tt∗ equations, localization and exact chiral rings in 4d N = 2 SCFTs

Baggio, Marco; Niarchos, Vasilis; Papadodimas, Kyriakos

Abstract

We compute exact 2- and 3-point functions of chiral primaries in four-dimensional NN = 2 superconformal field theories, including all perturbative and instanton contributions. We demonstrate that these correlation functions are nontrivial and satisfy exact differential equations with respect to the coupling constants. These equations are the analogue of the tt* equations in two dimensions. In the SU(2) NN = 2 SYM theory coupled to 4 hypermultiplets they take the form of a semi-infinite Toda chain. We provide the complete solution of this chain using input from supersymmetric localization. To test our results we calculate the same correlation functions independently using Feynman diagrams up to 2-loops and we find perfect agreement up to the relevant order. As a spin-off, we perform a 2-loop check of the recent proposal of arXiv:1405.7271 that the logarithm of the sphere partition function in NN = 2 SCFTs determines the Kähler potential of the Zamolodchikov metric on the conformal manifold. We also present the tt* equations in general SU(N) NN = 2 superconformal QCD theories and comment on their structure and implications.

Citation

Baggio, M., Niarchos, V., & Papadodimas, K. (2015). tt∗ equations, localization and exact chiral rings in 4d N = 2 SCFTs. Journal of High Energy Physics, 2015(2), Article 122. https://doi.org/10.1007/jhep02%282015%29122

• Journal Article Type: Article
• Acceptance Date: Jan 12, 2015
• Online Publication Date: Feb 18, 2015
• Publication Date: Feb 18, 2015
• Deposit Date: Oct 15, 2016
• Publicly Available Date: Feb 3, 2017
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2015
• Issue: 2
• Article Number: 122
• DOI: https://doi.org/10.1007/jhep02%282015%29122
• Public URL: https://durham-repository.worktribe.com/output/1374527