There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy.

Dynamics of dark energy

http://inspirehep.net/record/499969/files/arXiv:hep-th_9905111.pdf

Large N Field Theories, String Theory and Gravity

We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λ
 L
 ≤ 2πk
 B
 T/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.

A bound on chaos

Superstring theoryをめぐって(放談室)

We develop the embedding formalism to describe symmetric traceless tensors in Anti-de Sitter space. We use this formalism to construct the bulk-to-bulk propagator of massive spin J fields and check that it has the expected short distance and massless limits. We also find a split representation for the bulk-to-bulk propagator, by writing it as an integral over the boundary of the product of two bulk-to-boundary propagators. We exemplify the use of this representation with the computation of the conformal partial wave decomposition of Witten diagrams. In particular, we determine the Mellin amplitude associated to AdS graviton exchange between minimally coupled scalars of general dimension, including the regular part of the amplitude.

/pdf/spinning-ads-propagators-x0a1ziqv6e.pdf

Spinning AdS propagators

Eikonal approximation in AdS/CFT: Conformal partial waves and finite N four-point functions

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 \( \mathcal{D} \) that generates the deformation. This provides a scheme to compute the couplings \( {a_{\mathcal{D}AB}} \) between the operator \( \mathcal{D} \) and two arbitrary operators \( {\mathcal{O}_A} \) and \( {\mathcal{O}_B} \). We exemplify for the case of \( \mathcal{N} = 4 \) SYM, considering the simplest case of the exact Lagrangian deformation. In this case the deformed anomalous dimension matrix is determined by the derivative of the anomalous dimension matrix with respect to the coupling. We use integrability techniques to compute the one-loop couplings \( {a_{\mathcal{L}AB}} \) between the Lagrangian and two distinct large operators built with Magnons, in the SU(2) sector of the theory. Then we consider \( {a_{\mathcal{D}AA}} \) at strong coupling, and show how to compute it using the gauge/gravity duality, when \( \mathcal{D} \) is a chiral operator dual to any supergravity field and \( {\mathcal{O}_A} \) is dual to a heavy string state. We exemplify for the Lagrangian and operators \( {\mathcal{O}_A} \) dual to heavy string states, showing agreement with the prediction derived from the renormalization group arguments.

/pdf/on-three-point-correlation-functions-in-the-gauge-gravity-5ez4xe2yjl.pdf

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

We initiate a program to generalize the standard eikonal approximation to compute amplitudes in Anti-de Sitter spacetimes. Inspired by the shock wave derivation of the eikonal amplitude in flat space, we study the two-point function E ∼ hO 1O1i shock in the presence of a shock wave in Anti-de Sitter, where O1 is a scalar primary operator in the dual conformal field theory. At tree level in the gravitational coupling, we relate the shock two-point function E to the discontinuity across a kinematical branch cut of the conformal field theory four-point function A ∼ hO 1O2O1O2i , where O2 creates the shock geometry in Anti-de Sitter. Finally, we extend the above results by computing E in the presence of shock waves along the horizon of Schwarzschild BTZ black holes. This work gives new tools for the study of Planckian physics in Anti-de Sitter spacetimes.

/pdf/eikonal-approximation-in-ads-cft-from-shock-waves-to-four-3vybrt1amk.pdf

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

We study some aspects of the Kaluza-Klein Melvin solution in M-theory. The associated magnetic field has a maximal critical value B = ?1/R where R is the radius of the compactification circle. It is argued that the Melvin background of type IIA with magnetic field B and of type 0A with magnetic field B' = B?1/R are equivalent. Evidence for this conjecture is provided using a further circle compactification and a `9-11' flip. We show that partition functions of nine-dimensional type-IIA strings and of a (?1)F?1/2 type-IIA orbifold both with NS-NS Melvin fluxtubes are related by such shift of the magnetic field. Then the instabilities of both IIA and 0A Melvin solutions are analyzed. For each theory there is an instanton associated to the decay of spacetime. In the IIA case the decay mode is associated to the nucleation of D6/D-brane pairs, while in the 0A case spacetime decays through Witten's bubble production.

http://cds.cern.ch/record/479976/files/0012072.pdf

Miguel S. Costa

Papers

Spinning AdS propagators

Eikonal approximation in AdS/CFT: Conformal partial waves and finite N four-point functions

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

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

The Kaluza Klein Melvin solution in M-theory