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The Markov property of the CFT vacuum and the entropic a-theorem

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A state is called a Markov state if it fulfil the important condition of saturating the Strong Subadditivity inequality. I will show how the vacuum state of any relativistic QFT is a Markov state when reduced to certain geometric regions of spacetime. A characterisation of this regions will be presented as well as two independent proofs of the Markov condition in QFT. 

For the CFT vacuum, the Markov property is the key ingredient to prove the a-theorem (irreversibility of the RG flow in QFT in d=4 spacetime dimensions) using vacuum entanglement entropy. This extends the entropic proofs of the c and F theorems in dimensions d=2 and d=3 and gives a unified picture of all the known irreversibility theorems in QFT. 

I will also comment on the relation of this Markov property with the unitarity bound and other information theory inequalities.