Comments on contact terms and conformal manifolds in the AdS/CFT correspondence,Progress of Theoretical and Experimental Physics

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Comments on contact terms and conformal manifolds in the AdS/CFT correspondence
Progress of Theoretical and Experimental Physics Pub Date : 2020-11-25 , DOI: 10.1093/ptep/ptaa164
Tadakatsu Sakai _{1,

2} , Masashi Zenkai ₁

Affiliation

We study the contact terms that appear in the correlation functions of exactly marginal operators using the AdS/CFT correspondence. It is known that CFT with an exactly marginal deformation requires the existence of the contact terms with their coefficients having a geometrical interpretation in the context of conformal manifolds. We show that the AdS/CFT correspondence captures properly the mathematical structure of the correlation functions that is expected from the CFT analysis. For this purpose, we employ holographic RG to formulate a most general setup in the bulk for describing an exactly marginal deformation. The resultant bulk equations of motion are nonlinear and solved perturbatively to obtain the on-shell action. We compute three- and four-point functions of the exactly marginal operators using the GKP-Witten prescription, and show that they match with the expected results precisely. The cut-off surface prescription in the bulk serves as a regularization scheme for conformal perturbation theory in the boundary CFT. As an application, we examine a double OPE limit of the four-point functions. The anomalous dimensions of double trace operators are written in terms of the geometrical data of a conformal manifold.

更新日期：2020-11-25

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