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Axiomatic Conformal Theory in Dimensions >2 and AdS/CT Correspondence

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Abstract

We formulate axioms of conformal theory (CT) in dimensions >2 modifying Segal’s axioms for two-dimensional CFT. (In the definition of higher-dimensional CFT, one includes also a condition of existence of energy-momentum tensor.) We use these axioms to derive the AdS/CT correspondence for local theories on AdS. We introduce a notion of weakly local quantum field theory and construct a bijective correspondence between conformal theories on the sphere S d and weakly local quantum field theories on \({H^{d+1}}\) that are invariant with respect to isometries. (Here \({H^{d+1}}\) denotes hyperbolic space = Euclidean AdS space.) We give an expression of AdS correlation functions in terms of CT correlation functions. The conformal theory has conserved energy-momentum tensor iff the AdS theory has graviton in its spectrum.

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  1. Department of Mathematics, University of California, Davis, CA, 95616, USA

    Albert Schwarz

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  1. Albert Schwarz
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Correspondence to Albert Schwarz.

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To Sasha Polyakov with admiration and love

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Schwarz, A. Axiomatic Conformal Theory in Dimensions >2 and AdS/CT Correspondence. Lett Math Phys 106, 1181–1197 (2016). https://doi.org/10.1007/s11005-016-0866-2

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  • DOI: https://doi.org/10.1007/s11005-016-0866-2

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