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

作者：Schwarz Albert^*

来源：Letters in Mathematical Physics, 2016, 106(9): 1181-1197.

DOI：10.1007/s11005-016-0866-2

• Quantum field theory
• conformal theory
• AdS

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 that are invariant with respect to isometries. (Here 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.

• 出版日期2016-9