اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn Entanglement Entropy of Maxwell fields in 3+1 dimensions
64
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider entanglement entropy between two halves of space separated by a plane, in the theory of free photon in 3+1 dimensions. We show how to separate local gauge invariant quantities that belong to the two spatial regions. We calculate the entanglement entropy by integrating over the degrees of freedom in one half space using an approximation that assumes slow variation of the magnetic fields in longitudinal direction. We find that the entropy is proportional to the transverse area as expected. Interestingly the entanglement properties of the 2D transverse and longitudinal modes of magnetic field are quite different. While the transverse fields are entangled mostly in the neighborhood of the separation surface as expected, the longitudinal fields are entangled through an infrared mode which extends to large distances from the entanglement surface. This long range entanglement arises due to necessity to solve the no-monopole constraint condition for magnetic field.
قيم البحث
اقرأ أيضاً
We calculate the entanglement entropy of a slab of finite width in the pure Maxwell theory. We find that a large part of entropy is contributed by the entanglement of a mode, nonlocal in terms of the transverse magnetic field degrees of freedom. Even
though the entangled mode is nonlocal, its contribution to the entropy is local in the sense that the entropy of a slab of a finite thickness is equal to the entropy of the boundary plus a correction exponential in thickness of the slab.
Despite the seeming simplicity of the theory, calculating (and even defining) entanglement entropy for the Maxwell theory of a $U(1)$ gauge field in (3+1) dimensions has been the subject of controversy. It is generally accepted that the ground state
entanglement entropy for a region of linear size $L$ behaves as an area law with a subleading logarithm, $S = alpha L^2 -gamma log L$. While the logarithmic coefficient $gamma$ is believed to be universal, there has been disagreement about its precise value. After carefully accounting for subtle boundary corrections, multiple analyses in the high energy literature have converged on an answer related to the conformal trace anomaly, which is only sensitive to the local curvature of the partition. In contrast, a condensed matter treatment of the problem yielded a topological contribution which is not captured by the conformal field theory calculation. In this perspective piece, we review aspects of the various calculations and discuss the resolution of the discrepancy, emphasizing the important role played by charged states (the extended Hilbert space) in defining entanglement for a gauge theory. While the trace anomaly result is sufficient for a strictly pure gauge field, coupling the gauge field to dynamical charges of mass $m$ gives a topological contribution to $gamma$ which survives even in the $mrightarrowinfty$ limit. For many situations, the topological contribution from dynamical charges is physically meaningful and should be taken into account. We also comment on other common issues of entanglement in gauge theories, such as entanglement distillation, algebraic definitions of entanglement, and gauge-fixing procedures.
In this presentation we review our work on Abelian Maxwell-Chern-Simons theory in three-dimensional AdS black brane backgrounds, with both integer and non-integer Chern-Simons coupling. Such theories can be derived from several string theory construc
tions, and we found exact solutions in the low frequency, low momentum limit (omega, k << T, the hydrodynamic limit). Our results are translated into correlation functions of vector operators in the dual strongly coupled 1+1-dimensional quantum field theory with a chiral anomaly at non-zero temperature T, via the holographic correspondence. The applicability of the hydrodynamic limit is discussed, together with the comparison between an exact field theoretic computation and the found holographic correlation functions in the conformal case.
We study the fall-off behaviour of test electromagnetic fields in higher dimensions as one approaches infinity along a congruence of expanding null geodesics. The considered backgrounds are Einstein spacetimes including, in particular, (asymptoticall
y) flat and (anti-)de Sitter spacetimes. Various possible boundary conditions result in different characteristic fall-offs, in which the leading component can be of any algebraic type (N, II or G). In particular, the peeling-off of radiative fields F=Nr^{1-n/2}+Gr^{-n/2}+... differs from the standard four-dimensional one (instead it qualitatively resembles the recently determined behaviour of the Weyl tensor in higher dimensions). General p-form fields are also briefly discussed. In even n dimensions, the special case p=n/2 displays unique properties and peels off in the standard way as F=Nr^{1-n/2}+IIr^{-n/2}+.... A few explicit examples are mentioned.
A consistent ansatz for the Skyrme model in (3+1)-dimensions which is able to reduce the complete set of Skyrme field equations to just one equation for the profile in situations in which the Baryon charge can be arbitrary large is introduced: moreov
er, the field equation for the profile can be solved explicitly. Such configurations describe ordered arrays of Baryonic tubes living in flat space-times at finite density. The plots of the energy density (as well as of the Baryon density) clearly show that the regions of maximal energy density have the shape of a tube: the energy density and the Baryon density depend periodically on two spatial directions while they are constant in the third spatial direction. Thus, these topologically non-trivial crystal-like solutions can be intepreted as configurations in which most of the energy density and the baryon density are concentrated within tube-shaped regions. The positions of the energy-density peaks can be computed explicitly and they manifest a clear crystalline order. A non-trivial stability test is discussed.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
