On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra

The centrally extended su(2|2) superalgebra is an asymptotic symmetry of the light-cone string sigma model on AdS5 x S5. We consider an evaluation representation of the conventional Yangian built over a particular 16-dimensional long representation of the centrally extended su(2|2). Interestingly, we find that S-matrices compatible with this evaluation representation do not exist. On the other hand, by requiring centrally extended su(2|2) invariance and explicitly solving the Yang-Baxter equation, we find a scattering matrix for long-short representations of the Lie superalgebra. We notice that this S-matrix is invariant under a different representation of non-evaluation type, induced from the tensor product of short representations. Our findings concern the conventional Yangian only, and are not applied to possible algebraic extensions of the latter.Comment: Version accepted for publication in JHE

The Bound State S-matrix of the Deformed Hubbard Chain

In this work we use the q-oscillator formalism to construct the atypical (short) supersymmetric representations of the centrally extended Uq (su(2|2)) algebra. We then determine the S-matrix describing the scattering of arbitrary bound states. The crucial ingredient in this derivation is the affine extension of the aforementioned algebra.Comment: 44 pages, 3 figures. v2: minor correction

Secret Symmetries in AdS/CFT

We discuss special quantum group (secret) symmetries of the integrable system associated to the AdS/CFT correspondence. These symmetries have by now been observed in a variety of forms, including the spectral problem, the boundary scattering problem, n-point amplitudes, the pure-spinor formulation and quantum affine deformations.Comment: 20 pages, pdfLaTeX; Submitted to the Proceedings of the Nordita program `Exact Results in Gauge-String Dualities'; Based on the talk presented by A.T., Nordita, 15 February 201

An Exceptional Algebraic Origin of the AdS/CFT Yangian Symmetry

In the su(2|2) spin chain motivated by the AdS/CFT correspondence, a novel symmetry extending the superalgebra su(2|2) into u(2|2) was found. We pursue the origin of this symmetry in the exceptional superalgebra d(2,1;epsilon), which recovers su(2|2) when the parameter epsilon is taken to zero. Especially, we rederive the Yangian symmetries of the AdS/CFT spin chain using the exceptional superalgebra and find that the epsilon-correction corresponds to the novel symmetry. Also, we reproduce the non-canonical classical r-matrix of the AdS/CFT spin chain expressed with this symmetry from the canonical one of the exceptional algebra.Comment: 20 pages, 3 figures, v3: minor changes and references adde

Quantum Symmetries and Marginal Deformations

We study the symmetries of the N=1 exactly marginal deformations of N=4 Super Yang-Mills theory. For generic values of the parameters, these deformations are known to break the SU(3) part of the R-symmetry group down to a discrete subgroup. However, a closer look from the perspective of quantum groups reveals that the Lagrangian is in fact invariant under a certain Hopf algebra which is a non-standard quantum deformation of the algebra of functions on SU(3). Our discussion is motivated by the desire to better understand why these theories have significant differences from N=4 SYM regarding the planar integrability (or rather lack thereof) of the spin chains encoding their spectrum. However, our construction works at the level of the classical Lagrangian, without relying on the language of spin chains. Our approach might eventually provide a better understanding of the finiteness properties of these theories as well as help in the construction of their AdS/CFT duals.Comment: 1+40 pages. v2: minor clarifications and references added. v3: Added an appendix, fixed minor typo

Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane

We consider the worldsheet boundary scattering and the corresponding boundary algebras for the Z=0 giant graviton and the Z=0 D7-brane in the AdS/CFT correspondence. We consider two approaches to the boundary scattering, the usual one governed by the (generalized) twisted Yangians and the q-deformed model of these boundaries governed by the quantum affine coideal subalgebras. We show that the q-deformed approach leads to boundary algebras that are of a more compact form than the corresponding twisted Yangians, and thus are favourable to use for explicit calculations. We obtain the q-deformed reflection matrices for both boundaries which in the q->1 limit specialize to the ones obtained using twisted Yangians.Comment: 36 pages. v2: minor typos corrected, references updated; v3: published versio

Two-loop test of the N=6 Chern-Simons theory S-matrix

Starting from the integrable two-loop spin-chain Hamiltonian describing the anomalous dimensions of scalar operators in the planar N=6 superconformal Chern-Simons theory of ABJM, we perform a direct coordinate Bethe ansatz computation of the corresponding two-loop S-matrix. The result matches with the weak-coupling limit of the scalar sector of the all-loop S-matrix which we have recently proposed. In particular, we confirm that the scattering of A and B particles is reflectionless. As a warm up, we first review the analogous computation of the one-loop S-matrix from the one-loop dilatation operator for the scalar sector of planar N=4 superconformal Yang-Mills theory, and compare the result with the all-loop SU(2|2)^{2} S-matrix.Comment: 21 pages, no figure; references adde

Increasing vegetable intakes: rationale and systematic review of published interventions

Purpose While the health benefits of a high fruit and vegetable consumption are well known and considerable work has attempted to improve intakes, increasing evidence also recognises a distinction between fruit and vegetables, both in their impacts on health and in consumption patterns. Increasing work suggests health benefits from a high consumption specifically of vegetables, yet intakes remain low, and barriers to increasing intakes are prevalent making intervention difficult. A systematic review was undertaken to identify from the published literature all studies reporting an intervention to increase intakes of vegetables as a distinct food group. Methods Databases—PubMed, PsychInfo and Medline—were searched over all years of records until April 2015 using pre-specified terms. Results Our searches identified 77 studies, detailing 140 interventions, of which 133 (81 %) interventions were conducted in children. Interventions aimed to use or change hedonic factors, such as taste, liking and familiarity (n = 72), use or change environmental factors (n = 39), use or change cognitive factors (n = 19), or a combination of strategies (n = 10). Increased vegetable acceptance, selection and/or consumption were reported to some degree in 116 (83 %) interventions, but the majority of effects seem small and inconsistent. Conclusions Greater percent success is currently found from environmental, educational and multi-component interventions, but publication bias is likely, and long-term effects and cost-effectiveness are rarely considered. A focus on long-term benefits and sustained behaviour change is required. Certain population groups are also noticeably absent from the current list of tried interventions

Engineered Models of Metastasis with Application to Study Cancer Biomechanics

Three-dimensional complex biomechanical interactions occur from the initial steps of tumor formation to the later phases of cancer metastasis. Conventional monolayer cultures cannot recapitulate the complex microenvironment and chemical and mechanical cues that tumor cells experience during their metastatic journey, nor the complexity of their interactions with other, noncancerous cells. As alternative approaches, various engineered models have been developed to recapitulate specific features of each step of metastasis with tunable microenvironments to test a variety of mechanistic hypotheses. Here the main recent advances in the technologies that provide deeper insight into the process of cancer dissemination are discussed, with an emphasis on three-dimensional and mechanical factors as well as interactions between multiple cell types