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B.R.S. renormalisation of some on-shell closed algebras of symmetry transformations : N=2 and 4 supersymmetric non-linear sigma models

Guy Bonneau
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Abstract

We analyse with the algebraic, regularisation independant, cohomological B.R.S. methods, the renormalisability of torsionless N=2 and N= 4 supersymmetric non-linear $\si$ models built on Kähler spaces. Surprisingly enough with respect to the common wisdom, in the case of N=2 supersymmetry, we obtain an anomaly candidate, at least in the compact Kähler Ricci-flat case. If its coefficient does differ from zero, such anomaly would imply the breaking of global N=2 supersymmetry and get into trouble some schemes of superstring compactification as such non-linear $\si$ models offer candidates for the superstring vacuum state. In the compact homogeneous Kähler case, as expected, the anomaly candidate disappears. The same phenomena occurs when one enforces N=4 supersymmetry : in that case, we obtain the first rigorous proof of the expected all-orders renormalisability -`` in the space of metrics"- of the corresponding non-linear $\si$ models. PAR/LPTHE/94-11

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Guy Bonneau. 1994-06-06. B.R.S. renormalisation of some on-shell closed algebras of symmetry transformations : N=2 and 4 supersymmetric non-linear sigma models. https://arxiv.org/abs/hep-th/9406031

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