We study the target space entanglement entropy in a complex matrix model that describes the chiral primary sector in $$ \mathcal{N} $$
N
= 4 super Yang-Mills theory, which is associated with the bubbling AdS geometry. The target space for the matrix model is a two-dimensional plane where the eigenvalues of the complex matrix distribute. The eigenvalues are viewed as the position coordinates of fermions, and the eigenvalue distribution corresponds to a droplet formed by the fermions. The droplet is identified with one that specifies a boundary condition in the bubbling geometry. We consider states in the matrix model that correspond to AdS5× S5, an AdS giant graviton and a giant graviton in the bubbling geometry. We calculate the target space entanglement entropy of a subregion for each of the states in the matrix model as well as the area of the boundary of the subregion in the bubbling geometry, and find a qualitative agreement between them.
We study renormalization on the fuzzy sphere. We numerically simulate a scalar field theory on it, which is described by a Hermitian matrix model. We show that correlation functions defined by using the Berezin symbol are made independent of the matrix size, which is viewed as a UV cutoff, by tuning a parameter of the theory. We also find that the theories on the phase boundary are universal. They behave as a conformal field theory at short distances, while they show an effect of UV/IR mixing at long distances.
We study how information geometry is described by bulk geometry in the gauge/gravity correspondence. We consider a quantum information metric that measures the distance between the ground states of a CFT and a theory obtained by perturbing the CFT. We find a universal formula that represents the quantum information metric in terms of back reaction to the AdS bulk geometry.
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