147 research outputs found
Solving CFTs with Weakly Broken Higher Spin Symmetry
The method of large spin perturbation theory allows to analyse conformal
field theories (CFT) by turning the crossing equations into an algebraic
problem. We apply this method to a generic CFT with weakly broken higher spin
(HS) symmetry, to the first non-trivial order in the breaking parameter. We
show that the spectrum of broken currents, for any value of the spin, follows
from crossing symmetry. After discussing a generic model of a single scalar
field, we focus on vector models with global symmetry. We rediscover the
spectrum of several models, including the Wilson-Fisher model around
four dimensions, the large model in and cubic models around six
dimensions, not necessarily unitary. We also discuss models where the
fundamental field is not part of the spectrum. Examples of this are weakly
coupled gauge theories and our method gives an on-shell gauge invariant way to
study them. At first order in the coupling constant we show that again the
spectrum follows from crossing symmetry, to all values of the spin. Our method
provides an alternative to usual perturbation theory without any reference to a
Lagrangian.Comment: 30 pages,v2:typos correcte
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
Conformal Bootstrap With Slightly Broken Higher Spin Symmetry
We consider conformal field theories with slightly broken higher spin
symmetry in arbitrary spacetime dimensions. We analyze the crossing equation in
the double light-cone limit and solve for the anomalous dimensions of higher
spin currents with large spin . The result depends on the
symmetries and the spectrum of the unperturbed conformal field theory. We
reproduce all known results and make further predictions. In particular we make
a prediction for the anomalous dimensions of higher spin currents in the 3d
Ising model.Comment: 41 pages, 2 figures, %\draftmod
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
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
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
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
Gravitational S-matrix from CFT dispersion relations
We analyse the double-discontinuities of the four-point correlator of the
stress-tensor multiplet in N=4 SYM at large t' Hooft coupling and at order
, as a way to access one-loop effects in the dual supergravity theory.
From these singularities we extract CFT-data by using two inversion procedures:
one based on a recently proposed Froissart-Gribov inversion integral, and the
other based on large spin perturbation theory. Both procedures lead to the same
results and are shown to be equivalent more generally. Our computation
parallels the standard S-matrix reconstruction via dispersion relations. In a
suitable limit, the result of the conformal field theory calculation is
compared with the one-loop graviton scattering amplitude in ten-dimensional IIB
supergravity in flat space, finding perfect agreement.Comment: 39 pages, pretty figure
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