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Holographic entanglement entropy of the Coulomb branch
Journal of High Energy Physics, Volume: 2021, Issue: 4
Swansea University Author: Prem Kumar
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DOI (Published version): 10.1007/jhep04(2021)153
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 AdS5 × S5. We do so by generalising methods for computing EE from a probe brane action without having to determine...
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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 AdS5 × S5. We do so by generalising methods for computing EE from a probe brane action without having to determine the probe’s back- reaction. On the Coulomb branch with SU(N) broken to SU(N − 1) × 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) × 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.
AdS-CFT Correspondence; Conformal Field Theory; Gauge-gravity correspondence; Supersymmetric Gauge Theory
Faculty of Science and Engineering