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2PI effective action and evolution equations of \(\mathcal{N} = 4\) super Yang–Mills

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Abstract

We employ nPI effective action techniques to study \(\mathcal{N}=4\) super Yang–Mills, and write down the 2PI effective action of the theory to two-loop order in the symmetric phase. We also supply the evolution equations of two-point correlators within the theory.

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Acknowledgements

We would like to thank K. Skenderis and M. Taylor for initially suggesting this problem and for many useful discussions. We would also like to thank J. Smit for discussions. This work is part of a research program which is financially supported by the ‘Nederlandse Organisatie voor Wetenschappelijk Onderzoek’ (NWO). J.S. and M.S. acknowledge support via the NWO Vici grant of K. Skenderis.

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Authors and Affiliations

  1. Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Postbus 94485, 1090 GL, Amsterdam, The Netherlands

    Jelena Smolic & Milena Smolic

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  1. Jelena Smolic
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Correspondence to Jelena Smolic.

Appendix

Appendix

The corrections to the gluon propagator in \(\mathcal{N}=4\) SYM are given by the six diagrams in Fig. 4. Thus, we have

(A.1)
(A.2)

Fermion propagator corrections are shown in Fig. 5 and yield

(A.3)
(A.4)

Finally, the single ghost propagator correction is given in Fig. 6, with

(A.5)
(A.6)
Fig. 4
figure 4

Corrections to gluon propagator

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Fig. 5
figure 5

Corrections to fermion propagator

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Fig. 6
figure 6

Correction to ghost propagator

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Smolic, J., Smolic, M. 2PI effective action and evolution equations of \(\mathcal{N} = 4\) super Yang–Mills. Eur. Phys. J. C 72, 2106 (2012). https://doi.org/10.1140/epjc/s10052-012-2106-y

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