Exact results for the entanglement entropy and the energy radiated by a quark

Abstract

We consider a spherical region with a heavy quark in the middle. We compute the extra entanglement entropy due to the presence of a heavy quark both in N = 4 Super Yang Mills and in the N = 6 Chern-Simons matter theory (ABJM). This is done by relating the computation to the expectation value of a circular Wilson loop and a stress tensor insertion.We also give an exact expression for the Bremsstrahlung function that determines the energy radiated by a quark in the ABJM theory.

The full Quantum Spectral Curve for AdS4/CFT3

“…In particular, it would be very interesting to find an integrable description of some kind of generalized cusp anomalous dimension, such as the one described in [71]. This would give a direct way to test the proposals of [44,45] for the ABJM/ABJ interpolating functions, by comparison with localization results for the Brehmsstrahlung function [72][73][74][75].…”

BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis

“…• In conformal field theories Wilson loops allow for computing the energy radiated by a moving quark in the low energy limit (Bremsstrahlung function B(λ)) [47,48] and the contribution to the entanglement entropy due to a heavy quark sitting inside a finite region [49]. The Bremsstrahlung function also governs the small angle expansion of the cusp anomalous dimension Γ cusp (ϕ, θ) B(λ)(θ 2 − ϕ 2 ) for a generalized cusp.…”

“…Recently, for the ABJM theory a general formula has been proposed [49], which gives the Bremsstrahlung function B 1/6 for 1/6−BPS quark configurations as the derivative of a bosonic Wilson loop on a squashed sphere with respect to the squashing parameter b. An equivalent expression in terms of the n-derivative of a Wilson loop winding n times the great circle (with the dictionary b = √ n) has also been provided, which is amenable of explicit computations.…”

Holographic entanglement entropy for massive flavours in dS 4

“…For quantities calculated directly from the on-shell action, it is not necessary to go beyond the probe limit N f N c in which backreaction is neglected. This is not the case for flavour corrections to the EE, which are a topic of recent interest [10][11][12][13][14][15][16][17]. However, [13], building on [18], found a shortcut to the problem which does not require computing the backreaction.…”

“…3 One way to see this is to note that the future causal development is bounded by the null ray 15) and graphically plot the set of points generated by the boundary transformation (3.13) to see that it is bounded by this null ray. 4 Note that in the holographic correspondence between AdS5 × S 5 and N = 4 SYM,…”