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Complexity of the AdS soliton.

Reynolds, Alan P. and Ross, Simon F. (2018) 'Complexity of the AdS soliton.', Classical and quantum gravity., 35 (9). 095006.


We consider the holographic complexity conjectures in the context of the AdS soliton, which is the holographic dual of the ground state of a field theory on a torus with antiperiodic boundary conditions for fermions on one cycle. The complexity is a non-trivial function of the size of the circle with antiperiodic boundary conditions, which sets an IR scale in the dual geometry. We find qualitative differences between the calculations of complexity from spatial volume and action (CV and CA). In the CV calculation, the complexity for antiperiodic boundary conditions is smaller than for periodic, and decreases monotonically with increasing IR scale. In the CA calculation, the complexity for antiperiodic boundary conditions is larger than for periodic, and initially increases with increasing IR scale, eventually decreasing to zero as the IR scale becomes of order the UV cutoff. We compare these results to a simple calculation for free fermions on a lattice, where we find the complexity for antiperiodic boundary conditions is larger than for periodic.

Item Type:Article
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Publisher statement:This is an author-created, un-copyedited version of an article accepted for publication/published in Classical and quantum gravity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at [
Date accepted:01 March 2018
Date deposited:23 March 2018
Date of first online publication:22 March 2018
Date first made open access:22 March 2019

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