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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

Abstract

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.

Keywords

Supersymmetric gauge theory Extended Supersymmetry Gauge Symmetry Nonperturbative Effects 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    S. Cecotti and C. Vafa, Topological antitopological fusion, Nucl. Phys. B 367 (1991) 359 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  2. [2]
    K. Papadodimas, Topological Anti-Topological Fusion in Four-Dimensional Superconformal Field Theories, JHEP 08 (2010) 118 [arXiv:0910.4963] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  3. [3]
    W. Lerche, C. Vafa and N.P. Warner, Chiral Rings in N = 2 Superconformal Theories, Nucl. Phys. B 324 (1989) 427 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  4. [4]
    M. Baggio, V. Niarchos and K. Papadodimas, tt * equations, localization and exact chiral rings in 4d \( \mathcal{N}=2 \) SCFTs, JHEP 02 (2015) 122 [arXiv:1409.4212] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  5. [5]
    S. Cecotti and C. Vafa, Exact results for supersymmetric σ-models, Phys. Rev. Lett. 68 (1992) 903 [hep-th/9111016] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  6. [6]
    M. Baggio, V. Niarchos and K. Papadodimas, Exact correlation functions in SU(2) \( \mathcal{N}=2 \) superconformal QCD, Phys. Rev. Lett. 113 (2014) 251601 [arXiv:1409.4217] [INSPIRE].CrossRefADSGoogle Scholar
  7. [7]
    E. Gerchkovitz, J. Gomis and Z. Komargodski, Sphere Partition Functions and the Zamolodchikov Metric, JHEP 11 (2014) 001 [arXiv:1405.7271] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  8. [8]
    J. Gomis and N. Ishtiaque, Kähler potential and ambiguities in 4d \( \mathcal{N}=2 \) SCFTs, JHEP 04 (2015) 169 [arXiv:1409.5325] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  9. [9]
    V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  10. [10]
    T.W. Brown, R. de Mello Koch, S. Ramgoolam and N. Toumbas, Correlators, Probabilities and Topologies in N = 4 SYM, JHEP 03 (2007) 072 [hep-th/0611290] [INSPIRE].CrossRefADSGoogle Scholar
  11. [11]
    S. Lee, S. Minwalla, M. Rangamani and N. Seiberg, Three point functions of chiral operators in D = 4, N = 4 SYM at large-N, Adv. Theor. Math. Phys. 2 (1998) 697 [hep-th/9806074] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  12. [12]
    E. D’Hoker, D.Z. Freedman and W. Skiba, Field theory tests for correlators in the AdS/CFT correspondence, Phys. Rev. D 59 (1999) 045008 [hep-th/9807098] [INSPIRE].ADSMathSciNetGoogle Scholar
  13. [13]
    E. D’Hoker, D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Extremal correlators in the AdS/CFT correspondence, hep-th/9908160 [INSPIRE].
  14. [14]
    K.A. Intriligator, Bonus symmetries of N = 4 super Yang-Mills correlation functions via AdS duality, Nucl. Phys. B 551 (1999) 575 [hep-th/9811047] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  15. [15]
    K.A. Intriligator and W. Skiba, Bonus symmetry and the operator product expansion of N = 4 Super Yang-Mills, Nucl. Phys. B 559 (1999) 165 [hep-th/9905020] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  16. [16]
    B. Eden, P.S. Howe and P.C. West, Nilpotent invariants in N = 4 SYM, Phys. Lett. B 463 (1999) 19 [hep-th/9905085] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  17. [17]
    A. Petkou and K. Skenderis, A nonrenormalization theorem for conformal anomalies, Nucl. Phys. B 561 (1999) 100 [hep-th/9906030] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  18. [18]
    P.S. Howe, C. Schubert, E. Sokatchev and P.C. West, Explicit construction of nilpotent covariants in N = 4 SYM, Nucl. Phys. B 571 (2000) 71 [hep-th/9910011] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  19. [19]
    P.J. Heslop and P.S. Howe, OPEs and three-point correlators of protected operators in N = 4 SYM, Nucl. Phys. B 626 (2002) 265 [hep-th/0107212] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  20. [20]
    M. Baggio, J. de Boer and K. Papadodimas, A non-renormalization theorem for chiral primary 3-point functions, JHEP 07 (2012) 137 [arXiv:1203.1036] [INSPIRE].CrossRefADSGoogle Scholar
  21. [21]
    J. Louis, H. Triendl and M. Zagermann, \( \mathcal{N}=4 \) supersymmetric AdS 5 vacua and their moduli spaces, JHEP 10 (2015) 083 [arXiv:1507.01623] [INSPIRE].CrossRefADSGoogle Scholar
  22. [22]
    D. Binosi and L. Theussl, JaxoDraw: A graphical user interface for drawing Feynman diagrams, Comput. Phys. Commun. 161 (2004) 76 [hep-ph/0309015] [INSPIRE].CrossRefADSGoogle Scholar
  23. [23]
    D. Binosi, J. Collins, C. Kaufhold and L. Theussl, JaxoDraw: A graphical user interface for drawing Feynman diagrams. Version 2.0 release notes, Comput. Phys. Commun. 180 (2009) 1709 [arXiv:0811.4113] [INSPIRE].CrossRefADSGoogle Scholar
  24. [24]
    S. Penati, A. Santambrogio and D. Zanon, More on correlators and contact terms in N = 4 SYM at order g 4, Nucl. Phys. B 593 (2001) 651 [hep-th/0005223] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  25. [25]
    R. Andree and D. Young, Wilson Loops in N = 2 Superconformal Yang-Mills Theory, JHEP 09 (2010) 095 [arXiv:1007.4923] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar

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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