48 research outputs found
Revisiting N=4 superconformal blocks
21 pages; v2: version published in JHEPWe study four-point correlation functions of four generic half-BPS supermultiplets of N=4 SCFT in four dimensions. We use the two-particle Casimir of four-dimensional superconformal algebra to derive superconformal blocks which contribute to the partial wave expansion of such correlators. The derived blocks are defined on analytic superspace and allow us in principle to find any component of the four-point correlator. The lowest component of the result agrees with the superconformal blocks found by Dolan and Osborn.Peer reviewe
Loop Corrections to Supergravity on
We consider the four-point correlator of the stress-energy tensor multiplet
in SYM. In the planar limit and at large 't Hooft coupling such
correlator is given by the corresponding holographic correlation function in
IIB supergravity on . We consider subleading corrections in
the number of colours, i.e. order , at large 't Hooft coupling. This
corresponds to loop corrections to the supergravity result. Consistency
conditions, most notably crossing symmetry, constrain the form of such
corrections and lead to a complete determination of the spectrum of leading
twist intermediate operators.Comment: 6 pages, minor changes, added reference
Higher-spin correlators
We analyze the properly normalized three-point correlator of two protected
scalar operators and one higher spin twist-two operator in N=4 super
Yang-Mills, in the limit of large spin j. The relevant structure constant can
be extracted from the OPE of the four-point correlator of protected scalar
operators. We show that crossing symmetry of the four point correlator plus a
judicious guess for the perturbative structure of the three-point correlator,
allow to make a prediction for the structure constant at all loops in
perturbation theory, up to terms that remain finite as the spin becomes large.
Furthermore, the expression for the structure constant allows to propose an
expression for the all loops four-point correlator G(u,v), in the limit u,v ->
0. Our predictions are in perfect agreement with the large j expansion of
results available in the literature.Comment: 14 pages,v2:minor changes, refs adde
Modular interpolating functions for N=4 SYM
We construct interpolating functions fully compatible with S-duality. We then
consider the problem of resumming perturbative expansions for anomalous
dimensions of low twist non-protected operators in N=4 super Yang-Mills theory.
When the rank of the gauge group is small, the interpolations suggest that
anomalous dimensions of leading twist operators take their maximum value at the
point . For fixed spin and large enough rank, there is a
level-crossing region, where the anomalous dimension of the leading twist
operator reaches its maximum and then bounces back.Comment: 13 pages, 5 figures; v2: comments adde
Generalized bootstrap equations for N=4 SCFT
We study the consistency of four-point functions of half-BPS chiral primary
operators of weight p in four-dimensional N=4 superconformal field theories.
The resulting conformal bootstrap equations impose non-trivial bounds for the
scaling dimension of unprotected local operators transforming in various
representations of the R-symmetry group. These bounds generalize recent bounds
for operators in the singlet representation, arising from consistency of the
four-point function of the stress-energy tensor multiplet.Comment: 18 pages, 3 figure
The superconformal bootstrap for structure constants
We report on non-perturbative bounds for structure constants on N=4 SYM. Such
bounds are obtained by applying the conformal bootstrap recently extended to
superconformal theories. We compare our results with interpolating functions
suitably restricted by the S-duality of the theory. Within numerical errors,
these interpolations support the conjecture that the bounds found in this paper
are saturated at duality invariant values of the coupling. This extends recent
conjectures for the anomalous dimension of leading twist operators.Comment: 14 pages, 4 figure
On Three-point Functions in the AdS_4/CFT_3 Correspondence
We calculate planar, tree-level, non-extremal three-point functions of
operators belonging to the SU(2) x SU(2) sector of ABJM theory. First, we
generalize the determinant representation, found by Foda for the three-point
functions of the SU(2) sector of N=4 SYM, to the present case and find that the
ABJM result up to normalization factors factorizes into a product of two N=4
SYM correlation functions. Secondly, we treat the case where two operators are
heavy and one is light and BPS, using a coherent state description of the heavy
ones. We show that when normalized by the three-point function of three BPS
operators the heavy-heavy-light correlation function agrees, in the
Frolov-Tseytlin limit, with its string theory counterpart which we calculate
holographically.Comment: 24 pages. v2: typos corrected, references added, published versio
A constructive solution to the cosmological bootstrap
In this paper we revisit a generalised crossing equation that follows from
harmonic analysis on the conformal group, and is of particular interest for the
cosmological bootstrap programme. We present an exact solution to this
equation, for dimensions two or higher, in terms of 6j symbols of the Euclidean
conformal group, and discuss its relevance. In the process we provide a
detailed derivation of the analogue of the Biedenharn-Elliot identity for said
6j symbols.Comment: 37 pages, acknowledgements update
Rebooting quarter-BPS operators in Super Yang-Mills
We start a systematic study of quarter-BPS operators in four-dimensional
Super Yang-Mills with gauge group making use
of recently developed tools in conformal field theory. We adapt the technology
of embedding space tensor structures in four dimensions to the problem of
computing R-symmetry tensor structures and we use the underlying chiral algebra
to obtain the superconformal Ward identities. This allows us to fix the
protected part of the four-point correlators, up to few ambiguities. As
applications, we use the Lorentzian inversion formula to study the leading
order OPE data in the large~ supergravity limit and we make contact with the
OPE limit of the five-point function of half-BPS operators.Comment: 65 page