Modular discretization of the AdS(2)/CFT1 holography

作者：Axenides Minos^*; Floratos Emmanuel; Nicolis Stam

来源：The Journal of High Energy Physics, 2014, 2014(2): 109.

DOI：10.1007/JHEP02(2014)109

• Black Holes in String Theory
• AdS-CFT Correspondence

We propose a finite discretization for the black hole, near horizon, geometry and dynamics. We realize our proposal, in the case of extremal black holes, for which the radial and temporal near horizon geometry is known to be AdS(2) = SL(2, R)/SO(1, 1, R). We implement its discretization by replacing the set of real numbers R with the set of integers modulo N with AdS(2) going over to the finite geometry AdS(2)[N] = SL(2, Z(N))/SO(1, 1, Z(N)). We model the dynamics of the microscopic degrees of freedom by generalized Arnol'd cat maps, A is an element of SL(2, Z(N)) which are isometries of the geometry, at both the classical and quantum levels. These are well known to exhibit fast quantum information processing through the well studied properties of strong arithmetic chaos, dynamical entropy, nonlocality and factorization in the cutoff discretization N. We construct, finally, a new kind of unitary and holographic correspondence, for AdS(2)[N]/CFT1[N], via coherent states of the bulk and boundary geometries.

• 出版日期2014-2-25