Bethe Ansaetze for GKP strings

Studying the scattering of excitations around a dynamical background has a long history in the context of integrable models. The Gubser-Klebanov-Polyakov string solution provides such a background for the string/gauge correspondence. Taking the conjectured all-loop asymptotic equations for the AdS_4/CFT_3 correspondence as the starting point, we derive the S-matrix and a set of spectral equations for the lowest-lying excitations. We find that these equations resemble closely the analogous equations for AdS_5/CFT_4, which are also discussed in this paper. At large values of the coupling constant we show that they reproduce the Bethe equations proposed to describe the spectrum of the low-energy limit of the AdS_4xCP^3 sigma model.Comment: 60 pages, 5 figure

Unimodal bilingualism in the Deaf community: Language contact between two sign languages in Australia and the United Kingdom

Little is known about unimodal sign bilingualism: whether it resembles unimodal (spoken) bilingualism, or bimodal (spoken and signed) bilingualism, or whether it has unique qualities. This study is the first to examine this topic through a study of bilingualism in two Deaf communities in which dialects of unrelated languages: British Sign Language (BSL) and Irish Sign Language (ISL) are used. The research looks at previously unexplored aspects of code-blending and code-mixing, and compares the data with data on bimodal bilingualism (in a signed and a spoken language) and unimodal bilingualism (in two spoken languages) with a combination of experimental and naturalistic data. The experimental study used a picture naming task. Eleven participants were asked to name pictures as quickly as possible, and response latencies were analysed. It was found that there was indeed a switching cost, which did not appear to be asymmetrical. There was also a cognate facilitation effect. The second part of the study was based on interviews with bilinguals. As well as phenomena already described for unimodal spoken language bilingualism, including code-switching and code mixing, the study reports on mouthing, where spoken mouth patterns (in this case English) are produced simultaneously with manual signs. These are usually considered examples of code-blending, reflecting active mixing of two languages. This study provides an initial understanding of how modality interacts with bilingualism and suggests the need for further explorations

Review of AdS/CFT Integrability, Chapter I.3: Long-range spin chains

In this contribution we briefly review recent developments in the theory of long-range integrable spin chains. These spin chains constitute a natural generalisation of the well-studied integrable nearest-neighbour chains and are of particular relevance to the integrability in the AdS/CFT correspondence since the dilatation operator in the asymptotic region is conjectured to be a Hamiltonian of an integrable long-range psu spin chain.Comment: 17 pages, see also overview article arXiv:1012.3982, v2: references to other chapters updated, v3: minor typos corrected, references adde

The Yangian of sl(n|m) and the universal R-matrix

In this paper we study Yangians of sl(n|m) superalgebras. We derive the universal R-matrix and evaluate it on the fundamental representation obtaining the standard Yang R-matrix with unitary dressing factors. For m=0, we directly recover up to a CDD factor the well-known S-matrices for relativistic integrable models with su(N) symmetry. Hence, the universal R-matrix found provides an abstract plug-in formula, which leads to results obeying fundamental physical constraints: crossing symmetry, unitrarity and the Yang-Baxter equation. This implies that the Yangian double unifies all desired symmetries into one algebraic structure. In particular, our analysis is valid in the case of sl(n|n), where one has to extend the algebra by an additional generator leading to the algebra gl(n|n). We find two-parameter families of scalar factors in this case and provide a detailed study for gl(1|1).Comment: 24 pages, 2 figure

Asymptotic Properties of Difference Equations for Isotropic Loop Quantum Cosmology

In loop quantum cosmology, a difference equation for the wave function describes the evolution of a universe model. This is different from the differential equations that arise in Wheeler-DeWitt quantizations, and some aspects of general properties of solutions can appear differently. Properties of particular interest are boundedness and the presence of small-scale oscillations. Continued fraction techniques are used to show in different matter models the presence of special initial conditions leading to bounded solutions, and an explicit expression for these initial values is derived.Comment: 27 pages, 2 figure

A Generalized Scaling Function for AdS/CFT

We study a refined large spin limit for twist operators in the sl(2) sector of AdS/CFT. We derive a novel non-perturbative equation for the generalized two-parameter scaling function associated to this limit, and analyze it at weak coupling. It is expected to smoothly interpolate between weakly coupled gauge theory and string theory at strong coupling.Comment: 27 pages, no figures; v2: references added and typos fixe