26 research outputs found
Extremal Correlators in the AdS/CFT Correspondence
The non-renormalization of the 3-point functions of chiral primary operators in N=4 super-Yang-Mills theory is one of
the most striking facts to emerge from the AdS/CFT correspondence. A two-fold
puzzle appears in the extremal case, e.g. k_1 = k_2 + k_3. First, the
supergravity calculation involves analytic continuation in the k_i variables to
define the product of a vanishing bulk coupling and an infinite integral over
AdS. Second, extremal correlators are uniquely sensitive to mixing of the
single-trace operators with protected multi-trace operators in the
same representation of SU(4). We show that the calculation of extremal
correlators from supergravity is subject to the same subtlety of regularization
known for the 2-point functions, and we present a careful method which
justifies the analytic continuation and shows that supergravity fields couple
to single traces without admixture. We also study extremal n-point functions of
chiral primary operators, and argue that Type IIB supergravity requires that
their space-time form is a product of n-1 two-point functions (as in the free
field approximation) multiplied by a non-renormalized coefficient. This
non-renormalization property of extremal n-point functions is a new prediction
of the AdS/CFT correspondence. As a byproduct of this work we obtain the cubic
couplings and of fields in the dilaton and 5-sphere
graviton towers of Type IIB supergravity on .Comment: 26 pages, LateX, no figure
The group approach to AdS space propagators: A fast algorithm
In this letter we show how the method of [4] for the calculation of two-point
functions in d+1-dimensional AdS space can be simplified. This results in an
algorithm for the evaluation of the two-point functions as linear combinations
of Legendre functions of the second kind. This algorithm can be easily
implemented on a computer. For the sake of illustration, we displayed the
results for the case of symmetric traceless tensor fields with rank up to l=4.Comment: 14 pages, comment adde
A note on the perturbative properties of BPS operators
We discuss the perturbative behavior of the 1/2 BPS operators in N=2 SCFT on
the example of two very similar quadrilinear composite operators made out of
hypermultiplets. An explicit one-loop computation shows that one of them is
protected while the other acquires an anomalous dimension. Although both
operators are superconformal primaries in the free case, the quantum
corrections make the latter become a 1/2 BPS descendant of the Konishi
multiplet, while the former remains primary. The comparative study of these two
operators at higher orders may be helpful in understanding the quantum
properties of the Konishi multiplet
Universal properties of superconformal OPEs for 1/2 BPS operators in
We give a general analysis of OPEs of 1/2 BPS superfield operators for the
superconformal algebras OSp(8/4,R), PSU(2,2), F and
OSp() which underlie maximal AdS supergravity in . \\
The corresponding three-point functions can be formally factorized in a way
similar to the decomposition of a generic superconformal UIR into a product of
supersingletons. This allows for a simple derivation of branching rules for
primary superfields. The operators of protected conformal dimension which may
appear in the OPE are classified and are shown to be either 1/2 or 1/4 BPS, or
semishort. As an application, we discuss the "non-renormalization" of extremal
-point correlators.Comment: To be published in NJP Focus Issue: Supersymmetry in condensed matter
and high energy physic
Gravitino Propagator in anti de Sitter space
We construct the gauge invariant part of the propagator for the massless
gravitino in AdS(d+1) by coupling it to a conserved current. We also derive the
propagator for the massive gravitino.Comment: 24 pages; LaTe
Defect Conformal Field Theory and Locally Localized Gravity
Gravity may be "locally localized" over a wide range of length scales on a
d-dimensional anti-de Sitter (AdS) brane living inside AdS_{d+1}. In this paper
we examine this phenomenon from the point of view of the holographic dual
"defect conformal field theory". The mode expansion of bulk fields on the
gravity side is shown to be precisely dual to the "boundary operator product
expansion" of operators as they approach the defect. From the field theory
point of view, the condition for localization is that a "reduced operator"
appearing in this expansion acquires negative anomalous dimension. In
particular, a very light localized graviton exists when a mode arising from the
reduction of the ambient stress-energy tensor to the defect has conformal
dimension Delta ~ d-1. The part of the stress tensor containing the defect
dynamics has dimension Delta = d-1 in the free theory, but we argue that it
acquires an anomalous dimension in the interacting theory, and hence does not
participate in localization in the regime of small backreaction of the brane.
We demonstrate that such an anomalous dimension is consistent with the
conservation of the full stress-energy tensor. Finally, we analyze how to
compute the anomalous dimensions of reduced operators from gravity at leading
order in the interactions with the brane.Comment: 38 pages, LaTeX, 5 figures. v2: typos fixe
Bosonic Quadratic Actions for 11D Supergravity on AdS_7/4 x S_4/7
We determine from 11D supergravity the quadratic bulk action for the physical
bosonic fields relevant for the computation of correlation functions of
normalized chiral operators in D=6, N=(0,2) and D=3, N=8 supersymmetric CFT in
the large N limit, as dictated by the AdS/CFT duality conjecture.Comment: 16 pages, Plain TeX, no figures, requires AMS font files amssym.def
and amssym.tex, a few typos correcte
Positive energy unitary irreducible representations of D=6 conformal supersymmetry
We give a constructive classification of the positive energy (lowest weight)
unitary irreducible representations of the D=6 superconformal algebras
osp(8*/2N). Our results confirm all but one of the conjectures of Minwalla (for
N=1,2) on this classification. Our main tool is the explicit construction of
the norms of the states that has to be checked for positivity. We give also the
reduction of the exceptional UIRs.Comment: 27 pages, TeX with harvmac, amssym.def, amssym.tex; v.2: minor
corrections and references added; v.3: minor corrections; v.4: to appear in
J. Phys.