1,076 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
Some comments on spacelike minimal surfaces with null polygonal boundaries in
We discuss some geometrical issues related to spacelike minimal surfaces in
with null polygonal boundaries at conformal infinity. In particular for
, two holomorphic input functions for the Pohlmeyer reduced system are
identified. This system contains two coupled differential equations for two
functions and , related to curvature and
torsion of the surface. Furthermore, we conjecture that, for a polynomial
choice of the two holomorphic functions, the relative positions of their zeros
encode the conformal invariant data of the boundary null -gon.Comment: 13 pages, a note and references added, version to appear in JHE
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
Correlation functions, null polygonal Wilson loops, and local operators
We consider the ratio of the correlation function of n+1 local operators over
the correlator of the first n of these operators in planar N=4 super-Yang-Mills
theory, and consider the limit where the first n operators become pairwise null
separated. By studying the problem in twistor space, we prove that this is
equivalent to the correlator of a n-cusp null polygonal Wilson loop with the
remaining operator in general position, normalized by the expectation value of
the Wilson loop itself, as recently conjectured by Alday, Buchbinder and
Tseytlin. Twistor methods also provide a BCFW-like recursion relation for such
correlators. Finally, we study the natural extension where n operators become
pairwise null separated with k operators in general position. As an example, we
perform an analysis of the resulting correlator for k=2 and discuss some of the
difficulties associated to fixing the correlator completely in the strong
coupling regime.Comment: 34 pages, 6 figures. v2: typos corrected and references added; v3:
published versio
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
AGT on the S-duality Wall
Three-dimensional gauge theory T[G] arises on a domain wall between
four-dimensional N=4 SYM theories with the gauge groups G and its S-dual G^L.
We argue that the N=2^* mass deformation of the bulk theory induces a
mass-deformation of the theory T[G] on the wall. The partition functions of the
theory T[SU(2)] and its mass-deformation on the three-sphere are shown to
coincide with the transformation coefficient of Liouville one-point conformal
block on torus under the S-duality.Comment: 14 pages, 3 figures. v2: Revised the analysis in sections 3.3 and 4.
Notes and references added. Version to appear in JHE
Differential equations for multi-loop integrals and two-dimensional kinematics
In this paper we consider multi-loop integrals appearing in MHV scattering
amplitudes of planar N=4 SYM. Through particular differential operators which
reduce the loop order by one, we present explicit equations for the two-loop
eight-point finite diagrams which relate them to massive hexagons. After the
reduction to two-dimensional kinematics, we solve them using symbol technology.
The terms invisible to the symbols are found through boundary conditions coming
from double soft limits. These equations are valid at all-loop order for double
pentaladders and allow to solve iteratively loop integrals given lower-loop
information. Comments are made about multi-leg and multi-loop integrals which
can appear in this special kinematics. The main motivation of this
investigation is to get a deeper understanding of these tools in this
configuration, as well as for their application in general four-dimensional
kinematics and to less supersymmetric theories.Comment: 25 pages, 7 figure
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
Surface Operators in N=2 4d Gauge Theories
N=2 four dimensional gauge theories admit interesting half BPS surface
operators preserving a (2,2) two dimensional SUSY algebra. Typical examples are
(2,2) 2d sigma models with a flavor symmetry which is coupled to the 4d gauge
fields. Interesting features of such 2d sigma models, such as (twisted) chiral
rings, and the tt* geometry, can be carried over to the surface operators, and
are affected in surprising ways by the coupling to 4d degrees of freedom. We
will describe in detail a relation between the parameter space of twisted
couplings of the surface operator and the Seiberg-Witten geometry of the bulk
theory. We will discuss a similar result about the tt* geometry of the surface
operator. We will predict the existence and general features of a wall-crossing
formula for BPS particles bound to the surface operator.Comment: 25 pages, 4 figure
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