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Non-Local Effects of Multi-Trace Deformations in the AdS/CFT Correspondence

Ofer Aharony·Micha Berkooz·Boaz Katz
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Abstract

The AdS/CFT correspondence relates deformations of the CFT by "multi-trace operators" to "non-local string theories". The deformed theories seem to have non-local interactions in the compact directions of space-time; in the gravity approximation the deformed theories involve modified boundary conditions on the fields which are explicitly non-local in the compact directions. In this note we exhibit a particular non-local property of the resulting space-time theory. We show that in the usual backgrounds appearing in the AdS/CFT correspondence, the commutator of two bulk scalar fields at points with a large enough distance between them in the compact directions and a small enough time-like distance between them in AdS vanishes, but this is not always true in the deformed theories. We discuss how this is consistent with causality.

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Ofer Aharony, Micha Berkooz, Boaz Katz. 2005-09-19. Non-Local Effects of Multi-Trace Deformations in the AdS/CFT Correspondence. https://doi.org/10.1088/1126-6708%2F2005%2F10%2F097

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