Abstract
The cosmological Friedmann equation sourced by the trace anomaly of a conformal field theory that is dual to the five-dimensional Schwarzschild-AdS geometry can be derived from the first law of thermodynamics if the apparent horizon of the boundary spacetime acquires a logarithmically corrected Bekenstein-Hawking entropy. It is shown that such a correction to the entropy can arise when the generalized uncertainty principle (GUP) is invoked. The necessary condition for such a thermodynamic derivation directly relates the GUP parameter to the conformal anomaly. It is consistent with the existence of a gravitational cutoff at a scale for a theory containing light species. The absolute minimum in position uncertainty can be identified with the scale at which gravity becomes effectively five dimensional.
- Received 25 May 2012
DOI:https://doi.org/10.1103/PhysRevD.88.103519
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