Holographic dual effective field theory for an SYK model
arxiv(2024)
Abstract
We derive an emergent holographic dual description for an SYK model, where
the renormalization group (RG) flows of collective bi-local fields appear
manifestly in the bulk effective action with an emergent extradimension. This
holographic dual effective field theory reproduces 1/N quantum corrections
given by the Schwarzian action when we take the UV limit in the bulk effective
action. Going into the IR regime in the extradimension, we observe that the
field theoretic 1/N, 1/N^2, ... quantum corrections are resummed in the
all-loop order and reorganized to form a holographic dual effective field
theory in a large N fashion living on the one-higher dimensional spacetime.
Taking the large N limit in the holographic dual effective field theory, we
obtain nonlinearly coupled second-order bulk differential equations of motion
for the three bi-local order-parameter fields of fermion self-energy, Green's
function, and polarization function. Here, both UV and IR boundary conditions
are derived self-consistently from the boundary effective action. We solve
these highly intertwined nonlinear differential equations based on the so
called matching method. Our ansatz for the bi-local order-parameter fields
coincide with the conformally invariant solution of the field theoretic large
N limit in the UV limit, but their overall coefficients RG-flow along the
extradimensional space, respectively, reflecting effects of higher-order
quantum corrections. As a result, we find an insulating behavior, where the
self-energy diverges at IR. To confirm this insulating physics, we investigate
thermodynamics. We obtain an effective free energy functional in terms of such
bi-local dual order-parameter fields, which satisfy the Hamilton-Jacobi
equation of the holographic dual effective field theory. ...
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