94 research outputs found
Higher loops, integrability and the near BMN limit
In this note we consider higher-loop contributions to the planar dilatation
operator of N=4 SYM in the su(2) subsector of two complex scalar fields. We
investigate the constraints on the form of this object due to interactions of
two excitations in the BMN limit. We then consider two scenarios to uniquely
fix some higher-loop contributions: (i) Higher-loop integrability fixes the
dilatation generator up to at least four-loops. Among other results, this
allows to conjecture an all-loop expression for the energy in the near BMN
limit. (ii) The near plane-wave limit of string theory and the BMN
correspondence fix the dilatation generator up to three-loops. We comment on
the difference between both scenarios.Comment: 6 page
The su(2|3) Dynamic Spin Chain
The complete one-loop, planar dilatation operator of the N=4 superconformal
gauge theory was recently derived and shown to be integrable. Here, we present
further compelling evidence for a generalisation of this integrable structure
to higher orders of the coupling constant. For that we consider the su(2|3)
subsector and investigate the restrictions imposed on the spin chain
Hamiltonian by the symmetry algebra. This allows us to uniquely fix the energy
shifts up to the three-loop level and thus prove the correctness of a
conjecture in hep-th/0303060. A novel aspect of this spin chain model is that
the higher-loop Hamiltonian, as for N=4 SYM in general, does not preserve the
number of spin sites. Yet this dynamic spin chain appears to be integrable.Comment: 34 pages, 5 figures, v2: additional coefficient at three loops
explained, discussion of integrability enhanced, figures adde
On Yangian Symmetry in Planar N=4 SYM
Planar N=4 supersymmetric Yang-Mills theory appears to be perturbatively
integrable. This work reviews integrability in terms of a Yangian algebra and
compares the application to the problems of anomalous dimensions and scattering
amplitudes.Comment: 24 pages, To Lev Lipatov on the occasion of his 70th birthday, v2:
references and typos corrected, v3: no changes, references updated, published
in "Subtleties in Quantum Field Theory", pp. 175, ed: D. Diakonov and
"Gribov-80 Memorial Volume: Quantum Chromodynamics and Beyond", pp. 413, ed:
Yu. Dokshitzer, P. L\'evai, J. Ny\'ir
The Analytic Bethe Ansatz for a Chain with Centrally Extended su(2|2) Symmetry
We investigate the integrable structure of spin chain models with centrally
extended su(2|2) and psu(2,2|4) symmetry. These chains have their origin in the
planar AdS/CFT correspondence, but they also contain the one-dimensional
Hubbard model as a special case. We begin with an overview of the
representation theory of centrally extended su(2|2). These results are applied
in the construction and investigation of an interesting S-matrix with su(2|2)
symmetry. In particular, they enable a remarkably simple proof of the
Yang-Baxter relation. We also show the equivalence of the S-matrix to Shastry's
R-matrix and thus uncover a hidden supersymmetry in the integrable structure of
the Hubbard model. We then construct eigenvalues of the corresponding transfer
matrix in order to formulate an analytic Bethe ansatz. Finally, the form of
transfer matrix eigenvalues for models with psu(2,2|4) symmetry is sketched.Comment: 66 pages, v2: minor changes, references added, to appear in JSTA
Construction of Lax Connections by Exponentiation
We propose a method for constructing the Lax connection of two-dimensional
relativistic integrable sigma models on coset spaces by means of exponentiation
of a suitable operator. We derive a simple quadratic relation that this
operator must satisfy for an entire one-parameter family of connections to be
flat.Comment: 17 page
Higher-Loop Integrability in N=4 Gauge Theory
The dilatation operator measures scaling dimensions of local operator in a
conformal field theory. Algebraic methods of constructing the dilatation
operator in four-dimensional N=4 gauge theory are reviewed. These led to the
discovery of novel integrable spin chain models in the planar limit. Making use
of Bethe ansaetze, a superficial discrepancy in the AdS/CFT correspondence was
found, we discuss this issue and give a possible resolution.Comment: 13 pages, Talk given at Strings 2004, Paris, 28 June - 2 July, v2:
reference adde
Bonus Yangian Symmetry for the Planar S-Matrix of N=4 Super Yang-Mills
Recent developments in the determination of the planar S-matrix of N=4 Super
Yang-Mills are closely related to its Yangian symmetry. Here we provide
evidence for a yet unobserved additional symmetry: the Yangian level-one
helicity operator.Comment: 8 pages, v2: minor change
Maximally extended sl(2|2), q-deformed d(2,1;epsilon) and 3D kappa-Poincar\'e
We show that the maximal extension sl(2) times psl(2|2) times C3 of the
sl(2|2) superalgebra can be obtained as a contraction limit of the semi-simple
superalgebra d(2,1;epsilon) times sl(2). We reproduce earlier results on the
corresponding q-deformed Hopf algebra and its universal R-matrix by means of
contraction. We make the curious observation that the above algebra is related
to kappa-Poincar\'e symmetry. When dropping the graded part psl(2|2) we find a
novel one-parameter deformation of the 3D kappa-Poincar\'e algebra. Our
construction also provides a concise exact expression for its universal
R-matrix.Comment: 25 page
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