Effective action of β-deformed N=4 SYM theory: Farewell to two-loop BPS diagrams

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Within the background field approach, all two-loop sunset vacuum diagrams, which occur in the Coulomb branch of N = 2 superconformal theories (including N = 4 SYM), obey the BPS condition m(3) = m(1) + m2, where the masses are generated by the scalars belonging to a background N = 2 vector multiplet. These diagrams can be evaluated exactly, and prove to be homogeneous quadratic functions of the one-loop tadpoles J(m2/1), J(m2/2) and J(m2/3) with the coefficients being rational functions of the squared masses. We demonstrate that, if one switches on the beta-deformation of the N = 4 SYM theory, the BPS condition no longer holds. and then generic two-loop sunset vacuum diagrams with three non-vanishing masses prove to be characterized by the following property: 2(m2/1m2/2 + m2/1m2/3 + m2/2m2/3) > m4/1 + m4/2 + m4/3. In the literature, there exist several techniques to compute such diagrams. For the beta-deformed N = 4 SYM theory, we carry out explicit two-loop calculations of the Kabler potential and F-4 term. Our considerations are restricted to the case of real. (C) 2007 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)159-191
JournalNuclear Physics B
Issue number1-2
Publication statusPublished - 2007


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