Supersymmetry, black holes and holography in three dimensions
Başlık çevirisi mevcut değil.
- Tez No: 403362
- Danışmanlar: Prof. ERIC A. BERGSHOEFF
- Tez Türü: Doktora
- Konular: Fizik ve Fizik Mühendisliği, Physics and Physics Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2017
- Dil: İngilizce
- Üniversite: University of Groningen (Rijksuniversiteit Groningen)
- Enstitü: Yurtdışı Enstitü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 153
Özet
Özet yok.
Özet (Çeviri)
In this thesis, we have investigated a wide variety of 3D gravity theories from different perspectives, which include their supersymmetric completion in addition to background and black hole solutions. Our starting point was the fact that 3D Einstein gravity does not propagate any local degrees of freedom. In order to introduce local dynamics, theories de ned by Lagrangians with higher curvature terms were considered. In 3D, it is possible to avoid Ostragadski type instabilities, which generally appear in higher derivative gravity theories, and obtain theories that still preserve unitarity. In Chapter 2, considering Lagrangians with at most four derivatives of the metric, we reviewed those theories that are unitary around at spacetime. These theories are also unitary around an AdS spacetime for a certain range in parameter space. However, they are expected to be holographically dual to a boundary CFT, and the boundary CFT turns out to be non-unitary for the range of parameters that make bulk gravity theory unitary. We introduced this bulk-boundary unitarity con ict by taking NMG as an example. The main tools and concepts used in the subsequent chapters are also explained in this chapter. The superconformal method for constructing supergravity theories, which is particularly useful in the higher derivative theories, is explained in detail. Aspects of supersymmetric solutions, which are important for the purpose of this thesis, are recapitulated. In the end, the algebraic classi cation of 3D spacetimes is discussed with a particular emphasis on higher derivative theories. In Chapter 3, the N = 2 supersymmetric extension of 3D higher derivative gravity theories up to four derivatives of the metric is constructed mainly by using the superconformal method. Studying the two possibilities for the o -shell closure of the algebra, N = (1; 1) and N = (2; 0) supersymmetries, we nd that only the rst one allows for a ghost free AdS vacuum. Assuming the formula derived for the case of pure gravity theories still holds, we show that the bulk-boundary unitarity problem is not solved by supersymmetry. It is still useful to check the validity of the formula for the central charge for matter-coupled gravity theories, which still leaves some hope for a solution to the problem. It might be the case that the non-minimal couplings between graviton and matter elds lead to a di erent expression for the central charge. The general class of o -shell supergravities constructed in this chapter leads to a number of interesting possibilities for future work. One can perform a systematic study of supersymmetric solutions, where a special case is the subject of Chapter 4. Although we constructed vector multiplet actions by using an arbitrary function of vector multiplet scalars, as given in equation (3.2.45), we did not consider such constructions for the scalar multiplet. It would be interesting to consider the coupling of an arbitrary number of scalar multiplets and vector multiplets, since that would enable us to construct a much larger class of supergravity Lagrangians [120]. The composite expression we derived for both scalar and vector multiplets can also be used to construct matter-coupled higher derivative supergravity models. Three dimensional matter coupled theories such as these have attracted considerable attention in the context of rigid supersymmetric theories on three-manifolds [80, 121]. One important possibility arises from the fact that the R-symmetry remains as a local symmetry in the N = (2; 0) theory. One can use this setup to obtain an Einstein-Maxwell theory where the R-symmetry is dynamically gauged, which should admit new types of supersymmetric solutions. In Chapter 4, supersymmetric solutions of the N = (1; 1) NMG with cosmological constant were studied by employing the o -shell Killing spinor analysis, which was previously performed to study the solutions for the case of TMG. The analysis is still valid in our case since the bosonic eld con gurations are constrained only by supersymmetry without any reference to eld equations. Contrary to the N = 1 extension of the theory, where only spacetimes with a null Killing vectors are allowed, it is possible to obtain supersymmetric solutions with a time-like Killing vector. Various possible background solutions are extensively studied here and a comparison with the case of TMG is made. Embedding of some black hole solutions of NMG into a supersymmetric setup is also investigated. There are numerous directions one can consider for future study. An intriguing problem is to nd a supersymmetric Lifshitz black hole. Although our trials with the current model have failed, it is natural to consider di erent approaches. For instance, one could saturate the BPS bound with a U(1) charge. This can be achieved by coupling the N = (1; 1) CNMG model to an o -shell vector multiplet and repeat the analysis performed in this chapter. It is also worth mentioning that the same procedure can be applied to the N = (2; 0) CNMG model. This model has a di erent eld content consisting of two auxiliary vectors and a real scalar as well as the graviton and the gravitino. Given that the N = (2; 0) theory with matter couplings has new supersymmetric solutions [62], we expect that the N = (2; 0) CNMG model will exhibit di erent supersymmetric solutions. Therefore, it would be interesting to see what the consequences of the di erent eld content are for the supersymmetric solutions of the model. In Chapter 5, we studied the solutions of K-gravity based on the observation that the eld equations can be split into two parts one of which is the 3D Bach tensor that vanishes for conformally Einstein spaces and one of which is purely algebraic in the powers of the curvature. With this approach, the conformally Einstein solutions of the theory can be classi ed easily. We show that solutions of only three algebraic types are possible: Type-D, Type-II and Type-N. Since these solutions are conformally at, we extend them trivially to be the solutions to the Chern-Simons modi ed version of the theory. It is also shown that solutions survive in the Born-Infeld type modi cation. For these di erent possibilities, physical properties of the black hole solutions, conserved charges and entropy, are presented. In future work, an exhaustive reach for all solutions with nontrivial 3D Bach tensor (namely, H 6= 0) could be done in the K-gravity and the BIK gravity along the lines NMG and other extended 3D theories [52{54, 110, 122]. All the work that has been presented in this thesis is based on one central theme: Imagining a lower dimensional universe makes Einstein's theory trivial from many perspectives, but it also creates a whole new playground for ideas to modify it, which are not possible otherwise. Modi cations that we have considered yield, among many other things, di erent theoretical possibilities for achieving gravitational dynamics, a richer structure of black hole physics, along with the opportunity to study the holographic principle in a more general setup. One might argue that this should be enough to pursue such a research program. However, it seems that all these attempts always bring some new interesting features at a price. They can also be seen as just di erent ways to understand how unique Einstein's theory is. It is, of course, up to the reader to decide.
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