On AdS2/CFT1AdS_2/CFT_1 transfer matrices, Bethe ansatz and scale invariance

We explicitly calculate the $AdS_2 \times S^2 \times T^6$ transfer-matrix eigenvalues in the massless sector using the exact integrable S-matrix, for up to 5 particles. This enables us to conjecture the general pattern. We use the conjectured form of the eigenvalues to write down a set of massless Bethe ansatz equations. The same procedure applies to the relativistic as well as to the non-relativistic situation. In the relativistic case, the right and left modes decouple. We speculate that the relativistic massless Bethe ansatz we obtain in that case might capture the integrable structure of an underlying 2D critical theory. We finally take advantage of some remarkable simplifications to make progress in the massive case as well.Comment: 30 pages, 1 figure; v2: matching version accepted to J. Phys.

qq-Poincar\'e supersymmetry in AdS5/CFT4AdS_5/CFT_4

We consider the exact S-matrix governing the planar spectral problem for strings on $AdS_5\times S^5$ and $\mathcal N=4$ super Yang-Mills, and we show that it is invariant under a novel "boost" symmetry, which acts as a differentiation with respect to the particle momentum. This generator leads us also to reinterpret the usual centrally extended $\mathfrak{psu}(2|2)$ symmetry, and to conclude that the S-matrix is invariant under a $q$-Poincar\'e supersymmetry algebra, where the deformation parameter is related to the 't Hooft coupling. We determine the two-particle action (coproduct) that turns out to be non-local, and study the property of the new symmetry under crossing transformations. We look at both the strong-coupling (large tension in the string theory) and weak-coupling (spin-chain description of the gauge theory) limits; in the former regime we calculate the cobracket utilising the universal classical r-matrix of Beisert and Spill. In the eventuality that the boost has higher partners, we also construct a quantum affine version of 2D Poincar\'e symmetry, by contraction of the quantum affine algebra $U_q(\widehat{\mathfrak{sl}_2})$ in Drinfeld's second realisation.Comment: 35 pages. Added discussion on antipode in the presence of the phase. Published versio

AdS3/CFT2 and q-Poincare' superalgebras

We discover that a certain deformation of the 1+1 dimensional Poincare' superalgebra is exactly realised in the massless sector of the AdS3/CFT2 integrable scattering problem. Deformed Poincar\'e superalgebras were previously noticed to appear in the AdS5/CFT4 correspondence - which displays only massive excitations -, but they were there only a partial symmetry. We obtain a representation of the boost operator and its coproduct, and show that the comultiplication exactly satisfies the homomorphism property. We present a classical limit, and finally speculate on an analogy with the physics of phonons.Comment: 21 pages, no figures, pdfLaTeX; v2: typos corrected, references added; v3: matches journal versio

Open string pair creation from worldsheet instantons

Worldline instantons provide a particularly elegant way to derive Schwinger's well-known formula for the pair creation rate due to a constant electric field in quantum electrodynamics. In this note, we show how to extend this method to the corresponding problem of open string pair creation.Comment: 9 pages, no figure

Multi-parametric R-matrix for the sl(2|1) Yangian

We study the Yangian of the sl(2|1) Lie superalgebra in a multi-parametric four-dimensional representation. We use Drinfeld's second realization to independently rederive the R-matrix, and to obtain the antiparticle representation, the crossing and the unitarity condition. We consistently apply the Yangian antipode and its inverse to the individual particles involved in the scattering. We explicitly find a scalar factor solving the crossing and unitarity conditions, and study the analytic structure of the resulting dressed R-matrix. The formulas we obtain bear some similarities with those familiar from the study of integrable structures in the AdS/CFT correspondence, although they present obvious crucial differences.Comment: 25 pages, LaTeX, no figures; v2: typos corrected, minor changes, added pole analysis of the dressed R-matrix; v3: clarifications added, typos corrected, references added; v4: typos corrected, minor changes, version to appear in J. Math. Phy

qq-Poincar\'e invariance of the AdS3/CFT2AdS_3/CFT_2 RR-matrix

We consider the exact $R$-matrix of $AdS_3/CFT_2$, which is the building block for describing the scattering of worldsheet excitations of the light-cone gauge-fixed backgrounds $AdS_3 \times S^3 \times T^4$ and $AdS_3 \times S^3 \times S^3 \times S^1$ with pure Ramond-Ramond fluxes. We show that $R$ is invariant under a "deformed boost" symmetry, for which we write an explicit exact coproduct, i.e. its action on 2-particle states. When we include the boost, the symmetries of the $R$-matrix close into a $q$-Poincar\'e superalgebra. Our findings suggest that the recently discovered boost invariance in $AdS_5/CFT_4$ may be a common feature of $AdS/CFT$ systems that are treatable with the exact techniques of integrability. With the aim of going towards a universal formulation of the underlying Hopf algebra, we also propose a universal form of the $AdS_3/CFT_2$ classical $r$-matrix.Comment: 26 pages. Minor improvements and references added. Published versio