arXiv subjects

Georgios Pastras

Publications and source records attributed to Georgios Pastras.

36 records · Page 2Linked to original sources

arXiv2019

Stability Analysis of Classical String Solutions and the Dressing Method

The dressing method is a technique to construct new solutions in non-linear sigma models under the provision of a seed solution. This is analogous to the use of autoBacklund transformations for systems of the sine-Gordon type. In a recent work, this method was applied in the sigma model that describes string propagation on $\mathbb{R} \times \mathrm{S}^2$, using as seeds the elliptic classical string solutions. Some of the new solutions that emerge reveal instabilities of their elliptic precursors. The focus of the present work is the fruitful use of the dressing method in the study of the stability of closed string solutions. It establishes an equivalence between the dressing method and the conventional linear stability analysis. More importantly, this equivalence holds true in the presence of appropriate periodicity conditions that closed strings must obey. Our investigations point to the direction of the dressing method being a general tool for the study of the stability of classical string configurations in the diverse class of symmetric spacetimes.

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arXiv2019

Salient Features of Dressed Elliptic String Solutions on $\mathbb{R}\times$S$^2$

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.

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arXiv2018

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.

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arXiv2018

Elliptic String Solutions on RxS^2 and Their Pohlmeyer Reduction

We study classical string solutions on RxS^2 that correspond to elliptic solutions of the sine-Gordon equation. In this work, these solutions are systematically derived inverting Pohlmeyer reduction and classified with respect to their Pohlmeyer counterparts. These solutions include the spiky strings and other well-known solutions, such as the BMN particle, the GKP string or the giant magnons, which arise as special limits, and reveal many interesting features of the AdS/CFT correspondence. A mapping of the physical properties of the string solutions to those of their Pohlmeyer counterparts is established. An interesting element of this mapping is the correspondence of the number of spikes of the string to the topological charge in the sine-Gordon theory. In the context of the sine-Gordon/Thirring duality, the latter is mapped to the Thirring model fermion number, leading to a natural classification of the solutions to fermionic objects and bosonic condensates. Finally, the convenient parametrization of the solutions, enforced by the inversion of the Pohlmeyer reduction, facilitates the study of the string dispersion relation. This leads to the identification of an infinite set of trajectories in the moduli space of solutions, where the dispersion relation can be expressed in a closed form by means of some algebraic operations, arbitrarily far from the infinite size limit.

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arXiv2017

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.

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arXiv2017

On the Holographic Entanglement Entropy for Non-smooth Entangling Curves in AdS(4)

We extend the calculations of holographic entanglement entropy in AdS(4) for entangling curves with singular non-smooth points that generalize cusps. Our calculations are based on minimal surfaces that correspond to elliptic solutions of the corresponding Pohlmeyer reduced system. For these minimal surfaces, the entangling curve contains singular points that are not cusps, but the joint point of two logarithmic spirals one being the rotation of the other by a given angle. It turns out that, similarly to the case of cusps, the entanglement entropy contains a logarithmic term, which is absent when the entangling curve is smooth. The latter depends solely on the geometry of the singular points and not on the global characteristics of the entangling curve. The results suggest that a careful definition of the geometric characteristic of such a singular point that determines the logarithmic term is required, which does not always coincide with the definition of the angle. Furthermore, it is shown that the smoothness of the dependence of the logarithmic terms on this characteristic is not in general guaranteed, depending on the uniqueness of the minimal surface for the given entangling curve.

