De Sitter cosmic strings and supersymmetry

Oikonomou, V. K.

doi:10.1007/s10714-012-1339-2

Cited by 3 publications

(5 citation statements)

References 33 publications

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“…As we shall see shortly, the operators D and D † defined in relations (34) and (35) are Fredholm for the localized solutions (the localization entails specific boundary conditions for the operators which in the end render the operators to be Fredholm) around the vortex. The vector space kerD is given by the solutions of the equation DΦ = 0, with the solutions Φ being zero at spatial infinity.…”

Section: Superconductors and Vorticesmentioning

confidence: 99%

“…In the case of color superconductivity, the supersymmetry is due to the vortex, which actually causes localized fermionic solutions around it. Supersymmetric structures of the same kind around defects where studied in [35,36] where the case of a superconducting and a cosmic string where analyzed respectively. Supersymmetry in the case where fermionic quasinormal modes are studied in various gravitational backgrounds, was investigated in [37].…”

Section: Introductionmentioning

confidence: 99%

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One-Dimensional Supersymmetric Algebras in Color Superconductors and Reissner–nordström–anti-De Sitter Gravitational Systems

Oikonomou

2013

Int. J. Mod. Phys. A

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We study two fermionic systems that have an underlying supersymmetric structure, namely a color superconductor and Dirac fermion in a Reissner-Nordström-anti-de Sitter gravitational background. In the chiral limit of the color superconductor, the localized fermionic zero modes around the vortex form an N = 2 with zero central charge d = 1 quantum algebra, with all the operators being Fredholm. We compute the Witten index of this algebra and we find an unbroken supersymmetry. The fermionic gravitational system in the chiral limit too, has two underlying unbroken N = 2, d = 1 supersymmetric algebras. The unbroken supersymmetry in the later is guaranteed by the existence of fermionic quasinormal modes in the Reissner-Nordström-anti-de Sitter background. In this case the operators are not Fredholm and regularized indices are deployed.

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Section: Superconductors and Vorticesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

One-Dimensional Supersymmetric Algebras in Color Superconductors and Reissner–nordström–anti-De Sitter Gravitational Systems

Oikonomou

2013

Int. J. Mod. Phys. A

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“…(47). Now, if the operator tr We −t(D+C) 2 is trace class, the following theorem holds (see for example Ref.…”

Section: Massive Fermion Casementioning

confidence: 98%

“…The specific type of supersymmetry that we found is an N = 2 supersymmetric quantum mechanics [39-42, 44-47, 49-52] (shortened to SUSY QM hereafter) with zero central charge. The aforementioned supersymmetry is inherent to many gravitational systems [53,54]. In this paper the focus is on supersymmetries in gravitational backgrounds.…”

Section: Introductionmentioning

confidence: 99%

“…The aforementioned supersymmetry is inherent to many gravitational systems. 46,47 In this paper, the focus is on supersymmetries in gravitational backgrounds. We exploit the existence of the quasinormal modes in this backgrounds in order to establish the fact that, the Witten index of the corresponding underlying supersymmetric algebra is zero, with the kernels of the corresponding operators being nonempty and consequently, supersymmetry is unbroken.…”

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Hidden Supersymmetry in Dirac Fermion Quasinormal Modes of Black Holes

Oikonomou

2013

Int. J. Mod. Phys. A

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We connect the quasinormal modes corresponding to Dirac fermions in various curved space-time backgrounds to an N = 2 supersymmetric quantum mechanics algebra, which can be constructed from the radial part of the fermionic solutions of the Dirac equation. In the massless fermion case, the quasinormal modes are in bijective correspondence with the zero modes of the fermionic system and this results to unbroken supersymmetry. The massive case is more complicated, but as we demonstrate, supersymmetry remains unbroken even in this case.The perturbation of a black hole can be achieved either by directly perturbing the gravitational background or by simply adding matter or gauge fields in the black hole space-time. 4 In this paper, we shall use the latter approach, in the linear approximation, which suggests that the field has no back-reaction on the metric. Particularly, we shall study Dirac fermion systems around various black hole and space-time environments and study when the system possesses an unbroken hidden supersymmetry. Supersymmetry has been connected to quasinormal modes spectra in the past, but in a different context. 34-38 Most of these works studied bosonic quasinormal modes and their relation to supersymmetry. We study the zero modes of the fermionic system and directly relate these to the quasinormal modes. As we shall see, the zero modes and quasinormal modes have a bijective correspondence, a fact that can actually be very crucial for supersymmetry to be unbroken. The specific type of supersymmetry that we found is an N = 2 supersymmetric quantum mechanics (SUSY QM) 39-45 with zero central charge. The aforementioned supersymmetry is inherent to many gravitational systems. 46,47 In this paper, the focus is on supersymmetries in gravitational backgrounds. We exploit the existence of the quasinormal modes in this backgrounds in order to establish the fact that, the Witten index of the corresponding underlying supersymmetric algebra is zero, with the kernels of the corresponding operators being nonempty and consequently, supersymmetry is unbroken. This paper is organized as follows. In Sec. 2, we study the supersymmetric underlying structure for the case of a Kerr black hole, with the latter being the most physically interesting black hole satisfying the Einstein's equations. In Sec. 3, we study the massless and massive Dirac fermion in Kerr-Newman, Reissner-Nordström and Schwarzschild gravitational backgrounds. The massive case proves to be much more complicated compared to the massless case, but still, supersymmetry remains unbroken. In Sec. 4, the focus is on three different spacetimes, namely, the D-dimensional de Sitter, Kerr-Newman-de Sitter and Reissner-Nordström-anti-de Sitter space-times, finding the same results as in the previous sections. In reference to the Reissner-Nordström-anti-de Sitter space-time, we find that this fermionic system has two N = 2 SUSY QM algebras. In Sec. 5, we present some physical and mathematical implications of the SUSY QM on the fermionic system and also to the fibe...

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Color Superconductors, Fermions in Reissner-Nordström-anti-de Sitter Spacetimes and Zero Central Charge Supersymmetry

Oikonomou

2013

J. Phys.: Conf. Ser.

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De Sitter cosmic strings and supersymmetry

Cited by 3 publications

References 33 publications

One-Dimensional Supersymmetric Algebras in Color Superconductors and Reissner–nordström–anti-De Sitter Gravitational Systems

One-Dimensional Supersymmetric Algebras in Color Superconductors and Reissner–nordström–anti-De Sitter Gravitational Systems

Hidden Supersymmetry in Dirac Fermion Quasinormal Modes of Black Holes

Color Superconductors, Fermions in Reissner-Nordström-anti-de Sitter Spacetimes and Zero Central Charge Supersymmetry

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