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Displacement Operators and Constraints on Boundary Central Charges (1709.07431v1)
Published 21 Sep 2017 in hep-th and cond-mat.str-el
Abstract: Boundary conformal field theories have several additional terms in the trace anomaly of the stress tensor associated purely with the boundary. We constrain the corresponding boundary central charges in three- and four-dimensional conformal field theories in terms of two- and three-point correlation functions of the displacement operator. We provide a general derivation by comparing the trace anomaly with scale dependent contact terms in the correlation functions. We conjecture a relation between the a-type boundary charge in three dimensions and the stress tensor two-point function near the boundary. We check our results for several free theories.