京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19494号 / 理博第4154号 / 新制||理||1597(附属図書館) / 32530 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川合 光, 教授 畑 浩之, 教授 田中 貴浩 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

In the following thesis, I will conduct a thermodynamic analysis of the Taub-NUT spacetime in various dimensions, as well as show uses for Taub-NUT and other Hyper-Kahler spacetimes. <br /><br /> Thermodynamic analysis (by which I mean the calculation of the entropy and other thermodynamic quantities, and the analysis of these quantities) has in the past been done by use of background subtraction. The recent derivation of the (A)dS/CFT correspondences from String theory has allowed for easier and quicker analysis. I will use Taub-NUT space as a template to test these correspondences against the standard thermodynamic calculations (via the N&ouml;ether method), with (in the Taub-NUT-dS case especially) some very interesting results. <br /><br /> There is also interest in obtaining metrics in eleven dimensions that can be reduced down to ten dimensional string theory metrics. Taub-NUT and other Hyper-Kahler metrics already possess the form to easily facilitate the Kaluza-Klein reduction, and embedding such metrics into eleven dimensional metrics containing M2 or M5 branes produces metrics with interesting Dp-brane results.

In the following thesis, I will conduct a thermodynamic analysis of the Taub-NUT spacetime in various dimensions, as well as show uses for Taub-NUT and other Hyper-Kahler spacetimes. <br /><br /> Thermodynamic analysis (by which I mean the calculation of the entropy and other thermodynamic quantities, and the analysis of these quantities) has in the past been done by use of background subtraction. The recent derivation of the (A)dS/CFT correspondences from String theory has allowed for easier and quicker analysis. I will use Taub-NUT space as a template to test these correspondences against the standard thermodynamic calculations (via the N&ouml;ether method), with (in the Taub-NUT-dS case especially) some very interesting results. <br /><br /> There is also interest in obtaining metrics in eleven dimensions that can be reduced down to ten dimensional string theory metrics. Taub-NUT and other Hyper-Kahler metrics already possess the form to easily facilitate the Kaluza-Klein reduction, and embedding such metrics into eleven dimensional metrics containing M2 or M5 branes produces metrics with interesting Dp-brane results.

One of the most important results emerging from string theory is the gauge gravity duality (AdS/CFT correspondence) which tells us that certain problems in particular gravitational backgrounds can be exactly mapped to a particular dual gauge theory a quantum theory very similar to the one explaining the interactions between fundamental subatomic particles. The chief merit of the duality is that a difficult problem in one theory can be mapped to a simpler and solvable problem in the other theory. The duality can be used both ways. Most of the current theoretical framework is suited to study equilibrium systems, or systems where time dependence is at most adiabatic. However in the real world, systems are almost always out of equilibrium. Generically these scenarios are described by quenches, where a parameter of the theory is made time dependent. In this dissertation I describe some of the work done in the context of studying quantum quench using the AdS/CFT correspondence. We recover certain universal scaling type of behavior as the quenching is done through a quantum critical point. Another question that has been explored in the dissertation is time dependence of the gravity theory. Present cosmological observations indicate that our universe is accelerating and is described by a spacetime called de-Sitter(dS). In 2011 there had been a speculation over a possible duality between de-Sitter gravity and a particular field theory (Euclidean SP(N) CFT). However a concrete realization of this proposition was still lacking. Here we explicitly derive the dS/CFT duality using well known methods in field theory. We discovered that the time dimension emerges naturally in the derivation. We also describe further applications and extensions of dS/CFT.