Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-12-17
Phys.Lett. B375 (1996) 135-140
Physics
High Energy Physics
High Energy Physics - Theory
11 pages, Latex
Scientific paper
10.1016/0370-2693(96)00197-9
We consider the $N\!=\!1$ supersymmetric $\sigma$-model and we examine the transformation properties of the partition function under target-space duality. Contrary to what one would expect, we find that it is not, in general, invariant. In fact, besides the dilaton shift emerging from the Jacobian of the duality transformation of the bosonic part, there also exist a Jacobian for the fermionic part since fermions are also transform under the duality process. The latter is just the parity of the spin structure of the word sheet and since it cannot be compensated, the dual theory is not equvalent to the original one.
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