Information flows in strongly coupled ABJM theory

Abstract

We use holographic methods to characterize the RG flow of quantum information in a Chern-Simons theory coupled to massive fermions. First, we use entanglement entropy and mutual information between strips to derive the dimension of the RG-driving operator and a monotonic c-function. We then display a scaling regime where, unlike in a CFT, the mutual information between strips changes non-monotonically with strip width, vanishing in both IR and UV but rising to a maximum at intermediate scales. The associated information transitions also contribute to non-monotonicity in the conditional mutual information which characterizes the independence of neighboring strips after conditioning on a third. Finally, we construct a measure of extensivity which tests to what extent information that region A shares with regions B and C is additive. In general, mutual information is super-extensive in holographic theories, and we might expect super-extensivity to be maximized in CFTs since they are scale-free. Surprisingly, our massive theory is more superextensive than a CFT in a range of scales near the UV limit, although it is less super-extensive than a CFT at all lower scales. Our analysis requires the full ten-dimensional dual gravity background, and the extremal surfaces computing entanglement entropy explore all of these dimensions.

Notes on entanglement wedge cross sections

“…5 along with a phase diagram for a system where strips have widths l and are separated by a distance s [30]. 2 Notice that the slope of the phase diagram between the phases a and b, close to the UV, is given by the (conjugate) golden ratio ϕ −1 = ( [8]; in general d via the root of (3.2) [30]. In order to show results for the information measures, we will pick units in terms of z h .…”

“…We will consider the ABJM Chern-Simons matter theory [40] coupled with fundamental matter in 2 + 1 dimensions in the Veneziano limit [41]. The entanglement entropies for this system have been considered in previous works [8,42] and here we will comment on results for the entanglement wedge cross section. The background with fundamental matter we consider here are of two-fold: 3 either masses of the fundamentals are zero [43] or they are massive but at vanishing temperature [42].…”

“…Here b is a quantity depending on the numbers of flavors, taking values from 1 to 5/4 as N f changes between 0 to ∞: the deviation from unity is the mass anomalous dimension of the fundamentals [8,46]. The constant k is the Chern-Simons level and φ is a constant dilaton that we replaced for in terms of flavors.…”

“…In all of the cases we study in this paper we found that the inequality (1.1) is satisfied. However, this is more exciting than it sounds: I(A, B) can have very non-trivial features if conformal symmetry is broken [8], thus drawing attention to E W in same geometries. Moreover, the advances put forward in this paper enable one to test if E W could also satisfy further inequalities known to hold for E P involving three or more regions.…”

Holographic spontaneous anisotropy

“…It should be noted that similar non-monotonic behavior was observed in the boomerang supergravity solutions [57,58] and it is interesting to ask if a similar interpretation would apply in those cases, for instance in terms of background fluxes. In order to better understand the properties of the solutions along the full ten-dimensional anisotropic RG flow it would be interesting to study other observables that are also sensitive to the internal energy scales [82][83][84], such as mutual information, entanglement wedge cross sections, or Wilson loops. As we have mentioned, for a large enough brane density, preliminary results indicate that some of these quantities could go through different saddle points as their size is varied.…”