The planar limit of $\mathcal{N}=2$ superconformal field theories

Abstract

We obtain the perturbative expansion of the free energy on $S^4$ for four dimensional Lagrangian $\mathcal{N}=2$ superconformal field theories, to all orders in the 't Hooft coupling, in the planar limit. We do so by using supersymmetric localization, after rewriting the 1-loop factor as an effective action involving an infinite number of single and double trace terms. The answer we obtain is purely combinatorial, and involves a sum over tree graphs. We also apply these methods to the perturbative expansion of the free energy at finite $N$, and to the computation of the vacuum expectation value of the 1/2 BPS circular Wilson loop, which in the planar limit involves a sum over rooted tree graphs.

arXiv comment35 pages, 4 figures, reference added, published version

References in corpus (33)

• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• An Exact Prediction of N=4 SUSYM Theory for String Theory
• Group theory factors for Feynman diagrams
• Wilson-'t Hooft operators in four-dimensional gauge theories and S-duality
• An exact formula for the radiation of a moving quark in N=4 super Yang Mills
• Exact results for the entanglement entropy and the energy radiated by a quark
• Exact results for static and radiative fields of a quark in N=4 super Yang-Mills
• Rigorous Test of Non-conformal Holography: Wilson Loops in N=2* Theory
• Massive N=2 Gauge Theories at Large N
• Large N Limit of N=2 SU(N) Gauge Theories from Localization
• A note on perturbation series in supersymmetric gauge theories
• The Exact Bremsstrahlung Function in N=2 Superconformal Field Theories
• Two-point Correlators in N=2 Gauge Theories
• Non-Perturbative Solution of Matrix Models Modified by Trace-Squared Terms
• Wilson Loops in N=2 Super-Yang-Mills from Matrix Model
• Exact results for Wilson loops in arbitrary representations
• Classification of 4d N=2 gauge theories
• A Proposal for Strings at D>1
• Line defects and radiation in $\mathcal{N}=2$ theories
• M-theoretic matrix models
• Exact Results and Holography of Wilson Loops in N=2 Superconformal (Quiver) Gauge Theories
• Matrix Model Perturbed by Higher Order Curvature Terms
• BPS Wilson loops in generic conformal N=2 SU(N) SYM theories
• Correlators between Wilson loop and chiral operators in N=2 conformal gauge theories
• Wilson Loops in N=2 Superconformal Yang-Mills Theory
• Borel summability of perturbative series in 4d N=2 and 5d N=1 theories
• Probing N=2 superconformal field theories with localization
• Exact probes of orientifolds
• Correlators in the Simplest Gauge-String Duality
• Wilson loops in terms of color invariants
• Exact momentum fluctuations of an accelerated quark in N=4 super Yang-Mills
• The Bremsstrahlung function of $\mathcal{N}=2$ SCQCD
• Universality of Toda equation in $\mathcal{N}=2$ superconformal field theories

Cited by in corpus (16)

• N=2 Conformal SYM theories at large N
• Exact results in a N=2 superconformal gauge theory at strong coupling
• $1/N$ expansion of circular Wilson loop in $\mathcal{N}=2$ superconformal $SU(N)\times SU(N)$ quiver
• Three-point functions in a $\mathcal{N}=2$ superconformal gauge theory and their strong-coupling limit
• Exact strong coupling results in $\mathcal{N}$=2 $Sp(2N)$ superconformal gauge theory from localization
• Non-planar corrections in orbifold/orientifold $\mathcal{N}=2$ superconformal theories from localization
• The planar limit of $\mathcal{N}=2$ chiral correlators
• The planar limit of integrated 4-point functions
• Linear Quivers at Large-$N$
• Wilson loop correlators at strong coupling in $\mathcal{N}=2$ quiver gauge theories
• Defect correlators in a $\mathcal{N}=2$ SCFT at strong coupling
• Integrated correlators with a Wilson line in a $\mathcal{N}=2$ quiver gauge theory at strong coupling
• A derivation of the planar limit of $\mathcal{N}=2$ chiral correlators
• BPS Wilson loop in $\mathcal{N}=2$ superconformal $SU(N)$ "orientifold" gauge theory and weak-strong coupling interpolation
• Strong coupling expansion of free energy and BPS Wilson loop in $\mathcal{N}=2$ superconformal models with fundamental hypermultiplets
• On the planar free energy of matrix models