$ bundle in the formulation of the Lagrangian and transformation rules, thus allowing for arbitrary coordinatizations of the hyper-Kähler and quaternionic manifolds