Noncomutativity in near horizon symmetries in gravity

Understand

We have a new observation that near horizon symmetry generators, corresponding to diffeomorphisms which leave the horizon structure invariant, satisfy noncommutative Heisenberg algebra.

• The results are valid for any null surfaces (which has Rindler structure in the near null surface limit) and in any spacetime dimensions.
• Using Sugawara construction technique the central charge is identified.
• It is shown that the horizon entropy is consistent with the standard form of Cardy formula.