期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 10, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP10(2013)025
关键词
Supersymmetric gauge theory; Anomalies in Field and String Theories; AdS-CFT Correspondence; Differential and Algebraic Geometry
资金
- STFC [ST/J002798/1]
- ERC [304806]
- EPSRC [EP/D07150X/3]
- European Research Council (ERC) [304806] Funding Source: European Research Council (ERC)
- Engineering and Physical Sciences Research Council [EP/D07150X/3] Funding Source: researchfish
- Science and Technology Facilities Council [ST/J002798/1] Funding Source: researchfish
- EPSRC [EP/D07150X/3] Funding Source: UKRI
- STFC [ST/J002798/1] Funding Source: UKRI
We study the consequences of unbroken rigid supersymmetry of fourdimensional field theories placed on curved manifolds. We show that in Lorentzian signature the background vector field coupling to the R-current is determined by the Weyl tensor of the background metric. In Euclidean signature, the same holds if two supercharges of opposite R-charge are preserved, otherwise the (anti-) self-dual part of the vector fieldstrength is fixed by the Weyl tensor. As a result of this relation, the trace and R-current anomalies of superconformal field theories simplify, with the trace anomaly becoming purely topological. In particular, in Lorentzian signature, or in the presence of two Euclidean supercharges of opposite R-charge, supersymmetry of the background implies that the term proportional to the central charge c vanishes, both in the trace and R-current anomalies. This is equivalent to the vanishing of a superspace Weyl invariant. We comment on the implications of our results for holography.
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