Universal correlation functions in rank 1 SCFTs

Abstract

Carrying to higher precision the large-$\mathcal{J}$ expansion of Hellerman and Maeda, we calculate to all orders in $1/\mathcal{J}$ the power-law corrections to the two-point functions ${\mathcal{Y}}_n\equiv |x-y{|}^{2n{\Delta }_{\mathcal{O}}}⟨{\mathcal{O}}_n(x){\bar{\mathcal{O}}}_n(y)⟩$ for generators $\mathcal{O}$ of Coulomb branch chiral rings in four-dimensional $\mathcal{N}=2$ superconformal field theories. We show these correlators have the universal large-$n$ expansion \[ \log(\mathcal{Y}_n) \simeq \mathcal{J} \mathbf{A} + \mathbf{B} + \log(Γ( \mathcal{J} + α+ 1)) , \] where $\mathcal{J}\equiv 2n{\Delta }_{\mathcal{O}}$ is the total $R$-charge of ${\mathcal{O}}_n$, the $\mathbf{A}$ and $\mathbf{B}$ are theory-dependent coefficients, $\alpha$ is the coefficient of the Wess-Zumino term for the Weyl $a$-anomaly, and the $\simeq$ denotes equality up to terms exponentially small in $\mathcal{J}$. Our methods combine the structure of the Coulomb-branch effective field theory (EFT) with the supersymmetric recursion relations. However, our results constrain the power-law corrections to all orders, even for non-Lagrangian theories to which the recursion relations do not apply. For the case of $\mathcal{N}=2$ SQCD, we also comment on the nature of the exponentially small corrections, which can be calculated to high precision in the double-scaling limit recently discussed by Bourget et al. We show the exponentially small correction is consistent with the interpretation of the EFT breaking down due to the propagation of massive BPS particles over distances of order of the infrared scale $|x-y|$.

arXiv comment49 pages, typos fixed, references added. Matches published version in JHEP

References in corpus (51)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Bounding scalar operator dimensions in 4D CFT
• On Renormalization Group Flows in Four Dimensions
• Solving the 3D Ising Model with the Conformal Bootstrap
• New Phenomena in SU(3) Supersymmetric Gauge Theory
• Infinite Chiral Symmetry in Four Dimensions
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Reading between the lines of four-dimensional gauge theories
• Rigid Supersymmetric Theories in Curved Superspace
• New N=2 Superconformal Field Theories in Four Dimensions
• Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories
• EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions
• On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
• Large Spin Perturbation Theory
• Exploring Curved Superspace
• Sphere Partition Functions and the Zamolodchikov Metric
• Correlation Functions of Coulomb Branch Operators
• Supercurrents and Brane Currents in Diverse Dimensions
• Compensating strong coupling with large charge
• Comments on Higher Derivative Operators in Some SUSY Field Theories
• Spontaneous Breaking of Conformal Invariance and Trace Anomaly Matching
• Hypermultiplets, Hyperkahler Cones and Quaternion-Kahler Geometry
• Conformal dimensions via large charge expansion
• Negative Branes, Supergroups and the Signature of Spacetime
• $t{t}^{\ast }$ equations, localization and exact chiral rings in 4d N=2 SCFTs
• Loop operators and S-duality from curves on Riemann surfaces
• Conformal Bootstrap At Large Charge
• String theory of the Omega deformation
• Ghost D-branes
• On the CFT Operator Spectrum at Large Global Charge
• Feynman Rules in N=2 Projective Superspace I: Massless hypermultiplets
• Topological Anti-Topological Fusion in Four-Dimensional Superconformal Field Theories
• Goldstone modes and photonization for higher form symmetries
• On exact correlation functions in SU(N) $\mathcal{N}=2$ superconformal QCD
• Exact correlation functions in SU(2) N=2 superconformal QCD
• A limit for large $R$-charge correlators in $\mathcal{N}=2$ theories
• On the Large $R$-charge Expansion in $\mathcal{N}=2$ Superconformal Field Theories
• Feynman rules in N=2 projective Superspace II: Massive hypermultiplets
• Geometric constraints on the space of N=2 SCFTs I: physical constraints on relevant deformations
• Geometric classification of 4d $\mathcal{N}=2$ SCFTs
• Operator Dimensions from Moduli
• Nonunitary Lagrangians and unitary non-Lagrangian conformal field theories
• Geometric constraints on the space of N=2 SCFTs III: enhanced Coulomb branches and central charges
• Higher-Derivative Terms in N=2 Supersymmetric Effective Actions
• Matrix models at large charge
• Gauge Invariant Regularization in the AdS/CFT Correspondence and Ghost D-branes
• Scaling dimensions of Coulomb branch operators of 4d N=2 superconformal field theories
• Dilaton Effective Action with $\mathcal{N}=1$ Supersymmetry
• A matrix CFT at multiple large charges
• On Superspace Chern-Simons-like Terms
• Higher-Derivative Terms in N=2 SUSY Effective Actions

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