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 for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an index-free 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.

/pdf/spinning-conformal-correlators-40nzqig95u.pdf

Spinning conformal correlators

We generalize Regge theory to correlation functions in conformal field theories. This is done by exploring the analogy between Mellin amplitudes in AdS/CFT and S-matrix elements. In the process, we develop the conformal partial wave expansion in Mellin space, elucidating the analytic structure of the partial amplitudes. We apply the new formalism to the case of four point correlation functions between protected scalar operators in $ \mathcal{N}=4 $
 Super Yang Mills, in cases where the Regge limit is controlled by the leading twist operators associated to the pomeron-graviton Regge trajectory. At weak coupling, we are able to predict to arbitrary high order in the ’t Hooft coupling the behaviour near J = 1 of the OPE coefficients $ {C_{{\mathcal{OO}J}}} $
 between the external scalars and the spin J leading twist operators. At strong coupling, we use recent results for the anomalous dimension of the leading twist operators to improve current knowledge of the AdS graviton Regge trajectory — in particular, determining the next and next to next leading order corrections to the intercept. Finally, by taking the flat space limit and considering the Virasoro-Shapiro S-matrix element, we compute the strong coupling limit of the OPE coefficient $ {C_{{\mathcal{LL}J}}} $
 between two Lagrangians and the leading twist operators of spin J.

/pdf/conformal-regge-theory-532zizj0fc.pdf

Conformal Regge 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.

/pdf/a-new-cosmological-scenario-in-string-theory-4uawvu94ae.pdf

A New cosmological scenario in string theory

For 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.

/pdf/spinning-conformal-blocks-27b7qrzui2.pdf

Spinning Conformal Blocks

We derive an eikonal approximation to high energy interactions in Anti-de Sitter spacetime, by generalizing a position space derivation of the eikonal amplitude in flat space We are able to resum, in terms of a generalized phase shift, ladder and cross ladder graphs associated to the exchange of a spin j field, to all orders in the coupling constant Using the AdS/CFT correspondence, the resulting amplitude determines the behavior of the dual conformal field theory four-point function for small values of the cross ratios, in a Lorentzian regime Finally we show that the phase shift is dominated by graviton exchange and computes, in the dual CFT, the anomalous dimension of the double trace primary operators O-1 partial derivativepartial derivative O-2 of large dimension and spin, corresponding to the relative motion of the two interacting particles The results are valid at strong t'Hooft coupling and are exact in the 1/N expansion

https://iopscience.iop.org/article/10.1088/1126-6708/2007/09/037/pdf

Miguel S. Costa

Papers

Spinning conformal correlators

Conformal Regge theory

A New cosmological scenario in string theory

Spinning Conformal Blocks

Eikonal approximation in AdS/CFT: resumming the gravitational loop expansion