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Résumé |
The two-point function of exactly marginal operators leads to a universal contribution to the trace
anomaly in even dimensions. We study some aspects of this trace anomaly, emphasizing its
interpretation as a sigma model, whose target space M is the space of conformal field theories (a.k.a.
the conformal manifold). When the underlying quantum field theory is supersymmetric, this sigma
model has to be appropriately supersymmetrized. As examples, we consider in some detail N =
(2,2)supersymmetric theories in d = 2 and N = 2 supersymmetric theories in d = 4. This reasoning
leads to new information about the conformal manifolds of these theories, for example, we show that
the manifold is Kahler-Hodge and we further argue that it has vanishing Kahler class.We also show
that the relation between the sphere partition functions and the Kahler potential of M follows
immediately from the appropriate sigma models that we construct. We discuss further applications. |
