Topics in Field Theory

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

Eling-Oz Formula for Exotic Hairy Black Holes

We checked Eling-Oz formula [1] for the bulk viscosity of the holographic fluid dual to the exotic black holes [2]. Initially, Eling and Oz argued that the formula is valid in the high temperature and adiabatic limits. In [3] the validity of the formula for \caln=2^* plasma and cascading gauge theory was pushed forward for arbitrary temperatures. We successfully verified the formula with the computations of the bulk viscosity [4,5] for a wide range of the temperatures. Moreover, it correctly reproduces the critical behavior in the vicinity of the critical point, where the bulk-to-shear viscosity diverges.Comment: 9 pages, 4 figures, references added and corrected, minor clarifications added, accepted by Phys. Lett.

Differential sensitivity of brainstem vs cortical astrocytes to changes in pH reveals functional regional specialization of astroglia

Astrocytes might function as brain interoceptors capable of detecting different (chemo)sensory modalities and transmitting sensory information to the relevant neural networks controlling vital functions. For example, astrocytes which reside near the ventral surface of the brainstem (central respiratory chemosensitive area) respond to physiological decreases in pH with vigorous elevations in intracellular Ca(2+) and release of ATP. ATP transmits astroglial excitation to the brainstem respiratory network and contributes to adaptive changes in lung ventilation. Here we show that in terms of pH-sensitivity ventral brainstem astrocytes are clearly distinct from astrocytes residing in the cerebral cortex. We monitored vesicular fusion in cultured rat brainstem astrocytes using total internal reflection fluorescence microscopy and found that approximately 35% of them respond to acidification with an increased rate of exocytosis of ATP-containing vesicular compartments. These fusion events require intracellular Ca(2+) signaling and are independent of autocrine ATP actions. In contrast, the rate of vesicular fusion in cultured cortical astrocytes is not affected by changes in pH. Compared to cortical astrocytes, ventral brainstem astrocytes display higher levels of expression of genes encoding proteins associated with ATP vesicular transport and fusion, including vesicle-associated membrane protein-3 and vesicular nucleotide transporter. These results suggest that astrocytes residing in different parts of the rat brain are functionally specialized. In contrast to cortical astrocytes, astrocytes of the brainstem chemosensitive area(s) possess signaling properties which are functionally relevant – they are able to sense changes in pH and respond to acidification with enhanced vesicular release of ATP