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arXiv2017

Elliptic String Solutions in AdS(3) and Elliptic Minimal Surfaces in AdS(4)

Non-linear sigma models defined on symmetric target spaces have a wide set of applications in modern physics, including the description of string propagation in symmetric spaces, such as AdS or dS, or minimal surfaces in hyperbolic spaces. Although it is difficult to acquire solutions of these models, due to their non-linear nature, it is well known that they are reducible to integrable systems of the family of the sine- or sinh-Gordon equation. In this study, we develop a method to invert Pohlmeyer reduction for elliptic solutions of the reduced system, implementing a relation between NLSM solutions and the eigenstates of the n = 1 Lame problem. This method is applied to produce a family of classical string solutions in AdS(3), which includes the spiky strings, as well as hoop string solutions with singular evolution of their angular velocity and radius, which are interesting in the framework of holographic dualities. Furthermore, application of this method produces a wide family of static minimal surfaces in AdS(4), which includes helicoids and catenoids, and which are interesting in the framework of the Ryu-Takayanagi conjecture and the understanding of the emergence of gravity as an entropic force related to quantum entanglement statistics. The developed formalism allows the study of the area of the minimal surfaces and geometric phase transitions between them, which are relevant to confinement-deconfinement phase transitions.

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arXiv2017

Four Lectures on Weierstrass Elliptic Function and Applications in Classical and Quantum Mechanics

In these four lectures, aiming at senior undergraduate and junior graduate Physics and Mathematics students, basic elements of the theory of elliptic functions are presented. Simple applications in classical mechanics are discussed, including a point particle in a cubic, sinusoidal or hyperbolic potential, as well as simple applications in quantum mechanics, namely the n=1 Lame potential. These lectures were given at the School of Applied Mathematics and Physical Sciences of the National Technical University of Athens in May 2017.

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arXiv2016

Revisiting the O(3) Non-linear Sigma Model and Its Pohlmeyer Reduction

It is well known that sigma models in symmetric spaces accept equivalent descriptions in terms of integrable systems such as the sine-Gordon equation through Pohlmeyer reduction. In this paper, we study the mapping between known solutions of the Euclidean O(3) non-linear sigma model, such as instantons, merons and elliptic solutions that interpolate between the latter and solutions of the Pohlmeyer reduced theory, namely the sinh-Gordon equation. It turns out that instantons do not have a counterpart, merons correspond to the ground state, while the class of elliptic solutions is characterized by a two to one correspondence between solutions in the two descriptions.

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arXiv2016

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.

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arXiv2016

On Elliptic String Solutions in AdS(3) and dS(3)

Classical string actions in AdS(3) and dS(3) can be connected to the sinh-Gordon and cosh-Gordon equations through Pohlmeyer reduction. We show that the problem of constructing a classical string solution with a given static or translationally invariant Pohlmeyer counterpart is equivalent to solving four pairs of effective Schrodinger problems. Each pair consists of a flat potential and an n = 1 Lame potential whose eigenvalues are connected, and, additionally, the four solutions satisfy a set of constraints. An approach for solving this system is developed by employing an interesting connection between the specific class of classical string solutions and the band structure of the Lame potential. This method is used for the construction of several families of classical string solutions, one of which turns out to be the spiky strings in AdS(3). New solutions include circular rotating strings in AdS(3) with singular time evolution of their radius and angular velocity as well as classical string solutions in dS(3).

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arXiv2015

Holographic Renyi Entropies and Restrictions on Higher Derivative Terms

We perform a holographic calculation of the Entanglement Rényi entropy $S_q(μ,λ)$, for spherical entangling surfaces in boundary CFT's with Einstein-Gauss-Bonnet-Maxwell holographic gravitational duals. We find that for Gauss-Bonnet couplings $λ$, larger than a specific value, but still allowed by causality, a violation of an inequality that Rényi entropies must obey by definition occurs. This violation is related to the existence of negative entropy black holes and restricts the coefficient of the Gauss-Bonnet coupling in the bulk theory. Furthermore, we discover a distinction in the analytic structure of the analytic continuation of $S_q(μ,λ)$, between negative and non-negative $λ$, suggesting the existence of a phase transition.

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arXiv2015

Entanglement Entropy and Duality in AdS(4)

Small variations of the entanglement entropy δS and the expectation value of the modular Hamiltonian δE 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, δS = δE, 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.

