Abstract
The partition function of four-dimensional \( \mathcal{N} \) = 2 superconformal field theories on S4 computes the exact Kähler potential on the space of exactly marginal couplings [1]. We present a new elementary proof of this result using supersymmetry Ward identities. The partition function is a section rather than a function, and is subject to ambiguities coming from Kähler transformations acting on the Kähler potential. This ambiguity is realized by a local supergravity counterterm in the underlying SCFT. We provide an explicit construction of the Kähler ambiguity counterterm in the four dimensional \( \mathcal{N} \) = 2 off-shell supergravity theory that admits S4 as a supersymmetric background.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. Gerchkovitz, J. Gomis and Z. Komargodski, Sphere partition functions and the Zamolodchikov metric, JHEP 11 (2014) 001 [arXiv:1405.7271] [INSPIRE].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
J. Gomis and S. Lee, Exact Kähler potential from gauge theory and mirror symmetry, JHEP 04 (2013) 019 [arXiv:1210.6022] [INSPIRE].
H. Jockers, V. Kumar, J.M. Lapan, D.R. Morrison and M. Romo, Two-Sphere Partition Functions and Gromov-Witten Invariants, Commun. Math. Phys. 325 (2014) 1139 [arXiv:1208.6244] [INSPIRE].
F. Benini and S. Cremonesi, Partition Functions of \( \mathcal{N} \) = (2,2) Gauge Theories on S 2 and Vortices, Commun. Math. Phys. 334 (2015) 1483 [arXiv:1206.2356] [INSPIRE].
N. Doroud, J. Gomis, B. Le Floch and S. Lee, Exact results in D = 2 supersymmetric gauge theories, JHEP 05 (2013) 093 [arXiv:1206.2606] [INSPIRE].
N. Doroud and J. Gomis, Gauge theory dynamics and Kähler potential for Calabi-Yau complex moduli, JHEP 1312 (2013) 99 [arXiv:1309.2305] [INSPIRE].
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].
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].
P. Breitenlohner and M.F. Sohnius, An Almost Simple Off-shell Version of SU(2) Poincaré Supergravity, Nucl. Phys. B 178 (1981) 151 [INSPIRE].
A.V. Proeyen, \( \mathcal{N} \) = 2 supergravity in d = 4, 5, 6 and its matter couplings, http://itf.fys.kuleuven.be/toine/LectParis.pdf.
N. Seiberg, Naturalness versus supersymmetric nonrenormalization theorems, Phys. Lett. B 318 (1993) 469 [hep-ph/9309335] [INSPIRE].
G. Festuccia and N. Seiberg, Rigid supersymmetric theories in curved superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].
D.Z. Freedman and A.V. Proeyen, Supergravity, Cambridge University Press, New York, U.S.A. (2012).
B. de Wit, J.W. van Holten and A. Van Proeyen, Structure of N = 2 Supergravity, Nucl. Phys. B 184 (1981) 77 [INSPIRE].
N. Hama and K. Hosomichi, Seiberg-Witten theories on ellipsoids, JHEP 09 (2012) 033 [arXiv:1206.6359] [INSPIRE].
C. Klare and A. Zaffaroni, Extended supersymmetry on curved spaces, JHEP 10 (2013) 218 [arXiv:1308.1102] [INSPIRE].
S. Ferrara and P. van Nieuwenhuizen, Consistent supergravity with complex spin 3/2 gauge fields, Phys. Rev. Lett. 37 (1976) 1669 [INSPIRE].
B. de Wit, J.W. van Holten and A. Van Proeyen, Transformation Rules of N = 2 Supergravity Multiplets, Nucl. Phys. B 167 (1980) 186 [INSPIRE].
B. de Wit and J.W. van Holten, Multiplets of Linearized SO(2) Supergravity, Nucl. Phys. B 155 (1979) 530 [INSPIRE].
B. de Wit, R. Philippe and A. Van Proeyen, The Improved Tensor Multiplet in N = 2 Supergravity, Nucl. Phys. B 219 (1983) 143 [INSPIRE].
M. de Roo, J.W. van Holten, B. de Wit and A. Van Proeyen, Chiral Superfields in N = 2 Supergravity, Nucl. Phys. B 173 (1980) 175 [INSPIRE].
G. Lopes Cardoso, B. de Wit and T. Mohaupt, Corrections to macroscopic supersymmetric black hole entropy, Phys. Lett. B 451 (1999) 309 [hep-th/9812082] [INSPIRE].
D. Butter and S.M. Kuzenko, New higher-derivative couplings in 4D N = 2 supergravity, JHEP 03 (2011) 047 [arXiv:1012.5153] [INSPIRE].
B. de Wit, S. Katmadas and M. van Zalk, New supersymmetric higher-derivative couplings: full N = 2 superspace does not count!, JHEP 01 (2011) 007 [arXiv:1010.2150] [INSPIRE].
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].
S.M. Kuzenko, Super-Weyl anomalies in N = 2 supergravity and (non)local effective actions, JHEP 10 (2013) 151 [arXiv:1307.7586] [INSPIRE].
D. Butter, B. de Wit and I. Lodato, Non-renormalization theorems and N = 2 supersymmetric backgrounds, JHEP 03 (2014) 131 [arXiv:1401.6591] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1409.5325
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Gomis, J., Ishtiaque, N. Kähler potential and ambiguities in 4d \( \mathcal{N} \) = 2 SCFTs. J. High Energ. Phys. 2015, 169 (2015). https://doi.org/10.1007/JHEP04(2015)169
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2015)169