Modifying the sum over topological sectors and constraints on supergravity
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The standard lore about the sum over topological sectors in quantum field theory is that locality and cluster decomposition uniquely determine the sum over such sectors, thus leading to the usual θ-vacua. We show that without changing the local degrees of freedom, a theory can be modified such that the sum over instantons should be restricted; e.g. one should include only instanton numbers which are divisible by some integer p. This conclusion about the configuration space of quantum field theory allows us to carefully reconsider the quantization of parameters in supergravity. In particular, we show that FI-terms and nontrivial Kähler forms are quantized. This analysis also leads to a new derivation of recent results about linearized supergravity.
KeywordsSolitons Monopoles and Instantons Gauge Symmetry Discrete and Finite Symmetries Supergravity Models
- E. Witten, unpublished.Google Scholar
- J. Distler and B. Wecht, unpublished, mentioned in http://golem.ph.utexas.edu/∼distler/blog/archives/002180.html.