1,122 research outputs found
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
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
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
Supersymmetric Wilson loops in diverse dimensions
archiveprefix: arXiv primaryclass: hep-th reportnumber: AEI-2009-036, HU-EP-09-15 slaccitation: %%CITATION = ARXIV:0904.0455;%%archiveprefix: arXiv primaryclass: hep-th reportnumber: AEI-2009-036, HU-EP-09-15 slaccitation: %%CITATION = ARXIV:0904.0455;%%archiveprefix: arXiv primaryclass: hep-th reportnumber: AEI-2009-036, HU-EP-09-15 slaccitation: %%CITATION = ARXIV:0904.0455;%
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
Lessons from crossing symmetry at large N
20 pages, v2: Assumptions stated more clearly, version published in JHEPWe consider the four-point correlator of the stress tensor multiplet in N=4 SYM. We construct all solutions consistent with crossing symmetry in the limit of large central charge c ~ N^2 and large g^2 N. While we find an infinite tower of solutions, we argue most of them are suppressed by an extra scale \Delta_{gap} and are consistent with the upper bounds for the scaling dimension of unprotected operators observed in the numerical superconformal bootstrap at large central charge. These solutions organize as a double expansion in 1/c and 1/\Delta_{gap}. Our solutions are valid to leading order in 1/c and to all orders in 1/\Delta_{gap} and reproduce, in particular, instanton corrections previously found. Furthermore, we find a connection between such upper bounds and positivity constraints arising from causality in flat space. Finally, we show that certain relations derived from causality constraints for scattering in AdS follow from crossing symmetry.Peer reviewe
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
Irregular singularities in Liouville theory
Motivated by problems arising in the study of N=2 supersymmetric gauge
theories we introduce and study irregular singularities in two-dimensional
conformal field theory, here Liouville theory. Irregular singularities are
associated to representations of the Virasoro algebra in which a subset of the
annihilation part of the algebra act diagonally. In this paper we define
natural bases for the space of conformal blocks in the presence of irregular
singularities, describe how to calculate their series expansions, and how such
conformal blocks can be constructed by some delicate limiting procedure from
ordinary conformal blocks. This leads us to a proposal for the structure
functions appearing in the decomposition of physical correlation functions with
irregular singularities into conformal blocks. Taken together, we get a precise
prediction for the partition functions of some Argyres-Douglas type theories on
the four-sphere.Comment: 84 pages, 6 figure
- …