Year: 2014
Type: dissertation
Abstract: This thesis consists of two parts. The first part addresses the issue of conformal anomaly matching from the holographic perspective and is reported in chapter 2. The second part aims to the study of higher spin generalisations of black holes in 3D and is reported in chapters 3 and 4. In chapter 2 we discuss various issues related to the understanding of the conformal anomaly matching in CFT from the dual holographic viewpoint. First, we act with a PBH diffeomorphism on a generic 5D RG flow geometry and show that the corresponding on-shell bulk action reproduces the Wess-Zumino term for the dilaton of broken conformal symmetry, with the expected coefficient aUV − aIR. Then, we consider a specific 3D example of RG flow whose UV asymptotics is normalizable and admits a 6D lifting. We promote a modulus ρ appearing in the geometry to a function of boundary coordinates. In a 6D description ρ is the scale of an SU(2) instanton. We determine the smooth deformed background up to second order in the space- time derivatives of ρ and find that the 3D on-shell action reproduces a boundary kinetic term for the massless field τ = logρ with the correct coefficient δc = cUV − cIR. We further analyze the linearized fluctuations around the deformed background geometry and compute the one-point functions and show that they are reproduced by a Liouville-type action for the massless scalar τ, with background charge due to the coupling to the 2D curvature R(2). The resulting central charge matches δc. We give an interpretation of this action in terms of the (4,0) SCFT of the D1-D5 system in type I theory. The content of this chapter has been reported in arXiv:1307.3784v3 [hep-th] (JHEP 1311 (2013) 044). In chapter 3 we address some issues of recent interest, related to the asymptotic symmetry algebra of higher spin black holes in sl(3, R) × sl(3, R) Chern Simons (CS) formulation. In our analysis we resort to both, Regge-Teitelboim and Dirac bracket methods and when possible identify them. We compute explicitly the Dirac bracket algebra on the phase space, in both, diagonal and principal embeddings. The result for principal embedding is shown to be isomorphic to W (2) × W (2). 33 Our revision complements the viewpoints of [1, 2]. The content of this chapter has been reported in arXiv:1407.8241 [hep-th]. In chapter 4 we present a class of 3D black holes based on flat con- nections which are polynomials in the BTZ hs(λ) × hs(λ)-valued con- nection. We solve analytically the fluctuation equations of matter in their background and find the spectrum of their Quasi Normal Modes. We analyze the bulk to boundary two-point functions. We also relate our results and those arising in other backgrounds discussed recently in the literature on the subject. The content of this chapter has been reported in arXiv:1407.5203v2 [hep-th](submitted to JHEP).
Source: SDL
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2181729450