Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-05-03
JHEP 1106:114,2011
Physics
High Energy Physics
High Energy Physics - Theory
26 pages, uses harvmac; v2 with added references
Scientific paper
10.1007/JHEP06(2011)114
We present a uniform treatment of rigid supersymmetric field theories in a curved spacetime $\CM$, focusing on four-dimensional theories with four supercharges. Our discussion is significantly simpler than earlier treatments, because we use classical background values of the auxiliary fields in the supergravity multiplet. We demonstrate our procedure using several examples. For $\CM=AdS_4$ we reproduce the known results in the literature. A supersymmetric Lagrangian for $\CM=\S^4$ exists, but unless the field theory is conformal, it is not reflection positive. We derive the Lagrangian for $\CM=\S^3\times \R$ and note that the time direction $\R$ can be rotated to Euclidean signature and be compactified to $\S^1$ only when the theory has a continuous R-symmetry. The partition function on $\CM=\S^3\times \S^1$ is independent of the parameters of the flat space theory and depends holomorphically on some complex background gauge fields. We also consider R-invariant $\CN=2$ theories on $\S^3$ and clarify a few points about them.
Festuccia Guido
Seiberg Nathan
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