Partition functions and double-trace deformations in AdS/CFT
Feb, 200718 pages
Published in:
- JHEP 05 (2007) 046
e-Print:
- hep-th/0702163 [hep-th]
Report number:
- HU-EP-07-04
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Abstract:
We study the effect of a relevant double-trace deformation on the partition function (and conformal anomaly) of a CFT at large N and its dual picture in AdS. 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, fluctuational 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.- AdS/CFT
- IR-UV connection
- conformal anomaly
- space-time: anti-de Sitter
- field theory: conformal
- any-dimensional
- expansion 1/N
- field theory: deformation
- partition function
- effective action
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