Holographic entanglement entropy of the Coulomb branch

We compute entanglement entropy (EE) of a spherical region in (3 + 1)-dimensional N = 4 supersymmetric SU(N) Yang-Mills theory in states described holographically by probe D3-branes in AdS(5) x S-5. We do so by generalising methods for computing EE from a probe brane action without having to determine the probe's backreaction. On the Coulomb branch with SU(N) broken to SU(N - 1) x U(1), we find the EE monotonically decreases as the sphere's radius increases, consistent with the a-theorem. The EE of a symmetric-representation Wilson line screened in SU(N - 1) also monotonically decreases, although no known physical principle requires this. A spherical soliton separating SU(N) inside from SU(N - 1) x U(1) outside had been proposed to model an extremal black hole. However, we find the EE of a sphere at the soliton's radius does not scale with the surface area. For both the screened Wilson line and soliton, the EE at large radius is described by a position-dependent W-boson mass as a short-distance cutoff. Our holographic results for EE and one-point functions of the Lagrangian and stress-energy tensor show that at large distance the soliton looks like a Wilson line in a direct product of fundamental representations.

Automated summary

In this study, entanglement entropy of a spherical region in (3 + 1)-dimensional N = 4 supersymmetric SU(N) Yang-Mills theory was computed using holographic methods. It was found that the entanglement entropy monotonically decreases as the sphere's radius increases, which is consistent with certain theoretical expectations. The study also observed similar decreasing trends in the entanglement entropy of a symmetric-representation Wilson line screened in SU(N - 1), even though there is no established physical principle to explain this behavior.