Testing gauge/gravity duality on a quantum black hole

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Science  23 May 2014:
Vol. 344, Issue 6186, pp. 806-807
DOI: 10.1126/science.1254597

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In general relativity, gravity is formulated as a classical physics theory, and formulating its fully quantum version is a great challenge. Gauge/gravity duality conjectures that certain special quantum theories (typically gauge theories) are equivalent to theories of gravity in an emergent spacetime that has more dimensions than the ones appearing in the original quantum theory, and thereby provides an important bridge between quantum theory and gravity. A simple example involves a matrix quantum mechanics theory (1, 2) of interacting fundamental particles that gives rise to gravity in a 10-dimensional curved spacetime (3). Black holes in this spacetime are described by the quantum system at finite temperature. Testing the conjectured duality is difficult because the quantum system is very strongly coupled—it has no easy mathematical solution—when the standard Einstein-like gravity description is applicable. On page 882 of this issue, Hanada et al. (4) test this relation by numerically calculating the entropy of a black hole in the gauge theory. They also calculate this entropy with a gravity theory that includes the first quantum gravity correction. The agreement between the two computations is evidence for the validity of the gauge/gravity duality, as well as for the internal consistency of string theory as a quantum theory of gravity.