Spread complexity and the saturation of wormhole size

Recent proposals equate the size of Einstein-Rosen (ER) bridges in Jackiw-Teilboim (JT) gravity to spread complexity of a dual, double-scaled Sachdev-Ye-Kitaev theory (DSSYK). We show that the auxiliary “chord basis” of these proposals is an extrapolation from a subexponential part of the finite-dimensional physical Krylov basis of a spreading thermofield double state. The physical tridiagonal Hamiltonian coincides with the DSSYK approximation on the initial Krylov basis, but deviates markedly over an exponentially large part of the state space. We nonperturbatively extend the identification of ER bridge size and spread complexity to the complete Hilbert space, and show that it saturates at late times. We use…

• UD
  U.S. Department of Energy

  Award: DE-SC0020360
• SF
  Simons Foundation

  Awards: 1161654, 1023171-RC
• CN
  Consejo Nacional de Investigaciones Científicas y Técnicas
• BC
  Balliol College, University of Oxford