Abstract
It was demonstrated in [2,12] that d=4 unitary CFT's satisfy a special property: if a scalar operator with conformal dimension Δ exists in the operator spectrum, then the conformal bootstrap demands that large spin primary operators have to exist in the operator spectrum of the CFT with a conformal twist close to 2Δ+2N for any integer N. In this paper the conformal bootstrap methods in [1] that were used to find the anomalous dimension of the N=0 operators have been generalized to recursively find the anomalous dimension of all large spin operators of this class. In AdS these operators can be interpreted as the excited states of the product states of objects that were found in other works.
Highlights
Over the last 40 years there has been a large interest in conformal field theories (CFTs’)
Dimension of local operators satisfy a unitarity bound.) and a crossing symmetry, they have demonstrated that any CFT contains a sector of operators with large spin that behaves as a generalized free theory (GFT)
The operator product expansion is the most important conformal field theory technique applied in this paper, as all results obtained are derived from this principle
Summary
Over the last 40 years there has been a large interest in conformal field theories (CFTs’). The result is that as was predicted in [1] [2] that do operators have to exist with a conformal twist that lies in a region around 2∆ but there has to exist a tower of limit points in twist space at 2∆ + 2N for any integer N This supports the conclusion that every CFT has a region which behaves as a GFT. Beyond that the main focus of this paper is the anomalous dimensions associated with these higher order conformal blocks These have been calculated and have been shown to just as for the N = 0 case to be inversely proportional to spin.
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