Journal of High Energy Physics

, 2015:198 | Cite as

On exact correlation functions in SU(N) \( \mathcal{N}=2 \) superconformal QCD

  • Marco Baggio
  • Vasilis Niarchos
  • Kyriakos Papadodimas
Open Access
Regular Article - Theoretical Physics


We consider the exact coupling constant dependence of extremal correlation functions of \( \mathcal{N}=2 \) chiral primary operators in 4d \( \mathcal{N}=2 \) superconformal gauge theories with gauge group SU(N) and N f = 2N massless fundamental hypermultiplets. The 2- and 3-point functions, viewed as functions of the exactly marginal coupling constant and theta angle, obey the tt * equations. In the case at hand, the tt * equations form a set of complicated non-linear coupled matrix equations. We point out that there is an ad hoc self-consistent ansatz that reduces this set of partial differential equations to a sequence of decoupled semi-infinite Toda chains, similar to the one encountered previously in the special case of SU(2) gauge group. This ansatz requires a surprising new non-renormalization theorem in \( \mathcal{N}=2 \) superconformal field theories. We derive a general 3-loop perturbative formula for 2- and 3-point functions in the \( \mathcal{N}=2 \) chiral ring of the SU(N) theory, and in all explicitly computed examples we find agreement with the tt * equations, as well as the above-mentioned ansatz. This is suggestive evidence for an interesting non-perturbative conjecture about the structure of the \( \mathcal{N}=2 \) chiral ring in this class of theories. We discuss several implications of this conjecture. For example, it implies that the holonomy of the vector bundles of chiral primaries over the superconformal manifold is reducible. It also implies that a specific subset of extremal correlation functions can be computed in the SU(N) theory using information solely from the S 4 partition function of the theory obtained by supersymmetric localization.


Supersymmetric gauge theory Extended Supersymmetry Gauge Symmetry Nonperturbative Effects 


Open Access

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Marco Baggio
    • 1
  • Vasilis Niarchos
    • 2
  • Kyriakos Papadodimas
    • 3
    • 4
  1. 1.Institut fur Theoretische PhysikETH ZurichZurichSwitzerland
  2. 2.Crete Center for Theoretical Physics and Crete Center for Quantum Complexity and Nanotechnology, Department of PhysicsUniversity of CreteHeraklionGreece
  3. 3.Theory Group, Physics Department, CERNGeneva 23Switzerland
  4. 4.Van Swinderen Institute for Particle Physics and GravityUniversity of GroningenGroningenThe Netherlands

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