1,463 research outputs found
Bethe Ansaetze for GKP strings
Studying the scattering of excitations around a dynamical background has a
long history in the context of integrable models. The Gubser-Klebanov-Polyakov
string solution provides such a background for the string/gauge correspondence.
Taking the conjectured all-loop asymptotic equations for the AdS_4/CFT_3
correspondence as the starting point, we derive the S-matrix and a set of
spectral equations for the lowest-lying excitations. We find that these
equations resemble closely the analogous equations for AdS_5/CFT_4, which are
also discussed in this paper. At large values of the coupling constant we show
that they reproduce the Bethe equations proposed to describe the spectrum of
the low-energy limit of the AdS_4xCP^3 sigma model.Comment: 60 pages, 5 figure
Gluing Ladders into Fishnets
We use integrability at weak coupling to compute fishnet diagrams for
four-point correlation functions in planar theory. The results are
always multi-linear combinations of ladder integrals, which are in turn built
out of classical polylogarithms. The Steinmann relations provide a powerful
constraint on such linear combinations, leading to a natural conjecture for any
fishnet diagram as the determinant of a matrix of ladder integrals.Comment: 6 pages, 4 figures; v2, minor corrrections, e.g. in fig. 2 captio
Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
We consider light-like Wilson loops with hexagonal geometry in the planar
limit of N=4 Super-Yang-Mills theory. Within the Operator-Product-Expansion
framework these loops receive contributions from all states that can propagate
on top of the colour flux tube sourced by any two opposite edges of the loops.
Of particular interest are the two-particle contributions. They comprise
virtual effects like the propagation of a pair of scalars, fermions, and
gluons, on top of the flux tube. Each one of them is thoroughly discussed in
this paper. Our main result is the prediction of all the twist-2 corrections to
the expansion of the dual 6-gluons MHV amplitude in the near-collinear limit at
finite coupling. At weak coupling, our result was recently used by Dixon,
Drummond, Duhr and Pennington to predict the full amplitude at four loops. At
strong coupling, it allows us to make contact with the classical string
description and to recover the (previously elusive) AdS(3) mode from the
continuum of two-fermion states. More generally, the two-particle contributions
serve as an exemplar for all the multi-particle corrections.Comment: 40 pages + 37 pages of appendices, 24 figures, no footnote
Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
We elaborate on a non-perturbative formulation of scattering amplitudes/null
polygonal Wilson loops in planar N=4 Super-Yang-Mills theory. The construction
is based on a decomposition of the Wilson loop into elementary building blocks
named pentagon transitions. Our discussion expands on a previous letter of the
authors where these transitions were introduced and analyzed for the so-called
gluonic excitations. In this paper we revisit these transitions and extend the
analysis to the sector of scalar excitations. We restrict ourselves to the
single particle transitions and bootstrap their finite coupling expressions
using a set of axioms. Besides these considerations, the main focus of the
paper is on the extraction of perturbative data from scattering amplitudes at
weak coupling and its comparison against the proposed pentagon transitions. We
present several tests for both the hexagon and heptagon (MHV and NMHV)
amplitudes up to two- and three-loop orders. In attached notebooks we provide
explicit higher-loop predictions obtained from our method.Comment: 73 pages, 42 figures. v2,v3: typos correcte
Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
We analyze the pentagon transitions involving arbitrarily many flux-tube
gluonic excitations and bound states thereof in planar N=4 Super-Yang-Mills
theory. We derive all-loop expressions for all these transitions by
factorization and fusion of the elementary transitions for the lightest gluonic
excitations conjectured in a previous paper. We apply the proposals so obtained
to the computation of MHV and NMHV scattering amplitudes at any loop order and
find perfect agreement with available perturbative data up to four loops.Comment: 26+14 page
Hexagonal Wilson Loops in Planar SYM Theory at Finite Coupling
We report on the complete OPE series for the 6-gluon MHV and NMHV amplitudes
in planar SYM theory. Namely, we provide a finite coupling
prediction for all the terms in the expansion of these amplitudes around the
collinear limit. These furnish a non-perturbative representation of the full
amplitudes.Comment: 2 pages + reference
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