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)

As part of experiment PS198 at LEAR, complete angular distributions of the analyzing power in p − p elastic scattering have been recently measured Data were taken at three different momenta of the antiproton beam: 450, 550 and 700 MeV/c A polarized proton target was used together with the high resolution spectrometer SPES II Preliminary data at 700 MeV/c are presented and compared to theoretical predictions

Measurement of the analyzing power in elastic scattering at 700 MeV/c

We consider the N=4 SU(N) Super Yang Mills theory on the Coulomb branch with gauge symmetry broken to S(U(N_1) x U(N_2)). By integrating the W particles, the effective action near the IR SU(N_i) conformal fixed points is seen to be a deformation of the Super Yang Mills theory by a non-renormalized, irrelevant, dimension 8 operator. The correction to the two-point function of the dilaton field dual operator near the IR is related to a three-point function of chiral primary operators at the conformal fixed points and agrees with the classical gravity prediction, including the numerical factor.

A Test of the AdS/CFT Duality on the Coulomb Branch

We derive an optical theorem for perturbative CFTs which computes the double discontinuity of conformal correlators from the single discontinuities of lower order correlators, in analogy with the optical theorem for flat space scattering amplitudes. The theorem takes a purely multiplicative form in the CFT impact parameter representation used to describe high-energy scattering in the dual AdS theory. We use this result to study four-point correlation functions that are dominated in the Regge limit by the exchange of the graviton Regge trajectory (Pomeron) in the dual theory. At one-loop the scattering is dominated by double Pomeron exchange and receives contributions from tidal excitations of the scattering states which are efficiently described by an AdS vertex function, in close analogy with the known Regge limit result for one-loop string scattering in flat space at finite string tension. We compare the flat space limit of the conformal correlator to the flat space results and thus derive constraints on the one-loop vertex function for type IIB strings in AdS and also on general spinning tree level type IIB amplitudes in AdS.

/pdf/the-perturbative-cft-optical-theorem-and-high-energy-string-1yi5n1jrmv.pdf

The perturbative CFT optical theorem and high-energy string scattering in AdS at one loop

We report here on the experiment PS198 at LEAR which was completed in June 1988. The aim of that experiment was the measurement of spin observables in p − p and p − d elastic scattering in order to study the N − N interaction in the two isospin states I = 1 and I=0. It was foreseen to measure the full angular distribution of the differential cross section and of the analyzing power in p − p elastic scattering at few incident momenta between 450 and 750 MeV/c.

Measurement of Spin Dependent Observables in the \overline p — p Elastic Scattering from 450 to 700 MeV/c

We propose and explore the Regge limit for correlation functions of five local primary operators in conformal field theories. After reviewing some features of Regge theory for flat-space scattering amplitudes, we analyse the analytic structure of conformal blocks both in position and Mellin space in the Regge limit and propose an extension of conformal Regge theory for five-point functions. As a byproduct of our analysis we also introduce a new basis of three-point correlation functions for operators with spin and the associated Euclidean conformal blocks.

Miguel S. Costa

Papers

Measurement of the analyzing power in elastic scattering at 700 MeV/c

A Test of the AdS/CFT Duality on the Coulomb Branch

The perturbative CFT optical theorem and high-energy string scattering in AdS at one loop

Measurement of Spin Dependent Observables in the \overline p — p Elastic Scattering from 450 to 700 MeV/c

Conformal multi-Regge theory