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We study the Einstein field equations for spacetimes admitting a maximal two-dimensional abelian group of isometries acting orthogonally transitively on spacelike surfaces and, in addition, with at least one conformal Killing vector. The…
We derive and analyze the conditions for quantum conformal and Lorentz invariance of the duality symmetric interacting chiral boson sigma-models, which are conjectured to describe non-geometric string theory backgrounds. The one-loop Weyl…
We present a conformal isometry for static extremal black hole solutions in all four-dimensional Einstein-Maxwell-scalar theories with electromagnetic duality groups `of type $E_7$'. This includes, but is not limited to, all supergravity…
An exact time-dependent solution of a black hole is found in conformally invariant gravity on a warped Randall-Sundrum spacetime, by writing the metric $g_{\mu\nu}=\omega^{\frac{4}{n-2}}\tilde g_{\mu\nu}$. Here $\tilde g_{\mu\nu}$…
We review some recent developments in the conformal gravity theory that has been advanced as a candidate alternative to standard Einstein gravity. As a quantum theory the conformal theory is both renormalizable and unitary, with unitarity…
This is the 12th article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories" ed. J. Teschner. This article describes one way to understand an important part of the AGT-correspondence in terms of a triality…
Superconformal symmetry in six-dimensions is analyzed in terms of coordinate transformations on superspace. A superconformal Killing equation is derived and its solutions are identified in terms of supertranslations, dilations, Lorentz…
We review some properties of N=8 gauged supergravity in four dimensions with modified, but AdS invariant boundary conditions on the m^2=-2 scalars. There is a one-parameter class of asymptotic conditions on these fields and the metric…
A theoretical analysis of higher-order corrections to D=11 supergravity is given in a superspace framework. It is shown that any deformation of D=11 supergravity for which the lowest-dimensional component of the four-form $G_4$ vanishes is…
We illustrate the various ways in which the algebraic framework of noncommutative geometry naturally captures the short-distance spacetime properties of string theory. We describe the noncommutative spacetime constructed from a vertex…
We discuss various aspects of anisotropic gravity in $(d+D)$-dimensional spacetime where $D$ dimensions are treated as extra dimensions. It is based on the foliation preserving diffeomorphism invariance and anisotropic conformal invariance.…
We examine five-dimensional $\mathcal N=2$ gauged supergravity including terms up to four derivatives. These additional terms correspond to the supersymmetric completion of $R^2$, and were originally obtained in hep-th/0611329 using…
We discuss time-dependent backgrounds of type IIB supergravity realizing gravitation duals of gauge theories formulated in de Sitter space-time as a tool of embedding de Sitter in a supergravity. We show that only the gravitational duals to…
We study conformal gravity as an alternative theory of gravitation. For conformal gravity to be phenomenologically viable requires that the conformal symmetry is not manifest at the energy scales of the other known physical forces. Hence we…
A new 8-dim conformal gauging solves the auxiliary field problem and eliminates unphysical size change from Weyl's electromagnetic theory. We derive the Maurer-Cartan structure equations and find the zero curvature solutions for the…
For conformally K\"ahler Riemannian four-manifolds with a Killing field, we present a framework to solve the field equations for generalised gravitational instantons corresponding to conformal self-duality and to cosmological…
We present the locally supersymmetric formulation of unimodular gravity theory in D (1\le D \le 11) dimensions, namely supergravity theory with the metric tensor whose determinant is constrained to be unity. In such a formulation, the usual…
In this article I first give an abbreviated history of string theory and then describe the recently-conjectured field-string duality. This suggests a class of nonsupersymmetric gauge theories which are conformal (CGT) to leading order of…
In this paper we give an extensive description of Weyl quadratic gravity as the gauge theory of the Weyl group. The previously discovered (vectorial) torsion/non-metricity equivalence is shown to be built-in as it corresponds to a…
In this paper we examine in detail the implementation, with its associated difficulties, of the Killing conditions and gauge fixing into the variational principle formulation of Bianchi-Type cosmologies. We address problems raised in the…