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A NOTE ON SCALAR FIELD THEORY IN AdS₃/CFT₂

PABLO MINCES

Instituto de Astronomía y Física del Espacio (IAFE), C.C.67 – Suc. 28, 1428 Buenos Aires, Argentina

https://doi.org/10.1142/S0217751X10048500Cited by:0 (Source: Crossref)

Abstract

We consider a scalar field theory in AdS_d+1, and introduce a formalism on surfaces at equal values of the radial coordinate. In particular, we define the corresponding conjugate momentum. We compute the Noether currents for isometries in the bulk, and perform the asymptotic limit on the corresponding charges. We then introduce Poisson brackets at the border, and show that the asymptotic values of the bulk scalar field and the conjugate momentum transform as conformal fields of scaling dimensions Δ_- and Δ₊, respectively, where Δ_± are the standard parameters giving the asymptotic behavior of the scalar field in AdS. Then we consider the case d = 2, where we obtain two copies of the Virasoro algebra, with vanishing central charge at the classical level. An AdS₃/CFT₂ prescription, giving the commutators of the boundary CFT in terms of the Poisson brackets at the border, arises in a natural way. We find that the boundary CFT is similar to a generalized ghost system. We introduce two different ground states, and then compute the normal ordering constants and quantum central charges, which depend on the mass of the scalar field and the AdS radius. We discuss certain implications of the results.

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