Abstract
We explore properties of path integral complexity in field theories on time dependent backgrounds using its dual description in terms of Hartle-Hawking wavefunctions. In particular, we consider boundary theories with time dependent couplings which are dual to Kasner-AdS metrics in the bulk with a time dependent dilaton. We show that holographic path integral complexity decreases as we approach the singularity, consistent with earlier results from holographic complexity conjectures. Furthermore, we find examples where the complexity becomes universal i.e., independent of the Kasner exponents, but the properties of the path integral tensor networks depend sensitively on this data.
Highlights
We explore properties of path integral complexity in field theories on time dependent backgrounds using its dual description in terms of Hartle-Hawking wavefunctions
We show that holographic path integral complexity decreases as we approach the singularity, consistent with earlier results from holographic complexity conjectures
The Path Integral Optimization [6, 7] amounts to minimizing this proportionality factor that is defined as the exponent of the Path Integral Complexity action
Summary
We will briefly review some relevant aspects of the holographic path integral optimization in Lorentzian bulk following [33, 34]. The region M of our interest contains two pieces of the boundary (see figure 1 in [33, 34]): (i) a cutoff time-like surface Σ at z = and (ii) a co-dimension-1 surface Q which may be specified by an equation z = f (t, x). This surface can be space-like or time-like. To evaluate Hartle-Hawking wavefunctions we will need a modified Hawyard term4 [65]. The Lorentzian Hartle-Hawking wavefunctional (which may be thought of as a transition amplitude) is given by a path integral.
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