Sigma-models having supermanifolds as target spaces. (English) Zbl 0859.58004

Schwarz, Albert

Lett. Math. Phys. 38, No. 1, 91-96 (1996).

Summary: We study a topological sigma-model (\(A\)-model) in the case when the target space is an \((m_0|m_1)\)-dimensional supermanifold. We prove under certain conditions that such a model is equivalent to an \(A\)-model having an \((m_0-m_1)\)-dimensional manifold as a target space. We use this result to prove that in the case when the target space of \(A\)-model is a complete intersection in a toric manifold, this \(A\)-model is equivalent to an \(A\)-model having a toric supermanifold as a target space.

MSC:

58A50	Supermanifolds and graded manifolds
81T70	Quantization in field theory; cohomological methods
81S99	General quantum mechanics and problems of quantization

Keywords:

sigma-model; supermanifold; toxic manifold; \(T\)-duality

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