Miguel S. Costa

A New cosmological scenario in string theory

We consider new cosmological solutions with a collapsing, an intermediate and an expanding phase. The boundary between the expanding (collapsing) phase and the intermediate phase is seen by comoving observers as a cosmological past (future) horizon. The solutions are naturally embedded in string and M theory. In the particular case of a two-dimensional cosmology, space-time is flat with an identification under boost and translation transformations. We consider the corresponding string theory orbifold and calculate the modular invariant one-loop partition function. In this case there is a strong parallel with the BTZ black hole. The higher dimensional cosmologies have a timelike curvature singularity in the intermediate region. In some cases the string coupling can be made small throughout all of space-time but string corrections become important at the singularity. This happens where string winding modes become light which could resolve the singularity. The new proposed space-time causal structure could have implications for cosmology, independently of string theory.

Spinning conformal correlators

A bstractWe develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an indexfree notation where tensors are encoded by polynomials in auxiliary polarization vectors. The efficiency of the formalism is demonstrated by computing the tensor structures allowed in n-point conformal correlation functions of tensors operators. Constraints due to tensor conservation also take a simple form in this formalism. Finally, we obtain a perfect match between the number of independent tensor structures of conformal correlators in d dimensions and the number of independent structures in scattering amplitudes of spinning particles in (d + 1)-dimensional Minkowski space.

Spinning Conformal Blocks

A bstractFor conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the embedding space formalism, we show that one can express all such conformal blocks in terms of simple differential operators acting on the basic scalar conformal blocks. This method gives all conformal blocks for conformal field theories in three dimensions. We demonstrate how this formalism can be applied in a few simple examples.

On three-point correlation functions in the gauge/gravity duality

We study the effect of marginal and irrelevant deformations on the renormalization of operators near a CFT fixed point. New divergences in a given operator are determined by its OPE with the operator

Conformal Regge theory

\mathcal{D}

A RESOLUTION OF THE COSMOLOGICAL SINGULARITY WITH ORIENTIFOLDS

that generates the deformation. This provides a scheme to compute the couplings

Eikonal approximation in AdS/CFT: from shock waves to four-point functions

{a_{\mathcal{D}AB}}

Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions

between the operator

Deep Inelastic Scattering in Conformal QCD

\mathcal{D}

Superstring dualities and p-brane bound states

and two arbitrary operators