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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On relative entropy and global index


Author: Feng Xu
Journal: Trans. Amer. Math. Soc. 373 (2020), 3515-3539
MSC (2010): Primary 46L37; Secondary 81R15
DOI: https://doi.org/10.1090/tran/7989
Published electronically: February 19, 2020
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Abstract: Certain duality of relative entropy can fail for a chiral conformal net with nontrivial representations. In this paper we quantify such statement by defining a quantity which measures the failure of such duality, and identify this quantity with relative entropy and global index associated with multi-interval subfactors for a large class of conformal nets. As a consequence of such new formulation we show that the duality holds for a large class of conformal nets if and only if they are holomorphic. The same argument also applies to CFT in two dimensions. In particular we show that the duality holds for a large class of CFT in two dimensions if and only if they are modular invariant. We also obtain various limiting properties of relative entropies which naturally follow from our formula.


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Additional Information

Feng Xu
Affiliation: Department of Mathematics, University of California at Riverside, Riverside, California 92521
Email: xufeng@math.ucr.edu

DOI: https://doi.org/10.1090/tran/7989
Received by editor(s): January 4, 2019
Received by editor(s) in revised form: May 30, 2019, and September 2, 2019
Published electronically: February 19, 2020
Additional Notes: This work was supported in part by NSF grant DMS-1764157
Article copyright: © Copyright 2020 American Mathematical Society