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
A study of integrable form factors in massless relativistic AdS_3
We show that the massless integrable sector of the AdS_3 \times S^3 \times
T^4 superstring theory, which admits a non-trivial relativistic limit, provides
a setting where it is possible to determine exact minimal solutions to the form
factor axioms, in integral form, based on analiticity considerations, along the
same lines of ordinary relativistic integrable models. We construct in full
detail the formulas for the two- and three-particle case, and show the
similarities as well as the differences with respect to the off-shell Bethe
ansatz procedure of Babujian et al. We show that our expressions pass a series
of non-trivial consistency checks which are substantially more involved than in
the traditional case. We speculate on the problems concerned in a possible
generalisation to an arbitrary number of particles, and on a possible
connection with the hexagon programme.Comment: PDFLaTeX, 51 pages, 10 figure
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