113 research outputs found
Revisiting the dilatation operator of the Wilson-Fisher fixed point
We revisit the order dilatation operator of the Wilson-Fisher
fixed point obtained by Kehrein, Pismak, and Wegner in light of recent results
in conformal field theory. Our approach is algebraic and based only on symmetry
principles. The starting point of our analysis is that the first correction to
the dilatation operator is a conformal invariant, which implies that its form
is fixed up to an infinite set of coefficients associated with the scaling
dimensions of higher-spin currents. These coefficients can be fixed using
well-known perturbative results, however, they were recently re-obtained using
CFT arguments without relying on perturbation theory. Our analysis then implies
that all order- scaling dimensions of the Wilson-Fisher fixed
point can be fixed by symmetry.Comment: 23 pages, v2: typos corrected, references adde
central charge bounds from chiral algebras
We study protected correlation functions in SCFT whose
description is captured by a two-dimensional chiral algebra. Our analysis
implies a new analytic bound for the -anomaly as a function of the flavor
central charge , valid for any theory with a flavor symmetry . Combining
our result with older bounds in the literature puts strong constraints on the
parameter space of theories. In particular, it singles out a
special set of models whose value of is uniquely fixed once is given.
This set includes the canonical rank one SCFTs given by
Kodaira's classification.Comment: 12 pages, 2 figure
On correlation functions of BPS operators in superconformal theories
We introduce a novel harmonic superspace for
superconformal field theories that is tailor made for the study of correlation
functions of BPS operators. We calculate a host of two- and three-point
functions in full generality and put strong constraints on the form of
four-point functions of some selected BPS multiplets. For the four-point
function of -BPS operators we obtain the associated Ward
identities by imposing the absence of harmonic singularities. The latter imply
the existence of a solvable subsector in which the correlator becomes
topological. This mechanism can be explained by cohomological reduction with
respect to a special nilpotent supercharge.Comment: 41 pages, v2: typos corrected, references adde
Stress-tensor OPE in N=2 Superconformal Theories
We carry out a detailed superspace analysis of the OPE of two N=2
stress-tensor multiplets. Knowledge of the multiplets appearing in the
expansion, together with the two-dimensional chiral algebra description of N=2
SCFTs, imply an analytic bound on the central charge c. This bound is valid for
any N=2 SCFT regardless of its matter content and flavor symmetries, and is
saturated by the simplest Argyres-Douglas fixed point. We also present a
partial conformal block analysis for the scalar superconformal primary of the
multiplet.Comment: 29 page
Bootstrap equations for N = 4 SYM with defects
This paper focuses on the analysis of superconformal
theories in the presence of a defect from the point of view of the conformal
bootstrap. We will concentrate first on the case of codimension one, where the
defect is a boundary that preserves half of the supersymmetry. After studying
the constraints imposed by supersymmetry, we will obtain the Ward identities
associated to two-point functions of -BPS operators and write
their solution as a superconformal block expansion. Due to a surprising
connection between spacetime and R-symmetry conformal blocks, our results not
only apply to superconformal theories with a boundary, but
also to three more systems that have the same symmetry algebra:
superconformal theories with a line defect,
superconformal theories with no defect, and
superconformal quantum mechanics. The superconformal algebra implies that all
these systems possess a closed subsector of operators in which the bootstrap
equations become polynomial constraints on the CFT data. We derive these
truncated equations and initiate the study of their solutions.Comment: 44 pages, 2 figures, v3: typos fixed, to appear in JHE
Orientifold daughter of N=4 SYM and double-trace running
We study the orientifold daughter of N=4 super Yang-Mills as a candidate
non-supersymmetric large N conformal field theory. In a theory with vanishing
single-trace beta functions that contains scalars in the adjoint
representation, conformal invariance might still be broken by renormalization
of double-trace terms to leading order at large N. In this note we perform a
diagrammatic analysis and argue that the orientifold daughter does not suffer
from double-trace running. This implies an exact large N equivalence between
this theory and a subsector of N=4 SYM.Comment: 12 page
Bootstrapping Coulomb and Higgs branch operators
We apply the numerical conformal bootstrap to correlators of Coulomb and
Higgs branch operators in superconformal theories. We
start by revisiting previous results on single correlators of Coulomb branch
operators. In particular, we present improved bounds on OPE coefficients for
some selected Argyres-Douglas models, and compare them to recent work where the
same cofficients were obtained in the limit of large charge. There is solid
agreement between all the approaches. The improved bounds can be used to
extract an approximate spectrum of the Argyres-Douglas models, which can then
be used as a guide in order to corner these theories to numerical islands in
the space of conformal dimensions. When there is a flavor symmetry present, we
complement the analysis by including mixed correlators of Coulomb branch
operators and the moment map, a Higgs branch operator which sits in the same
multiplet as the flavor current. After calculating the relevant superconformal
blocks we apply the numerical machinery to the mixed system. We put general
constraints on CFT data appearing in the new channels, with particular emphasis
on the simplest Argyres-Douglas model with non-trivial flavor symmetry.Comment: 45 pages, 11 figures, minor changes in v
Multipoint correlators on the supersymmetric Wilson line defect CFT II: Unprotected operators
We continue our study of multipoint correlators of scalar fields on the
defect CFT generated by inserting operators along the Maldacena-Wilson line in
SYM. We present a weak-coupling recursion relation that
captures correlators at next-to-leading order involving an arbitrary number of
the elementary scalar fields and , the latter being
unprotected. We can then build correlators of composite operators by pinching
the scalar fields together. As a demonstration of our method, we give explicit
results for correlators containing up to six points. We also expand some
selected correlators using recently obtained conformal blocks in the comb and
snowflake channel, and check that the extracted low-lying CFT data is
consistent with explicit computations.Comment: 44 pages, ancillary Mathematica noteboo
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