End of the world brane in double scaled SYK
Kazumi Okuyama
Abstract
A bstract We study the end of the world (EOW) brane in double scaled SYK (DSSYK) model. We find that the boundary state of EOW brane is a coherent state of the q -deformed oscillators and the associated orthogonal polynomial is the continuous big q -Hermite polynomial. In a certain scaling limit, the big q -Hermite polynomial reduces to the Whittaker function, which reproduces the wavefunction of JT gravity with an EOW brane. We also compute the half-wormhole amplitude in DSSYK and show that the amplitude is decomposed into the trumpet and the factor coming from the EOW brane.
Topics & Concepts
PhysicsHermite polynomialsBraneAmplitudePolynomialLimit (mathematics)Boundary (topology)Mathematical physicsQuantum mechanicsMathematical analysisMathematicsBlack Holes and Theoretical PhysicsCosmology and Gravitation TheoriesNonlinear Waves and Solitons