882 research outputs found
Note About Integrability and Gauge Fixing for Bosonic String on AdS(5)xS(5)
This short note is devoted to the study of the integrability of the bosonic
string on AdS(5)xS(5) in the uniform light-cone gauge. We construct Lax
connection for gauge fixed theory and we argue that it is flat.Comment: 17 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
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
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;%
A finite analog of the AGT relation I: finite W-algebras and quasimaps' spaces
Recently Alday, Gaiotto and Tachikawa proposed a conjecture relating
4-dimensional super-symmetric gauge theory for a gauge group G with certain
2-dimensional conformal field theory. This conjecture implies the existence of
certain structures on the (equivariant) intersection cohomology of the
Uhlenbeck partial compactification of the moduli space of framed G-bundles on
P^2. More precisely, it predicts the existence of an action of the
corresponding W-algebra on the above cohomology, satisfying certain properties.
We propose a "finite analog" of the (above corollary of the) AGT conjecture.
Namely, we replace the Uhlenbeck space with the space of based quasi-maps from
P^1 to any partial flag variety G/P of G and conjecture that its equivariant
intersection cohomology carries an action of the finite W-algebra U(g,e)
associated with the principal nilpotent element in the Lie algebra of the Levi
subgroup of P; this action is expected to satisfy some list of natural
properties. This conjecture generalizes the main result of arXiv:math/0401409
when P is the Borel subgroup. We prove our conjecture for G=GL(N), using the
works of Brundan and Kleshchev interpreting the algebra U(g,e) in terms of
certain shifted Yangians.Comment: minor change
On Fermionic T-duality of Sigma modes on AdS backgrounds
We study the fermionic T-duality symmetry of integrable Green-Schwarz sigma
models on AdS backgrounds. We show that the sigma model on
background is self-dual under fermionic T-duality. We also construct new
integrable sigma models on . These backgrounds could be
realized as supercosets of SU supergroups for arbitrary , but could also be
realized as supercosets of OSp supergroups for . We find that the
supercosets based on SU supergroups are self-dual under fermionic T-duality,
while the supercosets based on OSp supergroups are not. However, the reasons of
OSp supercosets being not self-dual under fermionic T-duality are different.
For case, corresponding to background, the
failure is due to the singular fermionic quadratic terms, just like
case. For case, the failure is due to the
shortage of right number of -symmetry to gauge away the fermionic
degrees of freedom, even though the fermionic quadratic term is not singular
any more. More general, for the supercosets of the OSp supergroups with
superalgebra , including and
backgrounds, the sigma models are not self-dual under fermionic T-duality as
well, obstructed by the -symmetry.Comment: 17 pages; Clarfications on kappa symmetries, references
added;Published versio
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
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
On holographic three point functions for GKP strings from integrability
Adapting the powerful integrability-based formalism invented previously for
the calculation of gluon scattering amplitudes at strong coupling, we develop a
method for computing the holographic three point functions for the large spin
limit of Gubser-Klebanov- Polyakov (GKP) strings. Although many of the ideas
from the gluon scattering problem can be transplanted with minor modifications,
the fact that the information of the external states is now encoded in the
singularities at the vertex insertion points necessitates several new
techniques. Notably, we develop a new generalized Riemann bilinear identity,
which allows one to express the area integral in terms of appropriate contour
integrals in the presence of such singularities. We also give some general
discussions on how semiclassical vertex operators for heavy string states
should be constructed systematically from the solutions of the Hamilton-Jacobi
equation.Comment: 62 pages;v2 Typos and equation (3.7) corrected. Clarifying remarks
added in Section 4.1. Published version;v3 Minor errors found in version 2
are corrected. For explanation of the revision, see Erratum published in
http://www.springerlink.com/content/m67055235407vx67/?MUD=M
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
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