Abstract
An analytic static monopole solution is found in global AdS4, in the limit of small backreaction. This solution is mapped in Poincaré patch to a falling monopole configuration, which is dual to a local quench triggered by the injection of a condensate. Choosing boundary conditions which are dual to a time-independent Hamiltonian, we find the same functional form of the energy-momentum tensor as the one of a quench dual to a falling black hole. On the contrary, the details of the spread of entanglement entropy are very different from the falling black hole case, where the quench induces always a higher entropy compared to the vacuum, i.e. ∆S > 0. In the propagation of entanglement entropy for the monopole quench, there is instead a competition between a negative contribution to ∆S due to the scalar condensate and a positive one carried by the freely propagating quasiparticles generated by the energy injection.
Highlights
The AdS/CFT correspondence [1,2,3] provides a controlled environment to study the physics of a strongly-coupled conformal field theory (CFT) on the boundary by dealing with a weakly-coupled gravitational system in the Anti-de Sitter (AdS) bulk
We find a rather different behaviour for ∆S compared to the case of the falling black hole: for the monopole quench, ∆S for a region centered at the origin is always negative, while in the black holes (BH) case ∆S is positive
We found an approximate analytical solution for the monopole in the regime of small gauge coupling e which includes the leading-order backreaction on the metric
Summary
The AdS/CFT correspondence [1,2,3] provides a controlled environment to study the physics of a strongly-coupled conformal field theory (CFT) on the boundary by dealing with a weakly-coupled gravitational system in the Anti-de Sitter (AdS) bulk. We will consider the theoretical setting introduced in [51] In this situation, specialising to a multitrace deformation, the monopole in global AdS is dual to a theory with spontaneous symmetry breaking. For a particular choice of the multitrace deformation, given in eq (4.14), the monopole is dual to a theory with a timeindependent Hamiltonian In this case, the expectation value of the energy-momentum tensor has the same functional form as the one in the background of a falling black hole [31]. This trick transforms the global AdS static solution to a falling monopole in the Poincaré patch, which provides the holographic dual of the local quench.
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