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arXiv2014

Charged Rényi Entropies in CFTs with Einstein-Gauss-Bonnet Holographic Duals

We calculate the Rényi entropy $S_q(μ,λ)$, for a spherical entangling surface in CFT's with Einstein-Gauss-Bonnet-Maxwell holographic duals. Rényi entropies must obey some interesting inequalities by definition. However, for Gauss-Bonnet couplings $λ$, larger than a specific value, but still allowed by causality, we observe a violation of the inequality $\frac{\partial}{\partial q}\left({\frac{q - 1}{q}S_q(μ,λ)} \right) \ge 0$, 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 $S_q(μ,λ)$ for imaginary chemical potential, between negative and non-negative $λ$.

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arXiv2011

Exact Tunneling Solutions in Minkowski Spacetime and a Candidate for Dark Energy

We study exact tunneling solutions in scalar field theory for potential barriers composed of linear or quadratic patches. We analytically continue our solutions to imaginary Euclidean radius in order to study the profile of the scalar field inside the growing bubble. We find that generally there is a non-trivial profile of the scalar field, generating a stress-energy tensor, that depending on the form of the potential, can be a candidate for dark energy.

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arXiv2008

Thermal Evolution of the Non Supersymmetric Metastable Vacua in N=2 SU(2) SYM Softly Broken to N=1

It has been shown that four dimensional N=2 gauge theories, softly broken to N=1 by a superpotential term, can accommodate metastable non-supersymmetric vacua in their moduli space. We study the SU(2) theory at high temperatures in order to determine whether a cooling universe settles in the metastable vacuum at zero temperature. We show that the corrections to the free energy because of the BPS dyons are such that may destroy the existence of the metastable vacuum at high temperatures. Nevertheless we demonstrate the universe can settle in the metastable vacuum, provided that the following two conditions are hold: first the superpotential term is not arbitrarily small in comparison to the strong coupling scale of the gauge theory, and second the metastable vacuum lies in the strongly coupled region of the moduli space.

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arXiv2008

Thermodynamics of the Maxwell-Gauss-Bonnet anti-de Sitter Black Hole with Higher Derivative Gauge Corrections

The local and global thermal phase structure for asymptotically anti-de Sitter black holes charged under an abelian gauge group, with both Gauss-Bonnet and quartic field strength corrections, is mapped out for all parameter space. We work in the grand canonical ensemble where the external electric potential is held fixed. The analysis is performed in an arbitrary number of dimensions, for all three possible horizon topologies - spherical, flat or hyperbolic. For spherical horizons, new metastable configurations are exhibited both for the pure Gauss-Bonnet theory as well as the pure higher derivative gauge theory and combinations thereof. In the pure Gauss-Bonnet theory with negative coefficient and five or more spatial dimensions, two locally thermally stable black hole solutions are found for a given temperature. Either one or both of them may be thermally favored over the anti-de Sitter vacuum - corresponding to a single or a double decay channel for the metastable black hole. Similar metastable configurations are uncovered for the theory with pure quartic field strength corrections, as well combinations of the two types of corrections, in three or more spatial dimensions. Finally, a secondary Hawking-Page transition between the smaller thermally favored black hole and thermal anti-de Sitter space is observed when both corrections are turned on and their couplings are both positive.

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arXiv2007

Non Supersymmetric Metastable Vacua in N=2 SYM Softly Broken to N=1

We find non-supersymmetric metastable vacua in four dimensional N=2 gauge theories softly broken to N=1 by a superpotential term. First we study the simplest case, namely the SU(2) gauge theory without flavors. We study the spectrum and lifetime of the metastable vacuum and possible embeddings of the model in UV complete theories. Then we consider larger gauge group theories with flavors. We show that when we softly break them to N=1, the potential induced on specific submanifolds of their moduli space is identical to the potential in lower rank gauge theories. Then we show that the potential increases when we move away from this submanifold, allowing us to construct metastable vacua on them in the theories that can be reduced to the SU(2) case.

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