Complexity and shock wave geometries

Douglas Stanford, Leonard Susskind
2014 Physical Review D  
In this paper we refine a conjecture relating the time-dependent size of an Einstein-Rosen bridge to the computational complexity of the of the dual quantum state. Our refinement states that the complexity is proportional to the spatial volume of the ERB. More precisely, up to an ambiguous numerical coefficient, we propose that the complexity is the regularized volume of the largest codimension one surface crossing the bridge, divided by G_N l_AdS. We test this conjecture against a wide variety
more » ... of spherically symmetric shock wave geometries in different dimensions. We find detailed agreement.
doi:10.1103/physrevd.90.126007 fatcat:egwki4yzvjfgbga4aed6vfpcg4