BRS renormalization of some on-shell closed algebras of symmetry transformations. 2. N=2 and N=4 supersymmetric nonlinear sigma models
May, 199427 pages
Published in:
- Helv.Phys.Acta 67 (1994) 954-991
e-Print:
- hep-th/9406031 [hep-th]
Report number:
- PAR-LPTHE-94-11
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Abstract: (arXiv)
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 K\"ahler 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 K\"ahler 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 K\"ahler 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/94-11Note:
- 22 pages, latex, PAR/LPTHE/94-11
- sigma model: nonlinear
- supersymmetry: superfield
- dimension: 2
- transformation: Becchi-Rouet-Stora
- cohomology
- renormalization
- ghost
- anomaly
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