We study the effect of a relevant double-trace deformation on the partition function (and conformal anomaly) of a CFTd at large N and its dual picture in AdSd+1. Three complementary previous results are brought into full agreement with each other: bulk  and boundary  computations, as well as their formal identity . We show the exact equality between the dimensionally regularized partition functions or, equivalently, fluctuation determinants involved. A series of results then follows: (i) equality between the renormalized partition functions for all d; (ii) for all even d, correction to the conformal anomaly; (iii) for even d, the mapping entails a mixing of UV and IR effects on the same side (bulk) of the duality, with no precedent in the leading order computations; and finally, (iv) a subtle relation between overall coefficients, volume renormalization and IR-UV connection. All in all, we get a clean test of the AdS/CFT correspondence beyond the classical SUGRA approximation in the bulk and at subleading O(1) order in the large-N expansion on the boundary.
- 1/N expansion
- AdS-CFT correspondence
- Anomalies in field and string theories
ASJC Scopus subject areas
- Nuclear and High Energy Physics