![]() ![]() Oleg Kupervasser, in Application of New Cybernetics in Physics, 2017 4.2.1 Black Holes Indeed, on general field theoretic grounds, in the 't Hooft large N limit the entropy is given by Thus, the relative factor of 3/4 is not a discrepancy: it relates two different limits of the theory. As we argued above, the supergravity calculation of the BH entropy, (6.1), is relevant to the λ → ∞ limit of the N = 4 SU( N) gauge theory, while the free field calculation, (6.2), applies to the λ → 0 limit. ![]() But what is the explanation of the relative factor of 3/4 between S BH and S 0? In fact, this factor is not a contradiction but rather a prediction about the strongly coupled N = 4 SYM theory at finite temperature. Also, the N 2 scaling indicates the presence of O( N 2) unconfined degrees of freedom, which is exactly what we expect in the N = 4 supersymmetric U( N) gauge theory. ![]() It is remarkable that the 3-brane geometry captures the T 3 scaling characteristic of a conformal field theory (in a CFT this scaling is guaranteed by the extensivity of the entropy and the absence of dimensionful parameters). Indeed, on general field-theoretic grounds, we expect that in the ‘t Hooft large- N limit, the entropy is given by As we argued above, the supergravity calculation of the BH entropy,, is relevant to the λ → ∞ limit of the N = 4 SU( N) gauge theory, while the free-field calculation,, applies to the λ → 0 limit. It is remarkable that the 3-brane geometry captures the T 3 scaling characteristic of a conformal field theory (CFT) (in a CFT this scaling is guaranteed by the extensivity of the entropy and the absence of dimensionful parameters). ![]()
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