126 research outputs found
The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure
In this paper we investigate the algebraic structure of AdS/CFT in the
strong-coupling limit. We propose an expression for the classical r-matrix with
(deformed) u(2|2) symmetry, which leads to a quasi-triangular Lie bialgebra as
the underlying symmetry algebra. On the fundamental representation our r-matrix
coincides with the classical limit of the quantum R-matrix.Comment: 31 pages, v2: added comment on classical double structure in 4.5. new
section 5 on relation to other algebras (from old appendix and new results).
fixed typos and mathematical inaccuracies, added references, v3: improved
mathematical presentation, to appear in CM
Drinfeld second realization of the quantum affine superalgebras of via the Weyl groupoid
We obtain Drinfeld second realization of the quantum affine superalgebras
associated with the affine Lie superalgebra . Our results are
analogous to those obtained by Beck for the quantum affine algebras. Beck's
analysis uses heavily the (extended) affine Weyl groups of the affine Lie
algebras. In our approach the structures are based on a Weyl groupoid.Comment: 40 pages, 1 figure. close to the final version to appear in RIMS
Kokyuroku Bessatsu (Besstsu) B8 (2008) 171-21
The Yangian of sl(n|m) and the universal R-matrix
In this paper we study Yangians of sl(n|m) superalgebras. We derive the
universal R-matrix and evaluate it on the fundamental representation obtaining
the standard Yang R-matrix with unitary dressing factors. For m=0, we directly
recover up to a CDD factor the well-known S-matrices for relativistic
integrable models with su(N) symmetry. Hence, the universal R-matrix found
provides an abstract plug-in formula, which leads to results obeying
fundamental physical constraints: crossing symmetry, unitrarity and the
Yang-Baxter equation. This implies that the Yangian double unifies all desired
symmetries into one algebraic structure. In particular, our analysis is valid
in the case of sl(n|n), where one has to extend the algebra by an additional
generator leading to the algebra gl(n|n). We find two-parameter families of
scalar factors in this case and provide a detailed study for gl(1|1).Comment: 24 pages, 2 figure
Weakly coupled N=4 Super Yang-Mills and N=6 Chern-Simons theories from u(2|2) Yangian symmetry
In this paper we derive the universal R-matrix for the Yangian Y(u(2|2)),
which is an abstract algebraic object leading to rational solutions of the
Yang-Baxter equation on representations. We find that on the fundamental
representation the universal R-matrix reduces to the standard rational R-matrix
R = R_0(1 + P/u), where the scalar prefactor is surprisingly simple compared to
prefactors one finds e.g. for sl(n) R-matrices. This leads precisely to the
S-matrix giving the Bethe Ansatz of one-loop N = 4 Super Yang-Mills theory and
two-loop N = 6 Chern-Simons theory.Comment: 16 page
The AdS(4) x CP(3) string and its Bethe equations in the near plane wave limit
We perform a detailed study of bosonic type IIA string theory in a large
light-cone momentum / near plane wave limit of . In order to
attain this we derive the Hamiltonian up to cubic and quartic order in number
of fields and calculate the energies for string excitations in a subspace. The computation for the string energies is performed for
arbitrary length excitations utilizing an unitary transformation which allows
us to remove the cubic terms in the Hamiltonian. We then rewrite a recent set
of proposed all loop Bethe equations in a light-cone language and compare their
predictions with the obtained string energies. We find perfect agreement.Comment: 28 pages, references and footnote adde
The classical R-matrix of AdS/CFT and its Lie dialgebra structure
The classical integrable structure of Z_4-graded supercoset sigma-models,
arising in the AdS/CFT correspondence, is formulated within the R-matrix
approach. The central object in this construction is the standard R-matrix of
the Z_4-twisted loop algebra. However, in order to correctly describe the Lax
matrix within this formalism, the standard inner product on this twisted loop
algebra requires a further twist induced by the Zhukovsky map, which also plays
a key role in the AdS/CFT correspondence. The non-ultralocality of the
sigma-model can be understood as stemming from this latter twist since it leads
to a non skew-symmetric R-matrix.Comment: 22 pages, 2 figure
Two-loop Integrability of Planar N=6 Superconformal Chern-Simons Theory
Bethe ansatz equations have been proposed for the asymptotic spectral problem
of AdS_4/CFT_3. This proposal assumes integrability, but the previous
verification of weak-coupling integrability covered only the su(4) sector of
the ABJM gauge theory. Here we derive the complete planar two-loop dilatation
generator of N=6 superconformal Chern-Simons theory from osp(6|4)
superconformal symmetry. For the osp(4|2) sector, we prove integrability
through a Yangian construction. We argue that integrability extends to the full
planar two-loop dilatation generator, confirming the applicability of the Bethe
equations at weak coupling. Further confirmation follows from an analytic
computation of the two-loop twist-one spectrum.Comment: 45 pages, v2: typos in (D.9) fixed, reference added, many small
change
Balance of mechanical forces drives endothelial gap formation and may facilitate cancer and immune-cell extravasation
The formation of gaps in the endothelium is a crucial process underlying both cancer and immune cell extravasation, contributing to the functioning of the immune system during infection, the unfavorable development of chronic inflammation and tumor metastasis. Here, we present a stochastic-mechanical multiscale model of an endothelial cell monolayer and show that the dynamic nature of the endothelium leads to spontaneous gap formation, even without intervention from the transmigrating cells. These gaps preferentially appear at the vertices between three endothelial cells, as opposed to the border between two cells. We quantify the frequency and lifetime of these gaps, and validate our predictions experimentally. Interestingly, we find experimentally that cancer cells also preferentially extravasate at vertices, even when they first arrest on borders. This suggests that extravasating cells, rather than initially signaling to the endothelium, might exploit the autonomously forming gaps in the endothelium to initiate transmigration
The Morphology of N=6 Chern-Simons Theory
We tabulate various properties of the language of N=6 Chern-Simons Theory, in
the sense of Polyakov. Specifically we enumerate and compute character formulas
for all syllables of up to four letters, i.e. all irreducible representations
of OSp(6|4) built from up to four fundamental fields of the ABJM theory. We
also present all tensor product decompositions for up to four singletons and
list the (cyclically invariant) four-letter words, which correspond to
single-trace operators of length four. As an application of these results we
use the two-loop dilatation operator to compute the leading correction to the
Hagedorn temperature of the weakly-coupled planar ABJM theory on R \times S^2.Comment: 41 pages, 1 figure; v2: minor correction
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