Charged R\'enyi Entropies in CFTs with Einstein-Gauss-Bonnet Holographic Duals

We calculate the R\'enyi entropy $S_q(\mu,\lambda)$, for a spherical entangling surface in CFT's with Einstein-Gauss-Bonnet-Maxwell holographic duals. R\'enyi entropies must obey some interesting inequalities by definition. However, for Gauss-Bonnet couplings $\lambda$, larger than a specific value, but still allowed by causality, we observe a violation of the inequality $\frac{\partial}{{\partial q}}\left({\frac{{q - 1}}{q}S_q(\mu,\lambda)} \right) \ge 0$, which is related to the existence of negative entropy black holes, providing interesting restrictions in the bulk theory. Moreover, we find an interesting distinction of the behaviour of the analytic continuation of $S_q(\mu,\lambda)$ for imaginary chemical potential, between negative and non-negative $\lambda$.Comment: 50 pages, 16 figures. v3: Version to appear in JHE

Entanglement Entropy and Duality in AdS(4)

Small variations of the entanglement entropy \delta S and the expectation value of the modular Hamiltonian \delta E are computed holographically for circular entangling curves in the boundary of AdS(4), using gravitational perturbations with general boundary conditions in spherical coordinates. Agreement with the first law of thermodynamics, \delta S = \delta E, requires that the line element of the entangling curve remains constant. In this context, we also find a manifestation of electric-magnetic duality for the entanglement entropy and the corresponding modular Hamiltonian, following from the holographic energy-momentum/Cotton tensor duality.Comment: 43 pages, 2 figures, v2: a few clarifications have been added; final version to appear in Nucl. Phys.

An Inverse Mass Expansion for Entanglement Entropy in Free Massive Scalar Field Theory

We extend the entanglement entropy calculation performed in the seminal paper by Srednicki for free real massive scalar field theories in 1+1, 2+1 and 3+1 dimensions. We show that the inverse of the scalar field mass can be used as an expansion parameter for a perturbative calculation of the entanglement entropy. We perform the calculation for the ground state of the system and for a spherical entangling surface at third order in this expansion. The calculated entanglement entropy contains a leading area law term, as well as subleading terms that depend on the regularization scheme, as expected. Universal terms are non-perturbative effects in this approach. Interestingly, this perturbative expansion can be used to approximate the coefficient of the area law term, even in the case of a massless scalar field in 2+1 and 3+1 dimensions. The presented method provides the spectrum of the reduced density matrix as an intermediate result, which is an important advantage in comparison to the replica trick approach. Our perturbative expansion underlines the relation between the area law and the locality of the underlying field theory.Comment: 35 pages, 5 figure

Static Elliptic Minimal Surfaces in AdS(4)

The Ryu-Takayanagi conjecture connects the entanglement entropy in the boundary CFT to the area of open co-dimension two minimal surfaces in the bulk. Especially in AdS(4), the latter are two-dimensional surfaces, and, thus, solutions of a Euclidean non-linear sigma model on a symmetric target space that can be reduced to an integrable system via Pohlmeyer reduction. In this work, we invert Pohlmeyer reduction to construct static minimal surfaces in AdS(4) that correspond to elliptic solutions of the reduced system, namely the cosh-Gordon equation. The constructed minimal surfaces comprise a two-parameter family of surfaces that include helicoids and catenoids in H(3) as special limits. Minimal surfaces that correspond to identical boundary conditions are discovered within the constructed family of surfaces and the relevant geometric phase transitions are studied.Comment: 47 pages, 15 figure

Dressed Elliptic String Solutions on RxS^2

We obtain classical string solutions on RxS^2 by applying the dressing method on string solutions with elliptic Pohlmeyer counterparts. This is realized through the use of the simplest possible dressing factor, which possesses just a pair of poles lying on the unit circle. The latter is equivalent to the action of a single Backlund transformation on the corresponding sine-Gordon solutions. The obtained dressed elliptic strings present an interesting bifurcation of their qualitative characteristics at a specific value of a modulus of the seed solutions. Finally, an interesting generic feature of the dressed strings, which originates from the form of the simplest dressing factor and not from the specific seed solution, is the fact that they can be considered as drawn by an epicycle of constant radius whose center is running on the seed solution. The radius of the epicycle is directly related to the location of the poles of the dressing factor.Comment: 47 pages, 2 figure

Salient Features of Dressed Elliptic String Solutions on R×\mathbb{R}\timesS2^2

We analyse several physical aspects of the dressed elliptic strings propagating on $\mathbb{R} \times \mathrm{S}^2$ and of their counterparts in the Pohlmeyer reduced theory, i.e. the sine-Gordon equation. The solutions are divided into two wide classes; kinks which propagate on top of elliptic backgrounds and those which are non-localised periodic disturbances of the latter. The former class of solutions obey a specific equation of state that is in principle experimentally verifiable in systems which realize the sine-Gordon equation. Among both of these classes, there appears to be a particular class of interest the closed dressed strings. They in turn form four distinct subclasses of solutions. Unlike the closed elliptic strings, these four subclasses, exhibit interactions among their spikes. These interactions preserve a carefully defined turning number, which can be associated to the topological charge of the sine-Gordon counterpart. One particular class of those closed dressed strings realizes instabilities of the seed elliptic solutions. The existence of such solutions depends on whether a superluminal kink with a specific velocity can propagate on the corresponding elliptic sine-Gordon solution. Finally, the dispersion relations of the dressed strings are studied. A qualitative difference between the two wide classes of dressed strings is discovered. This would be an interesting subject for investigation in the dual field theory.Comment: 75 pages, 27 figure