91 research outputs found
On transfer matrices, Bethe ansatz and scale invariance
We explicitly calculate the 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.
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
-Poincar\'e supersymmetry in
We consider the exact S-matrix governing the planar spectral problem for
strings on and 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
symmetry, and to conclude that the S-matrix is invariant under a -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
in Drinfeld's second realisation.Comment: 35 pages. Added discussion on antipode in the presence of the phase.
Published 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
Review of AdS/CFT Integrability, Chapter VI.2: Yangian Algebra
We review the study of Hopf algebras, classical and quantum R-matrices,
infinite-dimensional Yangian symmetries and their representations in the
context of integrability for the N=4 vs AdS5xS5 correspondence.Comment: 16 pages, see also overview article arXiv:1012.3982; v2: references
to other chapters updated; v3: reference added; v4: acknowledgment added; v5:
Journal versio
Yangians, S-matrices and AdS/CFT
This review is meant to be an account of the properties of the
infinite-dimensional quantum group (specifically, Yangian) symmetry lying
behind the integrability of the AdS/CFT spectral problem. In passing, the
chance is taken to give a concise anthology of basic facts concerning Yangians
and integrable systems, and to store a series of remarks, observations and
proofs the author has collected in a five-year span of research on the subject.
We hope this exercise will be useful for future attempts to study Yangians in
field and string theories, with or without supersymmetry.Comment: 95 pages, pdfLaTeX, 1 figure. This is an author-created,
un-copyedited version of an invited topical review accepted for publication
in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is
not responsible for any errors or omissions in this version of the manuscript
or any version derived from it. v2: fixed sign in (15), added comment about
Jacobi identity in footnote 5
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