The (1+1)-dimensional cobordism category of closed 1-dimensional manifolds and oriented surfaces is a most basic mathematical structure. It has played a fundamental role in string theory and conformal field theory. We give a brief account of its structure and indicate what structure it gives vector spaces and other algebraic objects on which it (or an embellished version of it) acts. We explain...

We exhibit bound states in the spectrum of non-compact D-branes in N = 2 Liouville conformal field theory. We interpret these states in the study of D-branes in the near-horizon limit of Neveu-Schwarz five-branes spread on a topologically trivial circle. We match semiclassical di-electric and repulsion effects with exact conformal field theory results and describe the fate of D-branes hitting N...

We construct analytically an asymptotically Lifshitz black brane with dynamical exponent z = 1 + ǫ2 in an Einstein-Proca model, where ǫ is a small parameter. In previous work we showed that the holographic dual QFT is a deformation of a CFT by the time component of a vector operator and the parameter ǫ is the corresponding deformation parameter. In the black brane background this operator addit...

In this paper first it is proved that if ξ is a nontrivial closed conformal vector field on an n-dimensional compact Riemannian manifold (M, g) with constant scalar curvature S satisfying S ≤ λ1(n − 1), λ1 being first nonzero eigenvalue of the Laplacian operator ∆ on M and Ricci curvature in direction of a certain vector field is non-negative, then M is isometric to the n-sphere S(c), where S =...

We describe a supersymmetric RG flow between conformal fixed points of a two-dimensional quantum field theory as an analytic domain wall solution of the three-dimensional SO(4)×SO(4) gauged supergravity. Its ultraviolet fixed point is an N=(4, 4) superconformal field theory related, through the double D1-D5 system, to theories modeling the statistical mechanics of black holes. The flow is drive...

We give an exact spherically symmetric solution for the Einstein-scalar field system. The solution may be interpreted as an inhomogeneous dynamical scalar field cosmology. The spacetime has a timelike conformal Killing vector field and is asymptotically conformally flat. It also has black or white hole-like regions containing trapped surfaces. We describe the properties of the apparent horizon ...

Abstract We revisit the gauge symmetry related to integrable projective transformations in metric-affine formalism, identifying field of Weyl (conformal) as a dynamical component affine connection. In particular, we show how include local scaling large class geometric gravity theories, introducing compensator dilaton that naturally gives rise Stückelberg sector where spontaneous breaking mechan...

The recently introduced SLE growth processes are based on conformal maps from an open and simply-connected subset of the upper half-plane to the half-plane itself. We generalize this by considering a hierarchy of stochastic evolutions mapping open and simply-connected subsets of smaller and smaller fractions of the upper half-plane to these fractions themselves. The evolutions are all driven by...

Stochastic Loewner evolutions (SLEκ) are random growth processes of sets, called hulls, embedded in the two dimensional upper half plane. We elaborate and develop a relation between SLEκ evolutions and conformal field theories (CFT) which is based on a group theoretical formulation of SLEκ processes and on the identification of the proper hull boundary states. This allows us to define an infini...

Stochastic Loewner evolutions (SLEκ) are random growth processes of domains in the two dimensional upper half plane which represent critical clusters. We elaborate and developp a relation between SLEκ evolutions and conformal field theories (CFT) which is based on a group theoretical formulation of SLEκ processes and on the identification of the proper hull boundary states. This allows us to de...