Complexity of the AdS soliton

Reynolds, Alan P; Ross, Simon F

Abstract

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.

Citation

Reynolds, A. P., & Ross, S. F. (2018). Complexity of the AdS soliton. Classical and Quantum Gravity, 35(9), Article 095006. https://doi.org/10.1088/1361-6382/aab32d

• Journal Article Type: Article
• Acceptance Date: Mar 1, 2018
• Online Publication Date: Mar 22, 2018
• Publication Date: Mar 22, 2018
• Deposit Date: Mar 22, 2018
• Publicly Available Date: Mar 22, 2019
• Journal: Classical and Quantum Gravity
• Print ISSN: 0264-9381
• Electronic ISSN: 1361-6382
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 35
• Issue: 9
• Article Number: 095006
• DOI: https://doi.org/10.1088/1361-6382/aab32d
• Public URL: https://durham-repository.worktribe.com/output/1363659