Loop Groups and QNEC
Abstract
We investigate some analytical properties of loop group models, showing that a Positive Energy Representation (PER) of a loop group LG can be extended to a PER of H3/2(S1,G) for any compact, simple and simply connected Lie group G. We then explicitly compute the adjoint action of H5/2(S1,G) on the stress energy tensor and we use these results to prove the Quantum Null Energy Condition (QNEC) and the Bekenstein Bound for states obtained by applying a Sobolev loop to the vacuum. We also give a simpler proof of these last results in the case G=SU(n). Finally, we construct and study solitonic representations of the loop group conformal nets induced by the conjugation by a loop with a discontinuity in -1.
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