Revisiting the dilatation operator of the Wilson-Fisher fixed point

We revisit the order $\varepsilon$ 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-$\varepsilon$ scaling dimensions of the Wilson-Fisher fixed point can be fixed by symmetry.Comment: 23 pages, v2: typos corrected, references adde

N=2\mathcal{N}=2 central charge bounds from 2d2d chiral algebras

We study protected correlation functions in $\mathcal{N} = 2$ SCFT whose description is captured by a two-dimensional chiral algebra. Our analysis implies a new analytic bound for the $c$-anomaly as a function of the flavor central charge $k$, valid for any theory with a flavor symmetry $G$. Combining our result with older bounds in the literature puts strong constraints on the parameter space of $\mathcal{N}=2$ theories. In particular, it singles out a special set of models whose value of $c$ is uniquely fixed once $k$ is given. This set includes the canonical rank one $\mathcal{N}=2$ SCFTs given by Kodaira's classification.Comment: 12 pages, 2 figure

On correlation functions of BPS operators in 3d3d N=6\mathcal{N}=6 superconformal theories

We introduce a novel harmonic superspace for $3d$ $\mathcal{N}=6$ 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 $\frac{1}{2}$-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 N \mathcal{N} = 4 SYM with defects

This paper focuses on the analysis of $4d$ $\mathcal{N}=4$ 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 $\tfrac{1}{2}$-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 $4d$ $\mathcal{N}=4$ superconformal theories with a boundary, but also to three more systems that have the same symmetry algebra: $4d$ $\mathcal{N}=4$ superconformal theories with a line defect, $3d$ $\mathcal{N}=4$ superconformal theories with no defect, and $OSP(4^*|4)$ 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 $4d$ $\mathcal{N}=2$ 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 $r$ 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 $1d$ defect CFT generated by inserting operators along the Maldacena-Wilson line in $\mathcal{N} = 4$ 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 $\phi^i$ and $\phi^6$, 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