1,138 research outputs found
Some analytic results for two-loop scattering amplitudes
We present analytic results for the finite diagrams contributing to the
two-loop eight-point MHV scattering amplitude of planar N=4 SYM. We use a
recently proposed representation for the integrand of the amplitude in terms of
(momentum) twistors and focus on a restricted kinematics in which the answer
depends only on two independent cross-ratios. The theory of motives can be used
to vastly simplify the results, which can be expressed as simple combinations
of classical polylogarithms.Comment: 18 page
Wilson Loops @ 3-Loops in Special Kinematics
We obtain a compact expression for the octagon MHV amplitude / Wilson loop at
3 loops in planar N=4 SYM and in special 2d kinematics in terms of 7 unfixed
coefficients. We do this by making use of the cyclic and parity symmetry of the
amplitude/Wilson loop and its behaviour in the soft/collinear limits as well as
in the leading term in the expansion away from this limit. We also make a
natural and quite general assumption about the functional form of the result,
namely that it should consist of weight 6 polylogarithms whose symbol consists
of basic cross-ratios only (and not functions thereof). We also describe the
uplift of this result to 10 points.Comment: 26 pages. Typos correcte
Instantons on ALE spaces and Super Liouville Conformal Field Theories
We provide evidence that the conformal blocks of N=1 super Liouville
conformal field theory are described in terms of the SU(2) Nekrasov partition
function on the ALE space O_{P^1}(-2).Comment: 10 page
On correlation functions of Wilson loops, local and non-local operators
We discuss and extend recent conjectures relating partial null limits of
correlation functions of local gauge invariant operators and the expectation
value of null polygonal Wilson loops and local gauge invariant operators. We
point out that a particular partial null limit provides a strategy for the
calculation of the anomalous dimension of short twist-two operators at weak and
strong coupling.Comment: 29 pages, 8 figure
Form factors at strong coupling via a Y-system
We compute form factors in planar N=4 Super Yang-Mills at strong coupling.
Namely we consider the overlap between an operator insertion and 2n gluons.
Through the gauge/string duality these are given by minimal surfaces in AdS
space. The surfaces end on an infinite periodic sequence of null segments at
the boundary of AdS. We consider surfaces that can be embedded in AdS_3. We
derive set of functional equations for the cross ratios as functions of the
spectral parameter. These equations are of the form of a Y-system. The integral
form of the Y-system has Thermodynamics Bethe Ansatz form. The area is given by
the free energy of the TBA system or critical value of Yang-Yang functional. We
consider a restricted set of operators which have small conformal dimension
Singular Liouville fields and spiky strings in \rr^{1,2} and SL(2,\rr)
The closed string dynamics in \rr^{1,2} and SL(2,\rr) is studied within
the scheme of Pohlmeyer reduction. In both spaces two different classes of
string surfaces are specified by the structure of the fundamental quadratic
forms. The first class in \rr^{1,2} is associated with the standard lightcone
gauge strings and the second class describes spiky strings and their conformal
deformations on the Virasoro coadjoint orbits. These orbits correspond to
singular Liouville fields with the monodromy matrixes . The first class
in SL(2,\rr) is parameterized by the Liouville fields with vanishing chiral
energy functional. Similarly to \rr^{1,2}, the second class in SL(2,\rr)
describes spiky strings, related to the vacuum configurations of the
SL(2,\rr)/U(1) coset model.Comment: 37 p. 6 fi
Double-helix Wilson loops: case of two angular momenta
Recently, Wilson loops with the shape of a double helix have played an
important role in studying large spin operators in gauge theories. They
correspond to a quark and an anti-quark moving in circles on an S3 (and
therefore each of them describes a helix in RxS3). In this paper we consider
the case where the particles have two angular momenta on the S3. The string
solution corresponding to such Wilson loop can be found using the relation to
the Neumann-Rosochatius system allowing the computation of the energy and
angular momenta of the configuration. The particular case of only one angular
momentum is also considered. It can be thought as an analytic continuation of
the rotating strings which are dual to operators in the SL(2) sector of N=4
SYM.Comment: 30 pages, 2 figures, LaTeX. v2: Small corrections, reference adde
BRST Invariance of Non-local Charges and Monodromy Matrix of Bosonic String on AdS(5)xS(5)
Using the generalized Hamiltonian method of Batalin, Fradkin and Vilkovsky we
develop the BRST formalism for the bosonic string on AdS(5)xS(5) formulated as
principal chiral model. Then we show that the monodromy matrix and non-local
charges are BRST invariant.Comment: 26. page
Modern and late Holocene foraminiferal record of restricted environmental conditions in the Albufeira Lagoon, SW Portugal
Benthic foraminifera from twenty stations sampled twice were analyzed in order to examine the environmental conditions of the Albufeira coastal lagoon. Foraminiferal assemblages show an increase in the abundance, species diversity and allochthonous content seaward. Three zones have been defined: the inner and more restricted area of the lagoon where the main species are the euryhaline Ammonia tepida and Haynesina germanica; these two species together with Bulimina gibba and Brizalina britannica dominated the middle area; and, finally, in the mouth and marine- influenced back-barrier area the assemblages are made up of brackish and marine species such as A. tepida, Cribroelphidium williamsoni, Cibicides lobatulus and H. germanica. Additionally, samples from three cores were also examined. Sedimentological and micropalaeontological contents represent the last 2500 years of environmental evolution of the lagoon. Foraminiferal assemblages are not very abundant and they are dominated by H. germanica, A. tepida and Jadammina macrescens indicating very restricted conditions through time. In a regional context, and during the Late Holocene, after the development of a detrital barrier circa 5.5 cal yr BP, eustasy is considered to be a minor environmental control of the barrier-lagoonal system dynamics. Instead, environmental conditions were forced by local factors, such as frequency and duration of lagoon-ocean water exchanges, induced by both natural and artificial changes in the permeability of the sand-barrier
Comments on operators with large spin
We consider high spin operators. We give a general argument for the
logarithmic scaling of their anomalous dimensions which is based on the
symmetries of the problem. By an analytic continuation we can also see the
origin of the double logarithmic divergence in the Sudakov factor. We show that
the cusp anomalous dimension is the energy density for a flux configuration of
the gauge theory on . We then focus on operators in super Yang Mills which carry large spin and SO(6) charge and show that in
a particular limit their properties are described in terms of a bosonic O(6)
sigma model. This can be used to make certain all loop computations in the
string theory.Comment: 33 pages, 1 figure,v2:reference to more recent work added, minor
correction
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