Dvali, Gia
(2018):
Area law microstate entropy from criticality and spherical symmetry.
In: Physical Review D, Vol. 97, No. 10, 105005

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Abstract
It is often assumed that the area law of microstate entropy and the holography are intrinsic properties exclusively of the gravitational systems, such as black holes. We construct a nongravitational model that exhibits an entropy that scales as area of a sphere of one dimension less. It is represented by a nonrelativistic bosonic field living on a ddimensional sphere of radius R and experiencing an angularmomentumdependent attractive interaction. We show that the system possesses a quantum critical point with the emergent gapless modes. Their number is equal to the area of a d  1dimensional sphere of the same radius R. These gapless modes create an exponentially large number of degenerate microstates with the corresponding microstate entropy given by the area of the same d  1dimensional sphere. Thanks to a doublescaling limit, the counting of the entropy and of the number of the gapless modes is made exact. The phenomenon takes place for arbitrary number of dimensions and can be viewed as a version of holography.