60 research outputs found
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 . 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
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