Loop Groups and QNEC
| Autor: | Lorenzo Panebianco |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
Semidirect product Pure mathematics Bekenstein bound relative entropy 010102 general mathematics Null (mathematics) FOS: Physical sciences Lie group Statistical and Nonlinear Physics Mathematical Physics (math-ph) 01 natural sciences Exponential map (Lie theory) Loop groups Loop (topology) Loop group 0103 physical sciences Simply connected space positive energy representations 010307 mathematical physics 0101 mathematics Mathematical Physics |
| Zdroj: | Communications in Mathematical Physics. 387:397-426 |
| ISSN: | 1432-0916 0010-3616 |
| DOI: | 10.1007/s00220-021-04170-3 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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