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New higher-derivative invariants in N = 2 supergravity and the Gauss-Bonnet term

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Abstract

A new class of N = 2 locally supersymmetric higher-derivative invariants is constructed based on logarithms of conformal primary chiral superfields. They characteristically involve a coupling to \( {{\mathcal{R}}_{uv}}^2-\frac{1}{3}{{\mathcal{R}}^2} \), which equals the non-conformal part of the Gauss-Bonnet term. Upon combining one such invariant with the known supersymmetric version of the square of the Weyl tensor, one obtains the supersymmetric extension of the Gauss-Bonnet term. The construction is carried out in the context of both conformal superspace and the superconformal multiplet calculus. The new class of supersymmetric invariants resolves two open questions. The first concerns the proper identification of the 4D supersymmetric invariants that arise from dimensional reduction of the 5D mixed gauge-gravitational Chern-Simons term. The second is why the pure Gauss-Bonnet term without supersymmetric completion has reproduced the correct result in calculations of the BPS black hole entropy in certain models.

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Authors and Affiliations

  1. Nikhef, Science Park 105, 1098 XG, Amsterdam, The Netherlands

    Daniel Butter, Bernard de Wit & Ivano Lodato

  2. Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE, Utrecht, The Netherlands

    Bernard de Wit

  3. School of Physics M012, The University of Western Australia, 35 Stirling Highway, Crawley, W.A., 6009, Australia

    Sergei M. Kuzenko

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  1. Daniel Butter
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  2. Bernard de Wit
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  3. Sergei M. Kuzenko
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  4. Ivano Lodato
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Correspondence to Daniel Butter.

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ArXiv ePrint: 1307.6546

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Butter, D., de Wit, B., Kuzenko, S.M. et al. New higher-derivative invariants in N = 2 supergravity and the Gauss-Bonnet term. J. High Energ. Phys. 2013, 62 (2013). https://doi.org/10.1007/JHEP12(2013)062

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