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We construct and study solitonic representations of the conformal net associated to some vacuum Positive Energy Representation (PER) of a loop group LG. For the corresponding solitonic states, we prove the Quantum Null Energy Condition (QNEC) and the Bekenstein Bound. As an intermediate result, we show that a Positive Energy Representation of a loop group LG can be extended to a PER of $$H^{s}(S^1,G)$$ H s ( S 1 , G ) for $$s>3/2$$ s > 3 / 2 , where G is any compact, simple and simply connected Lie group. We also show the existence of the exponential map of the semidirect product $$LG \rtimes R$$ L G ⋊ R , with R a one-parameter subgroup of $$\mathrm{Diff}_+(S^1)$$ Diff + ( S 1 ) , and we compute the adjoint action of $$H^{s+1}(S^1,G)$$ H s + 1 ( S 1 , G ) on the stress energy tensor.

In the framework of Algebraic Quantum Field Theory, several operator algebraic notions of entanglement entropy can be associated to any couple of causally disjoint and distant spacetime regions SA and SB. In this work we show that the mutual information is finite in any local QFT verifying a modular p-nuclearity condition for some 0 < p < 1. A similar result is proved for another recently studied entanglement measure. Furthermore, if we assume conformal covariance then by comparison with other entanglement measures we can state that the mutual information satisfies lower bounds of area law type when the distance between SA and SB approaches to zero. As application, in 1 + 1-dimensional integrable models with factorizing S-matrices we study the asymptotic behavior of different entanglement measures as the distance between two causally disjoint wedges diverges.