Doctor of Philosophy
This thesis consists of different projects in classical and quantum field theory on a curved background which are connected by a common usage of theoretical ideas as well as cal- culation techniques. The introduction clarifies such connections. In the second chapter we apply the Dirac constraint formalism to the second and first order 1 + 1 dimensional gravitational action coupled to a scalar field. The third chapter is devoted to a calculation of the one loop effective action for a spinor field coupled to a constant background chiral vector field. In the fourth chapter we find a new expression for the running coupling through the conformal anomaly in a strong background gauge field. We compare this expression with the value obtained by the standard procedure. This expression should be useful for finding all loop order contributions to the effective action of a gauge the- ory. The second part of the thesis is devoted to the applied aspects of the AdS/CFT correspondence and related issues. In the fifth chapter we review a three dimensional model of a strongly correlated holographic plasma dual to a 3 + 1 dimensional gravity model of exotic black holes. Then we consider the extension of the Correlated Stability Conjecture which attempts to connect mechanical instabilities of black holes with the thermodynamical instabilities of the related holographic plasma by adding to the the- ory additional conserved chargers connected with the values of the scalar field at the boundary of a black brane. Also, we propose a simple thermodynamic model to test the generalized conjecture. Then, we focus on some transport properties of the model. Namely we check Eling-Oz formula for the bulk-to-shear viscosity of holographic plasmas for different temperature regimes. The last chapter is devoted to a CFT calculation of the entanglement entropy on a sphere for free theories. We try to connect the results with the calculations based on AdS/CFT approach. For this purpose the heat kernel technique is used in this chapter. In our discussion proposals for future work are stated.
Patrushev, Alexander, "Topics in Field Theory" (2012). Electronic Thesis and Dissertation Repository. Paper 864.