57 research outputs found
AdS/CFT for Unprotected Operators
We consider the four-point function of the lowest scalar in the stress-energy
tensor multiplet in ABJ(M) theory \cite{Aharony:2008ug,
Aharony:2008gk}. At large central charge , this correlator is
given by the corresponding holographic correlation function in 11d supergravity
on . We use Mellin space techniques to compute the leading
correction to anomalous dimensions and OPE coefficients of operators
that appear in this holographic correlator. For half and quarter-BPS operators,
we find exact agreement with previously computed localization results. For the
other BPS and non-BPS operators, our results match the
numerical bootstrap for ABJ(M) at large , which provides a precise check
of unprotected observables in AdS/CFT.Comment: 22 pages, 1 figure, v4, fixed typo
M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture
We study various aspects of the M-theory uplift of the series of
CFTs in 6d, which describe the worldvolume theory of M5 branes in
flat space. We show how knowledge of OPE coefficients and scaling dimensions
for this CFT can be directly translated into features of the momentum expansion
of M-theory. In particular, we develop the expansion of the four-graviton
S-matrix in M-theory via the flat space limit of four-point Mellin amplitudes.
This includes correctly reproducing the known contribution of the term
from 6d CFT data. Central to the calculation are the OPE coefficients for
half-BPS operators not in the stress tensor multiplet, which we obtain for
finite via the previously conjectured relation [arXiv:1404.1079] between
the quantum algebra and the CFT. We further
explain how the expansion of structure constants exhibits
the structure of protected vertices in the M-theory action. Conversely, our
results provide strong evidence for the chiral algebra conjecture.Comment: 30+18 pages. v2: added refs, fixed typos/notatio
Towards Bootstrapping QED
We initiate the conformal bootstrap study of Quantum Electrodynamics in
space-time dimensions (QED) with flavors of charged fermions by
focusing on the 4-point function of four monopole operators with the lowest
unit of topological charge. We obtain upper bounds on the scaling dimension of
the doubly-charged monopole operator, with and without assuming other gaps in
the operator spectrum. Intriguingly, we find a (gap-dependent) kink in these
bounds that comes reasonably close to the large extrapolation of the
scaling dimensions of the singly-charged and doubly-charged monopole operators
down to and .Comment: 29 pages plus an appendix, 5 figures, v2 minor improvements, refs
adde
Anomalous dimensions of monopole operators in scalar QED with Chern-Simons term
We study monopole operators with the lowest possible topological charge
at the infrared fixed point of scalar electrodynamics in
dimension (scalar QED) with complex scalars and Chern-Simons coupling
. In the large expansion, monopole operators in this theory with
spins and associated flavor representations are expected to
have the same scaling dimension to sub-leading order in . We use the
state-operator correspondence to calculate the scaling dimension to sub-leading
order with the result , which improves on existing leading
order results. We also compute the term that breaks the degeneracy
to sub-leading order for monopoles with spins .Comment: 21 pages plus appendices, no figures, v2 minor typos fixed, accepted
to JHE
Bootstrapping Vector Models in
We use the conformal bootstrap to study conformal field theories with
global symmetry in and spacetime dimensions that have a scalar
operator transforming as an vector. The crossing symmetry of
the four-point function of this vector operator, along with unitarity
assumptions, determine constraints on the scaling dimensions of conformal
primary operators in the OPE. Imposing a lower bound on
the second smallest scaling dimension of such an -singlet conformal
primary, and varying the scaling dimension of the lowest one, we obtain an
allowed region that exhibits a kink located very close to the interacting
-symmetric CFT conjectured to exist recently by Fei, Giombi, and
Klebanov. Under reasonable assumptions on the dimension of the second lowest
singlet in the OPE, we observe that this kink
disappears in for small enough , suggesting that in this case an
interacting CFT may cease to exist for below a certain critical
value.Comment: 24 pages, 5 figures; v2 minor improvement
Solving M-theory with the Conformal Bootstrap
We use the conformal bootstrap to perform a precision study of 3d maximally
supersymmetric () SCFTs that describe the IR physics on
coincident M2-branes placed either in flat space or at a \C^4/\Z_2
singularity. First, using the explicit Lagrangians of ABJ(M)
\cite{Aharony:2008ug,Aharony:2008gk} and recent supersymmetric localization
results, we calculate certain half and quarter-BPS OPE coefficients, both
exactly at small , and approximately in a large expansion that we
perform to all orders in . Comparing these values with the numerical
bootstrap bounds leads us to conjecture that some of these theories obey an OPE
coefficient minimization principle. We then use this conjecture as well as the
extremal functional method to reconstruct the first few low-lying scaling
dimensions and OPE coefficients for both protected and unprotected multiplets
that appear in the OPE of two stress tensor multiplets for all values of .
We also calculate the half and quarter-BPS operator OPE coefficients in the
BLG theory for all values of the Chern-Simons
coupling , and show that generically they do not obey the same OPE
coefficient minimization principle.Comment: 30 pages, 5 figures, v2 submitted for publicatio
A New Duality Between Superconformal Field Theories in Three Dimensions
We propose a new duality between two 3d superconformal
Chern-Simons-matter theories: the ABJM theory and a
theory consisting of the product between the BLG theory and a free theory of
eight real scalars and eight Majorana fermions. As evidence supporting this
duality, we show that the moduli spaces, superconformal indices,
partition functions, and certain OPE coefficients of BPS operators in the two
theories agree.Comment: 29 pages, 2 figure
Monopole operators from the expansion
Three-dimensional quantum electrodynamics with charged fermions contains
monopole operators that have been studied perturbatively at large . Here, we
initiate the study of these monopole operators in the expansion by
generalizing them to codimension-3 defect operators in
spacetime dimensions. Assuming the infrared dynamics is described by an
interacting CFT, we define the "conformal weight" of these operators in terms
of the free energy density on in the
presence of magnetic flux through the , and calculate this quantity to
next-to-leading order in . Extrapolating the conformal weight to
gives an estimate of the scaling dimension of the monopole
operators in that does not rely on the expansion. We also perform
the computation of the conformal weight in the large expansion for any
and find agreement between the large and the small expansions in
their overlapping regime of validity.Comment: 45 pages, 3 figures, version accepted by journa
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