76 research outputs found
Energy-energy correlations in N=4 SYM
We present a new approach to computing energy-energy correlations in gauge
theories that exploits their relation to correlation functions and bypasses the
use of scattering amplitudes. We illustrate its power by calculating
energy-energy correlations in the maximally supersymmetric Yang-Mills theory
(N=4 SYM) in the next-to-leading order approximation.Comment: 5 page
From correlation functions to event shapes
We present a new approach to computing event shape distributions or, more
precisely, charge flow correlations in a generic conformal field theory (CFT).
These infrared finite observables are familiar from collider physics studies
and describe the angular distribution of global charges in outgoing radiation
created from the vacuum by some source. The charge flow correlations can be
expressed in terms of Wightman correlation functions in a certain limit. We
explain how to compute these quantities starting from their Euclidean analogues
by means of a non-trivial analytic continuation which, in the framework of CFT,
can elegantly be performed in Mellin space. The relation between the charge
flow correlations and Euclidean correlation functions can be reformulated
directly in configuration space, bypassing the Mellin representation, as a
certain Lorentzian double discontinuity of the correlation function integrated
along the cuts. We illustrate the general formalism in N=4 SYM, making use of
the well-known results on the four-point correlation function of half-BPS
scalar operators. We compute the double scalar flow correlation in N=4 SYM, at
weak and strong coupling and show that it agrees with known results obtained by
different techniques. One of the remarkable features of the N=4 theory is that
the scalar and energy flow correlations are proportional to each other.
Imposing natural physical conditions on the energy flow correlations
(finiteness, positivity and regularity), we formulate additional constraints on
the four-point correlation functions in N=4 SYM that should be valid at any
coupling and away from the planar limit.Comment: 40 pages, 1 figure; v2: typos correcte
Event shapes in N=4 super-Yang-Mills theory
We study event shapes in N=4 SYM describing the angular distribution of
energy and R-charge in the final states created by the simplest half-BPS scalar
operator. Applying the approach developed in the companion paper
arXiv:1309.0769, we compute these observables using the correlation functions
of certain components of the N=4 stress-tensor supermultiplet: the half-BPS
operator itself, the R-symmetry current and the stress tensor. We present
master formulas for the all-order event shapes as convolutions of the Mellin
amplitude defining the correlation function of the half-BPS operators, with a
coupling-independent kernel determined by the choice of the observable. We find
remarkably simple relations between various event shapes following from N=4
superconformal symmetry. We perform thorough checks at leading order in the
weak coupling expansion and show perfect agreement with the conventional
calculations based on amplitude techniques. We extend our results to strong
coupling using the correlation function of half-BPS operators obtained from the
AdS/CFT correspondence.Comment: 52 pages, 6 figures; v2: typos correcte
Infrared Finite Observables in N=8 Supergravity
Using the algorithm of constructing the IR finite observables suggested and discussed in details in our previous publications, we consider construction of such observables in N=8 SUGRA in NLO of PT. In general, contrary to the amplitudes defined in the presence of some IR regulator, such observables do not reveal any simple structure
Applications of dispersive sum rules: -expansion and holography
We use Mellin space dispersion relations together with Polyakov conditions to
derive a family of sum rules for Conformal Field Theories (CFTs). The defining
property of these sum rules is suppression of the contribution of the double
twist operators. Firstly, we apply these sum rules to the Wilson-Fisher model
in dimensions. We re-derive many of the known results to order
and we make new predictions. No assumption of analyticity down to
spin was made. Secondly, we study holographic CFTs. We use dispersive sum
rules to obtain tree-level and one-loop anomalous dimensions. Finally, we
briefly discuss the contribution of heavy operators to the sum rules in UV
complete holographic theories.Comment: 36p, 5 fi
Conformal field theories and deep inelastic scattering
Theoretical Physic
Aspects of the N=4 SYM amplitude -- Wilson polygon duality
We discuss formulation of Wilson polygon - MHV amplitude duality at the
perturbative level in various regularizations. For four gluons it is shown that
at one loop one can formulate diagrammatic correspondence interpolating between
the dimensional regularization and the off-shell one. We suggest new
interpretation of all types of box diagrams in terms of the dual simplex in
dimensional regularization and describe its degeneration to the Wilson polygon.
The interesting nullification phenomena for the low-energy amplitudes in the
Higgsed phase has been found.Comment: 26 pages, 9 figure
Mixed-symmetry tensor conserved currents and AdS/CFT correspondence
We present the full list of conserved currents built of two massless spinor
fields in Minkowski space and their derivatives multiplied by Clifford algebra
elements. The currents have particular mixed-symmetry type described by Young
diagrams with one row and one column of arbitrary lengths and heights. Along
with Yukawa-like totally antisymmetric currents the complete set of constructed
currents exactly matches the spectrum of AdS mixed-symmetry fields arising in
the generalized Flato-Fronsdal theorem for two spinor singletons. As a
by-product, we formulate and study general properties of primary fields and
conserved currents of mixed-symmetry type.Comment: 17 pages; v2: typos corrected, clarifications and refs added; v3:
more explanations and refs added; contribution to the J.Phys.A special volume
on "Higher Spin Theories and AdS/CFT" edited by Matthias Gaberdiel and
Mikhail Vasilie
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