Abstract
We study eight fermion terms in the effective action of the ABJM model. We show the non-renormalization of v2 terms. After classifying all the possible eight fermion structures, we show that N=6 supersymmetry determines all these terms completely up to an overall constant. This confirms the one loop non-renormalization of v4 terms.
Highlights
Introduction and ConclusionRecently there have been much interests in the N = 6 superconformal U (N ) × U (N ) ChernSimons-matter theory (ABJM Model) [1] which is conjectured to be dual to M-theory on AdS4 × S7/Zk
There have been much interests in the N = 6 superconformal U (N ) × U (N ) ChernSimons-matter theory (ABJM Model) [1] which is conjectured to be dual to M-theory on AdS4 × S7/Zk
It corresponds to the effective action for the symmetry breaking, in the simplest context, of U (2) × U (2) to U (1) × U (1) × U (1) × U (1) by giving the vacuum expectation values to the scalar fields as Y A = diag (0, bA)
Summary
Nontrivial terms in the effective action have weight four among which they are related by supersymmetry In this context, the most crucial terms are those with the largest number of fermions, i.e. eight fermion terms, as they are typically determined among themselves by supersymmetry. Since there are no corrections in supercharges, the supersymmetry transformations acting on these scalar fields in eight fermion terms are the only source for nine fermion terms and they should vanish by themselves. In this way we determine the eight fermion terms modulo an overall constant. Since they come from one loop, our results naturally imply one-loop non-renormalization of the |∂b|4 terms
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