66 research outputs found
Analytic results for planar three-loop integrals for massive form factors
We use the method of differential equations to analytically evaluate all planar three-loop Feynman integrals relevant for form factor calculations involving massive particles. Our results for ninety master integrals at general q2 are expressed in terms of multiple polylogarithms, and results for fiftyone master integrals at the threshold q2 = 4m2 are expressed in terms of multiple polylogarithms of argument one, with indices equal to zero or to a sixth root of unity
Magic identities for conformal four-point integrals
We propose an iterative procedure for constructing classes of off-shell
four-point conformal integrals which are identical. The proof of the identity
is based on the conformal properties of a subintegral common for the whole
class. The simplest example are the so-called `triple scalar box' and `tennis
court' integrals. In this case we also give an independent proof using the
method of Mellin--Barnes representation which can be applied in a similar way
for general off-shell Feynman integrals.Comment: 13 pages, 12 figures. New proof included with neater discussion of
contact terms. Typo correcte
All tree-level amplitudes in N=4 SYM
We give an explicit formula for all tree amplitudes in N=4 SYM, derived by
solving the recently presented supersymmetric tree-level recursion relations.
The result is given in a compact, manifestly supersymmetric form and we show
how to extract from it all possible component amplitudes for an arbitrary
number of external particles and any arrangement of external particles and
helicities. We focus particularly on extracting gluon amplitudes which are
valid for any gauge theory. The formula for all tree-level amplitudes is given
in terms of nested sums of dual superconformal invariants and it therefore
manifestly respects both conventional and dual superconformal symmetry.Comment: 26 pages. Boundary terms in sums corrected. Additional references.
Acknowledgement added. Extended discussion. One new figur
A planar four-loop form factor and cusp anomalous dimension in QCD
We compute the fermionic contribution to the photon-quark form factor to four-loop order in QCD in the planar limit in analytic form. From the divergent part of the latter the cusp and collinear anomalous dimensions are extracted. Results are also presented for the finite contribution. We briefly describe our method to compute all planar master integrals at four-loop order
Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
Tree-level scattering amplitudes in N=4 super Yang-Mills theory have recently
been shown to transform covariantly with respect to a 'dual' superconformal
symmetry algebra, thus extending the conventional superconformal symmetry
algebra psu(2,2|4) of the theory. In this paper we derive the action of the
dual superconformal generators in on-shell superspace and extend the dual
generators suitably to leave scattering amplitudes invariant. We then study the
algebra of standard and dual symmetry generators and show that the inclusion of
the dual superconformal generators lifts the psu(2,2|4) symmetry algebra to a
Yangian. The non-local Yangian generators acting on amplitudes turn out to be
cyclically invariant due to special properties of psu(2,2|4). The
representation of the Yangian generators takes the same form as in the case of
local operators, suggesting that the Yangian symmetry is an intrinsic property
of planar N=4 super Yang-Mills, at least at tree level.Comment: 23 pages, no figures; v2: typos corrected, references added; v3:
minor changes, references adde
On planar gluon amplitudes/Wilson loops duality
There is growing evidence that on-shell gluon scattering amplitudes in planar
N=4 SYM theory are equivalent to Wilson loops evaluated over contours
consisting of straight, light-like segments defined by the momenta of the
external gluons. This equivalence was first suggested at strong coupling using
the AdS/CFT correspondence and has since been verified at weak coupling to one
loop in perturbation theory. Here we perform an explicit two-loop calculation
of the Wilson loop dual to the four-gluon scattering amplitude and demonstrate
that the relation holds beyond one loop. We also propose an anomalous conformal
Ward identity which uniquely fixes the form of the finite part (up to an
additive constant) of the Wilson loop dual to four- and five-gluon amplitudes,
in complete agreement with the BDS conjecture for the multi-gluon MHV
amplitudes.Comment: 16 pages, 1 figure. v2: minor correction
Review of AdS/CFT Integrability, Chapter V.2: Dual Superconformal Symmetry
Scattering amplitudes in planar N=4 super Yang-Mills theory reveal a
remarkable symmetry structure. In addition to the superconformal symmetry of
the Lagrangian of the theory, the planar amplitudes exhibit a dual
superconformal symmetry. The presence of this additional symmetry imposes
strong restrictions on the amplitudes and is connected to a duality relating
scattering amplitudes to Wilson loops defined on polygonal light-like contours.
The combination of the superconformal and dual superconformal symmetries gives
rise to a Yangian, an algebraic structure which is known to be related to the
appearance of integrability in other regimes of the theory. We discuss two dual
formulations of the symmetry and address the classification of its invariants.Comment: 22 pages, see also overview article arXiv:1012.3982, v2: references
to other chapters updated, v3 added references, typos fixe
C-axis lattice dynamics in Bi-based cuprate superconductors
We present results of a systematic study of the c axis lattice dynamics in
single layer Bi2Sr2CuO6 (Bi2201), bilayer Bi2Sr2CaCu2O8 (Bi2212) and trilayer
Bi2Sr2Ca2Cu3O10 (Bi2223) cuprate superconductors. Our study is based on both
experimental data obtained by spectral ellipsometry on single crystals and
theoretical calculations. The calculations are carried out within the framework
of a classical shell model, which includes long-range Coulomb interactions and
short-range interactions of the Buckingham form in a system of polarizable
ions. Using the same set of the shell model parameters for Bi2201, Bi2212 and
Bi2223, we calculate the frequencies of the Brillouin-zone center phonon modes
of A2u symmetry and suggest the phonon mode eigenvector patterns. We achieve
good agreement between the calculated A2u eigenfrequencies and the experimental
values of the c axis TO phonon frequencies which allows us to make a reliable
phonon mode assignment for all three Bi-based cuprate superconductors. We also
present the results of our shell model calculations for the Gamma-point A1g
symmetry modes in Bi2201, Bi2212 and Bi2223 and suggest an assignment that is
based on the published experimental Raman spectra. The
superconductivity-induced phonon anomalies recently observed in the c axis
infrared and resonant Raman scattering spectra in trilayer Bi2223 are
consistently explained with the suggested assignment.Comment: 29 pages, 13 figure
Review of AdS/CFT Integrability: An Overview
This is the introductory chapter of a review collection on integrability in
the context of the AdS/CFT correspondence. In the collection we present an
overview of the achievements and the status of this subject as of the year
2010.Comment: 31 pages, v2: reference added, references to other chapters updated,
v3: footnote 1 on location of references added, v4: minor changes, references
added, accepted for publication in Lett. Math. Phys, v5: minor corrections,
links to chapters updated, attached IntAdS.pdf with all chapters in one file,
see http://arxiv.org/src/1012.3982/anc/IntAdS.pdf or
http://www.phys.ethz.ch/~nbeisert/IntAdS.pd
Hexagon Wilson loop = six-gluon MHV amplitude
We compare the two-loop corrections to the finite part of the light-like
hexagon Wilson loop with the recent numerical results for the finite part of
the MHV six-gluon amplitude in N=4 SYM theory by Bern, Dixon, Kosower, Roiban,
Spradlin, Vergu and Volovich (arXiv:0803.1465 [hep-th]) and demonstrate that
they coincide within the error bars and, at the same time, they differ from the
BDS ansatz by a non-trivial function of (dual) conformal kinematical
invariants. This provides strong evidence that the Wilson loop/scattering
amplitude duality holds in planar N=4 SYM theory to all loops for an arbitrary
number of external particles.Comment: 34 pages, 3 figures; v2: appendix added, minor corrections made, new
references inserte
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