The origin of the SYK model and ER=EPR in disorder field theory.

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Abstract

We first show how spatially all to all interaction can be induced out of the local action quantum mechanically in the presence of the disorder.

Then we show that if we consider disorder   in Lorentzian signature, there is a tunneling effect given by a time-non-local interaction, leading to the wormhole picture in disorder field theory. We suggest that the two point function of the random coupling play the role of the wormhole.

In large N limit, for a given diagram in quenched picture with field theory wormhole, there is a corresponding unique Feynman diagram in the effective theory of the annealed avearage whose basic time-non-local vertex creates entangled pair of particle sets.  We call this as disorder field theory version of ER=EPR.

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