10,039 research outputs found
Classical Polylogarithms for Amplitudes and Wilson Loops
We present a compact analytic formula for the two-loop six-particle MHV
remainder function (equivalently, the two-loop light-like hexagon Wilson loop)
in N = 4 supersymmetric Yang-Mills theory in terms of the classical
polylogarithm functions Li_k with cross-ratios of momentum twistor invariants
as their arguments. In deriving our result we rely on results from the theory
of motives.Comment: 11 pages, v2: journal version, minor corrections and simplifications,
additional details available at http://goo.gl/Cl0
Estimates for parameters and characteristics of the confining SU(3)-gluonic field in neutral kaons and chiral limit for pseudoscalar nonet
First part of the paper is devoted to applying the confinement mechanism
proposed earlier by the author to estimate the possible parameters of the
confining SU(3)-gluonic field in neutral kaons. The estimates obtained are
consistent with the widths of the electromagnetic decays
too. The corresponding estimates of the gluon
concentrations, electric and magnetic colour field strengths are also adduced
for the mentioned field at the scales of the mesons under consideration. The
second part of the paper takes into account the results obtained previously by
the author to estimate the purely gluonic contribution to the masses of all the
mesons of pseudoscalar nonet and also to consider a possible relation with a
phenomenological string-like picture of confinement. Finally, the problem of
masses in particle physics is shortly discussed within the framework of
approach to the chiral symmetry breaking in quantum chromodynamics (QCD)
proposed recently by the author.Comment: LaTeX, 16 pages, 2 figure
Euler complexes and geometry of modular varieties
There is a mysterious connection between the multiple polylogarithms at N-th
roots of unity and modular varieties. In this paper we "explain" it in the
simplest case of the double logarithm.
We introduce an Euler complex data on modular curves. It includes a length
two complex on every modular curve. Their second cohomology groups recover the
Beilinson-Kato Euler system in K_2 of modular curves. We show that the above
connection in the double logarithm case is provided by the specialization at a
cusp of the Euler complex data on the modular curve Y_1(N).
Furthermore, specializing the Euler complexes at CM points we find new
examples of the connection with geometry of modular varieties, this time
hyperbolic 3-folds.Comment: Dedicated to Joseph Bernstein for his 60th birthday. The final
version. Some corrections were made. To appear in GAFA, special volume
dedicated to J. Bernstei
Polylogarithms, regulators and Arakelov motivic complexes
We construct an explicit regulator map from the weigh n Bloch Higher Chow
group complexto the weight n Deligne complex of a regular complex projective
algebraic variety X. We define the Arakelovweight n motivic complex as the cone
of this map shifted by one. Its last cohomology group is (a version of) the
Arakelov Chow group defined by H. Gillet. and C.Soule.
We relate the Grassmannian n-logarithms (defined as in [G5]) to geometry of
the symmetric space for GL_n(C). For n=2 we recover Lobachevsky's formula for
the volume of an ideal geodesic tetrahedron via the dilogarithm.
Using the relationship with symmetric spaces we construct the Borel regulator
on K_{2n-1}(C) via the Grassmannian n-logarithms.
We study the Chow dilogarithm and prove a reciprocity law which strengthens
Suslin's reciprocity law for Milnor's K_3 on curves.Comment: Version 3: It is the final version, as it will appear in JAMS. 71
pages, 12 figure
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