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

Abstract

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 + m_2, 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(m_1^2), J(m_2^2) and J(m_3^2), 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(m_1^2 m_2^2 +m_1^2 m_3^2 +m_2^2 m_3^2) > m_1^4 +m_2^4 +m_3^4. 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 Kahler potential and F^4 term. Our considerations are restricted to the case of beta real.

arXiv comment42 pages, latex, 1 eps figure; V2: references added

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Cited by in corpus (4)

• Two-loop low-energy effective action in Abelian supersymmetric Chern-Simons matter models
• On the non-planar beta-deformed N=4 super-Yang-Mills theory
• Studies of low-energy effective actions in supersymmetric field theories
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