62 research outputs found
Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal
Recently, an asymptotic Bethe Ansatz that is claimed to describe anomalous
dimensions of "long" operators in the planar N=6 supersymmetric
three-dimensional Chern-Simons-matter theory dual to quantum superstrings in
AdS_4 x CP^3 was proposed. It initially passed a few consistency checks but
subsequent direct comparison to one-loop string-theory computations created
some controversy. Here we suggest a resolution by pointing out that, contrary
to the initial assumption based on the algebraic curve considerations, the
central interpolating function h(\lambda) entering the BMN or magnon dispersion
relation receives a non-zero one-loop correction in the natural string-theory
computational scheme. We consider a basic example which has already played a
key role in the AdS_5 x S^5 case: a rigid circular string stretched in both
AdS_4 and along an S^1 of CP^3 and carrying two spins. Computing the leading
one-loop quantum correction to its energy allows us to fix the constant
one-loop term in h(\lambda) and also to suggest how one may establish a
correspondence with the Bethe Ansatz proposal, including the non-trivial
one-loop phase factor. We discuss some problems which remain in trying to match
a part of world-sheet contributions (sensitive to compactness of the string
direction) and their Bethe Ansatz counterparts.Comment: 37 pages; v2: references added and typos fixe
One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
Recently it has been argued that tree-level scattering amplitudes in N=4
Yang-Mills theory are uniquely determined by a careful study of their
superconformal and Yangian symmetries. However, at one-loop order these
symmetries are known to become anomalous due to infrared divergences. We
compute these one-loop anomalies for amplitudes defined through dimensional
regularisation by studying the tree-level symmetry transformations of the
unitarity branch cuts, keeping track of the crucial collinear terms arising
from the holomorphic anomaly. We extract the superconformal anomalies and show
that they may be cancelled through a universal one-loop deformation of the
tree-level symmetry generators which involves only tree-level data.
Specialising to the planar theory we also obtain the analogous deformation for
the level-one Yangian generator of momentum. Explicit checks of our one-loop
deformation are performed for MHV and the 6-point NMHV amplitudes.Comment: 64 pages, v2: typos and minor corrections in (6.14) and (6.17), to
appear in JHE
New Relations for Three-Dimensional Supersymmetric Scattering Amplitudes
We provide evidence for a duality between color and kinematics in
three-dimensional supersymmetric Chern-Simons matter theories. We show that the
six-point amplitude in the maximally supersymmetric, N=8, theory can be
arranged so that the kinematic factors satisfy the fundamental identity of
three-algebras. We further show that the four- and six-point N=8 amplitudes can
be "squared" into the amplitudes of N=16 three-dimensional supergravity, thus
providing evidence for a hidden three-algebra structure in the dynamics of the
supergravity.Comment: 8 pages, 2 figure
A light-cone approach to three-point functions in AdS_5 x S^5
We consider worldsheet correlation functions for strings in AdS_5 x S^5 using
a light-cone gauge for the worldsheet theory. We compute the saddle-point
approximation to three-point functions of BMN vertex operators, all with large
charges, by explicitly finding the intersection of three euclidean BMN strings.
We repeat this calculation for non-BPS circular winding strings extended along
a great circle of the S^5, though in this case the appropriate form of the
vertex operator is uncertain. Furthermore, we compute the spectrum of
fluctuations about euclidean BMN strings for generic boundary conditions, and
show that the spectrum depends only on the total charge and not the details of
the string configuration. We extend our considerations to include near-BMN
vertex operators and through the evaluation of the string path integral make
contact with the light-cone string field theory calculations of gauge theory
three-point structure constants.Comment: 42 pages, 2 figures; v2: typos corrected, references added; v3:
significant changes in section 7, in particular corrected saddle point for
three-point functio
Worldsheet Form Factors in AdS/CFT
We formulate a set of consistency conditions appropriate to worldsheet form
factors in the massive, integrable but non-relativistic, light-cone gauge fixed
AdS(5) x S**5 string theory. We then perturbatively verify that these
conditions hold, at tree level in the near-plane-wave limit and to one loop in
the near-flat (Maldacena-Swanson) limit, for a number of specific cases. We
further study the form factors in the weakly coupled dual description,
verifying that the relevant conditions naturally hold for the one-loop
Heisenberg spin-chain. Finally, we note that the near-plane-wave expressions
for the form factors, when further expanded in small momentum or, equivalently,
large charge density, reproduce the thermodynamic limit of the spin-chain
results at leading order.Comment: 30 pages, 12 figures, v3: typos fixed, improved discussion of bound
states and bound state axio
Exacting N=4 Superconformal Symmetry
Tree level scattering amplitudes in N=4 super Yang-Mills theory are almost,
but not exactly invariant under the free action of the N=4 superconformal
algebra. What causes the non-invariance is the holomorphic anomaly at poles
where external particles become collinear. In this paper we propose a
deformation of the free superconformal representation by contributions which
change the number of external legs. This modified classical representation not
only makes tree amplitudes fully invariant, but it also leads to additional
constraints from symmetry alone mediating between hitherto unrelated
amplitudes. Moreover, in a constructive approach it appears to fully constrain
all tree amplitudes when combined with dual superconformal alias Yangian
symmetry.Comment: 47 pages. v2: minor corrections, clarifications and additions;
algebraic derivation of {S,Sbar}=K, v3: section 4.4 restored (it was dropped
by mistake in v2), minor corrections, to appear in JHE
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