The Weinberg-Witten theorem on massless particles: an essay

In this essay we deal with the Weinberg-Witten theorem [1] which imposes limitations on massless particles. First we motivate a classification of massless particles given by the Poincaré group as the symmetry group of Minkowski spacetime. We then use the fundamental structure of the background in the form of Poincaré covariance to derive restrictions on charged massless particles known as the Weinberg-Witten theorem. We address possible misunderstandings in the proof of this theorem motivated by several papers on this topic. In the last section the consequences of the theorem are discussed. We treat it in the context of known particles and as a constraint for emergent theories

Open Perturbatively Long-Range Integrable gl(N) Spin Chains

We construct the most general perturbatively long-range integrable spin chain with spins transforming in the fundamental representation of gl(N) and open boundary conditions. In addition to the previously determined bulk moduli we find a new set of parameters determining the reflection phase shift. We also consider finite-size contributions and comment on their determination.Comment: 21 page

Open Perturbatively Long-Range Integrable GL(N) Spin Chains

We construct the most general perturbatively long-range integrable spin chain with spins transforming in the fundamental representation of gl(N) and open boundary conditions. In addition to the previously determined bulk moduli we find a new set of parameters determining the reflection phase shift. We also consider finite-size contributions and comment on their determination

Symmetries of tree-level scattering amplitudes in N=6 superconformal Chern-Simons theory

Constraints of the osp(6|4) symmetry on tree-level scattering amplitudes in N=6 superconformal Chern-Simons theory are derived. Supplemented by Feynman diagram calculations, solutions to these constraints, namely, the four- and six-point superamplitudes, are presented and shown to be invariant under Yangian symmetry. This introduces integrability into the amplitude sector of the theory. © 2010 The American Physical Society

Boosting Nearest-Neighbour to Long-Range Integrable Spin Chains

We present an integrability-preserving recursion relation for the explicit construction of long-range spin chain Hamiltonians. These chains are generalizations of the Haldane-Shastry and Inozemtsev models and they play an important role in recent advances in string/gauge duality. The method is based on arbitrary nearest-neighbour integrable spin chains and it sheds light on the moduli space of deformation parameters. We also derive the closed chain asymptotic Bethe equations.Comment: 10 pages, v2: reference added, minor changes, v3: published version with added/updated reference

Reflecting magnons from D7 and D5 branes

We obtain the reflection matrices for the scattering of elementary magnons from certain open boundaries, corresponding to open strings ending on D7 and D5 branes in $AdS_5\times S^5$. In each case we consider two possible orientations for the vacuum state. We show that symmetry arguments are sufficient to determine the reflection matrices up to at most two unknown functions. The D7 reflection matrices obey the boundary Yang Baxter-Equation. This is automatic for one vacuum orientation, and requires a natural choice of ratio between two unknowns for the other. In contrast, the D5 reflection matrices do not obey the boundary Yang Baxter-Equation. In both cases we show consistency with the existent weak and strong coupling results.Comment: 32 pages, 1 figure; v2: added references and minor changes; v3: error in boundary Yang-Baxter equation for D5 reflection matrix note

Hidden Simplicity of Gauge Theory Amplitudes

These notes were given as lectures at the CERN Winter School on Supergravity, Strings and Gauge Theory 2010. We describe the structure of scattering amplitudes in gauge theories, focussing on the maximally supersymmetric theory to highlight the hidden symmetries which appear. Using the BCFW recursion relations we solve for the tree-level S-matrix in N=4 super Yang-Mills theory, and describe how it produces a sum of invariants of a large symmetry algebra. We review amplitudes in the planar theory beyond tree-level, describing the connection between amplitudes and Wilson loops, and discuss the implications of the hidden symmetries.Comment: 46 pages, 15 figures. v2 ref added, typos fixe

Long-Range Deformations for Integrable Spin Chains

We present a recursion relation for the explicit construction of integrable spin chain Hamiltonians with long-range interactions. Based on arbitrary short-range (e.g. nearest-neighbor) integrable spin chains, it allows to construct an infinite set of conserved long-range charges. We explain the moduli space of deformation parameters by different classes of generating operators. The rapidity map and dressing phase in the long-range Bethe equations are a result of these deformations. The closed chain asymptotic Bethe equations for long-range spin chains transforming under a generic symmetry algebra are derived. Notably, our construction applies to generalizations of standard nearest-neighbor chains such as alternating spin chains. We also discuss relevant properties for its application to planar D=4, N=4 and D=3, N=6 supersymmetric gauge theories. Finally, we present a map between long-range and inhomogeneous spin chains delivering more insight into the structures of these models as well as their limitations at wrapping order.Comment: 63 pages, v2: references added, v3: typos corrected in eqs (8.20) and (8.24