156 research outputs found
Matrix factorization for solutions of the Yang-Baxter equation
We study solutions of the Yang-Baxter equation on a tensor product of an
arbitrary finite-dimensional and an arbitrary infinite-dimensional
representations of the rank one symmetry algebra. We consider the cases of the
Lie algebra sl_2, the modular double (trigonometric deformation) and the
Sklyanin algebra (elliptic deformation). The solutions are matrices with
operator entries. The matrix elements are differential operators in the case of
sl_2, finite-difference operators with trigonometric coefficients in the case
of the modular double or finite-difference operators with coefficients
constructed out of Jacobi theta functions in the case of the Sklyanin algebra.
We find a new factorized form of the rational, trigonometric, and elliptic
solutions, which drastically simplifies them. We show that they are products of
several simply organized matrices and obtain for them explicit formulae
Yang-Baxter operators and scattering amplitudes in super-Yang-Mills theory
Yangian symmetry of amplitudes in super Yang-Mills theory is
formulated in terms of eigenvalue relations for monodromy matrix operators. The
Quantum Inverse Scattering Method provides the appropriate tools to treat the
extended symmetry and to recover as its consequences many known features like
cyclic and inversion symmetry, BCFW recursion, Inverse Soft Limit construction,
Grassmannian integral representation, -invariants and on-shell
diagram approach.Comment: 32 pages, 10 figures, final version for publicatio
New elliptic solutions of the Yang-Baxter equation
We consider finite-dimensional reductions of an integral operator with the
elliptic hypergeometric kernel describing the most general known solution of
the Yang-Baxter equation with a rank 1 symmetry algebra. The reduced
R-operators reproduce at their bottom the standard Baxter's R-matrix for the
8-vertex model and Sklyanin's L-operator. The general formula has a remarkably
compact form and yields new elliptic solutions of the Yang-Baxter equation
based on the finite-dimensional representations of the elliptic modular double.
The same result is also derived using the fusion formalism.Comment: 34 pages, to appear in Commun. Math. Phy
A note on four-point correlators of half-BPS operators in N=4 SYM
International audienceWe calculate the four-point correlation function of half-BPS operators withweights 2, 3, 3, 4 in N=4 SYM to two-loop order. The OPE of this correlationfunction provides a nontrivial check of the integrability conjecture for aclass of three-point functions formulated in arXiv:1311.6404. Our perturbativecalculation exploits the supergraph formalism in N=2 harmonic superspace
The two-loop five-particle amplitude in supergravity
We compute for the first time the two-loop five-particle amplitude in
supergravity. Starting from the known integrand, we perform an
integration-by-parts reduction and express the answer in terms of uniform
weight master integrals. The latter are known to evaluate to non-planar
pentagon functions, described by a 31-letter symbol alphabet. We express the
final result for the amplitude in terms of uniform weight four symbols,
multiplied by a small set of rational factors. The amplitude satisfies the
expected factorization properties when one external graviton becomes soft, and
when two external gravitons become collinear. We verify that the soft
divergences of the amplitude exponentiate, and extract the finite remainder
function. The latter depends on fewer rational factors, and is independent of
one of the symbol letters. By analyzing identities involving rational factors
and symbols we find a remarkably compact representation in terms of a single
seed function, summed over all permutations of external particles. Finally, we
work out the multi-Regge limit, and present explicitly the leading logarithmic
terms in the limit. The full symbol of the IR-subtracted hard function is
provided as an ancillary file.Comment: 22 pages, 1 figure, 8 ancillary file
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