Moduli anomalies and local terms in the operator product expansion

  • Adam Schwimmer
  • Stefan TheisenEmail author
Open Access
Regular Article - Theoretical Physics


Local terms in the Operator Product Expansion in Superconformal Theories with extended supersymmetry are identified. Assuming a factorized structure for these terms their contributions are discussed.


Anomalies in Field and String Theories Conformal Field Theory Extended Supersymmetry 


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.


  1. [1]
    A. Bzowski, P. McFadden and K. Skenderis, Implications of conformal invariance in momentum space, JHEP 03 (2014) 111 [arXiv:1304.7760] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    A. Bzowski, P. McFadden and K. Skenderis, Scalar 3-point functions in CFT: renormalisation, β-functions and anomalies, JHEP 03 (2016) 066 [arXiv:1510.08442] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    A. Bzowski, P. McFadden and K. Skenderis, Renormalised 3-point functions of stress tensors and conserved currents in CFT, arXiv:1711.09105 [INSPIRE].
  4. [4]
    A. Dymarsky et al., Scale invariance, conformality and generalized free fields, JHEP 02 (2016) 099 [arXiv:1402.6322] [INSPIRE].
  5. [5]
    Y. Nakayama, On the realization of impossible anomalies, arXiv:1804.02940 [INSPIRE].
  6. [6]
    D. Kutasov, Geometry on the space of conformal field theories and contact terms, Phys. Lett. B 220 (1989) 153 [INSPIRE].
  7. [7]
    J. Gomis et al., Anomalies, conformal manifolds and spheres, JHEP 03 (2016) 022 [arXiv:1509.08511] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    S. Deser, M.J. Duff and C.J. Isham, Nonlocal conformal anomalies, Nucl. Phys. B 111 (1976) 45 [INSPIRE].
  9. [9]
    S. Deser and A. Schwimmer, Geometric classification of conformal anomalies in arbitrary dimensions, Phys. Lett. B 309 (1993) 279 [hep-th/9302047] [INSPIRE].
  10. [10]
    D. Friedan and A. Konechny, Curvature formula for the space of 2D conformal field theories, JHEP 09 (2012) 113 [arXiv:1206.1749] [INSPIRE].
  11. [11]
    J. Gomis et al., Shortening anomalies in supersymmetric theories, JHEP 01 (2017) 067 [arXiv:1611.03101] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    S.M. Kuzenko, Super-Weyl anomalies in N = 2 supergravity and (non)local effective actions, JHEP 10 (2013) 151 [arXiv:1307.7586] [INSPIRE].
  13. [13]
    D. Butter, B. de Wit, S.M. Kuzenko and I. Lodato, New higher-derivative invariants in N = 2 supergravity and the Gauss-Bonnet term, JHEP 12 (2013) 062 [arXiv:1307.6546] [INSPIRE].
  14. [14]
    H. Osborn, Weyl consistency conditions and a local renormalization group equation for general renormalizable field theories, Nucl. Phys. B 363 (1991) 486 [INSPIRE].
  15. [15]
    J. Erdmenger and H. Osborn, Conserved currents and the energy momentum tensor in conformally invariant theories for general dimensions, Nucl. Phys. B 483 (1997) 431 [hep-th/9605009] [INSPIRE].
  16. [16]
    S.J. Gates, Jr., M.T. Grisaru and M.E. Wehlau, A Study of general 2D, N = 2 matter coupled to supergravity in superspace, Nucl. Phys. B 460 (1996) 579 [hep-th/9509021] [INSPIRE].
  17. [17]
    N. Seiberg, Y. Tachikawa and K. Yonekura, Anomalies of duality groups and extended conformal manifolds, arXiv:1803.07366 [INSPIRE].
  18. [18]
    Y. Tachikawa and K. Yonekura, Anomalies involving the space of couplings and the Zamolodchikov metric, JHEP 12 (2017) 140 [arXiv:1710.03934] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    H. Osborn and A.C. Petkou, Implications of conformal invariance in field theories for general dimensions, Annals Phys. 231 (1994) 311 [hep-th/9307010] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    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].
  21. [21]
    H. Osborn, Local couplings and SL(2, ℝ) invariance for gauge theories at one loop, Phys. Lett. B 561 (2003) 174 [hep-th/0302119] [INSPIRE].
  22. [22]
    K. Hori et al., Mirror symmetry, Clay Mathematics Monographs volume 1, American Mathematical Society, U.S.A. (2003).Google Scholar
  23. [23]
    I.L. Buchbinder, N.G. Pletnev and A.A. Tseytlin, “Induced” N = 4 conformal supergravity, Phys. Lett. B 717 (2012) 274 [arXiv:1209.0416] [INSPIRE].
  24. [24]
    F. Ciceri and B. Sahoo, Towards the full N = 4 conformal supergravity action, JHEP 01 (2016) 059 [arXiv:1510.04999] [INSPIRE].
  25. [25]
    D. Butter, F. Ciceri, B. de Wit and B. Sahoo, Construction of all N = 4 conformal supergravities, Phys. Rev. Lett. 118 (2017) 081602 [arXiv:1609.09083] [INSPIRE].

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Weizmann Institute of ScienceRehovotIsrael
  2. 2.Max-Planck-insitut für Gravitationsphysik, Albert-Einstein-InstitutGolmGermany

Personalised recommendations