Over the past decade, the AdS/CFT correspondence has proven to be a remarkable tool to study various properties of strongly coupled field theories. In the context of the holography, Ryu and Takayanagi have proposed an elegant method to calculate entanglement entropy for these field theories. In this thesis, we use this holographic entanglement entropy to study a candidate c-theorem and entanglement entropy for singular surfaces. We use holographic entanglement entropy for strip geometry and construct a candidate c-function in arbitrary dimensions. For holographic theories dual to Einstein gravity, this c-function is shown to decrease monotonically along RG flows. A sufficient condition required for this monotonic flow is that the stress tensor of the matter fields driving the holographic RG flow must satisfy the null energy condition over the holographic surface used to calculate the entanglement entropy. In the case where the bulk theory is described by Gauss-Bonnet gravity, the latter condition alone is not sufficient to establish the monotonic flow of the c-function. We also observe that for certain holographic RG flows, the entanglement entropy undergoes a ‘phase transition’ as the size of the system grows and as a result, evolution of the c-function may exhibit a discontinuous drop. Then, we turn towards studying the holographic entanglement entropy for regions with a singular boundary in higher dimensions. Here, we find that various singularities make new universal contributions. When the boundary CFT has an even spacetime dimension, we find that the entanglement entropy of a conical surface contains a term quadratic in the logarithm of the UV cut-off. In four dimensions, the coefficient of this contribution is proportional to the central charge c. A conical singularity in an odd number of spacetime dimensions contributes a term proportional to the logarithm of the UV cut-off. We also study the entanglement entropy for various boundary surfaces with extended singularities. In these cases, extended singularities contribute through new linear or quadratic terms in logarithm only when the locus of the singularity is even dimensional and curved.

Gauge-string duality has provided a powerful framework for the study of strongly coupled gauge theories and non-perturbative string models. This thesis analyzes the holographic description of non-local gauge theory operators and some aspects of the Bagger-Lambert theory. The latter, as a proposal for a multiple M2-branes effective theory, is conjectured to be the holographic dual of a compactification of M-theory. We show that all half-BPS Wilson loop operators in N=4 SYM - which are labeled by Young tableaus - have a gravitational dual description in terms of D5-branes or alternatively in terms of D3-branes in AdS5xS5. We prove that the insertion of a half-BPS Wilson loop operator in the N=4 SYM path integral is achieved by integrating out the degrees of freedom on a configuration of bulk D5-branes or alternatively on a configuration of bulk D3-branes. We construct a new class of supersymmetric surface operators in N=4 SYM and find the corresponding dual supergravity solutions. Consistency requires constructing N=4 SYM in the D7 supergravity background and not in flat space. This enlarges the class of holographic gauge theories dual to string theory backgrounds to gauge theories in non-trivial supergravity backgrounds. We write down a maximally supersymmetric one parameter deformation of the field theory action of Bagger and Lambert and we show that this theory on RxT2 is invariant under the superalgebra of the maximally supersymmetric Type IIB plane wave. It is argued that this theory holographically describes the Type IIB plane wave in the discrete light-cone quantization (DLCQ). Finally, we show by explicit computation that the Bagger-Lambert Lagrangian realizes the M2-brane superalgebra, including also two p-form central charges that encode the M-theory intersections involving M2-branes.

The purpose of this thesis is to design and fabricate Gigahertz range voltage controlled oscillator based on intrinsically tunable film bulk acoustic resonator.Modified Butterworth Van Dyke (MBVD) model was studied and implemented to simulate FBAR behavior. Advanced designed system (ADS) was used as the simulation tool.Oscillator theory is studied and an oscillator based on non-tunable FBAR at 2GHz is simulated which shows -132 dBc/Hz phase noise @ 100 kHz offset frequency.A 5.5 GHz Voltage controlled oscillator based on intrinsically tunable FBAR is designed. Frequency tuning of 129 MHz with phase noise of -106 dBc/Hz @ 100 kHz is achieved. The circuit is designed on a novel carrier substrate which includes integrated resonators and passive components. Bipolar junction transistors are mounted on the carrier substrate by silver epoxy. The thesis describes the design, development and processing of the carrier substrate, BSTO based resonators, and the oscillator circuit.

Gauge-string duality has provided a powerful framework for the study of strongly coupled gauge theories and non-perturbative string models. This thesis analyzes the holographic description of non-local gauge theory operators and some aspects of the Bagger-Lambert theory. The latter, as a proposal for a multiple M2-branes effective theory, is conjectured to be the holographic dual of a compactification of M-theory. We show that all half-BPS Wilson loop operators in N=4 SYM - which are labeled by Young tableaus - have a gravitational dual description in terms of D5-branes or alternatively in terms of D3-branes in AdS5xS5. We prove that the insertion of a half-BPS Wilson loop operator in the N=4 SYM path integral is achieved by integrating out the degrees of freedom on a configuration of bulk D5-branes or alternatively on a configuration of bulk D3-branes. We construct a new class of supersymmetric surface operators in N=4 SYM and find the corresponding dual supergravity solutions. Consistency requires constructing N=4 SYM in the D7 supergravity background and not in flat space. This enlarges the class of holographic gauge theories dual to string theory backgrounds to gauge theories in non-trivial supergravity backgrounds. We write down a maximally supersymmetric one parameter deformation of the field theory action of Bagger and Lambert and we show that this theory on RxT2 is invariant under the superalgebra of the maximally supersymmetric Type IIB plane wave. It is argued that this theory holographically describes the Type IIB plane wave in the discrete light-cone quantization (DLCQ). Finally, we show by explicit computation that the Bagger-Lambert Lagrangian realizes the M2-brane superalgebra, including also two p-form central charges that encode the M-theory intersections involving M2-branes.

We report on the first systematic study of correlation functions in N=4 super Yang-Mills theory using integrability techniques. In particular, we show how to compute three- and four- point functions of single-trace gauge-invariant operators at tree level in the SU(2) sector of the theory. Using the AdS/CFT correspondence, the correlation functions that we compute can be thought of as the joining or splitting of strings moving in AdS5 × S5. We show that when one (two) of the operators in the three-(four-)point function are taken to be small BPS operators, our weak coupling results match perfectly with the strong coupling results in the Frolov-Tseytlin limit. We conclude by presenting some results that will be needed to extend the methods presented in this thesis beyond the SU(2) sector of N=4 super Yang-Mills.

A novel holographic model of chiral symmetry breaking has been proposed by Kuperstein and Sonnenschein by embedding non-supersymmetric probe D7 and anti-D7 branes in the Klebanov-Witten background. We study the dynamics of the probe flavours in this model in the presence of finite temperature and a constant electromagnetic field. In keeping with the weakly coupled field theory intuition, we find the magnetic field promotes spontaneous breaking of chiral symmetry whereas the electric field restores it. The former effect is universally known as the ``magnetic catalysis" in chiral symmetry breaking. In the presence of an electric field such a condensation is inhibited and a current flows. Thus we are faced with a steady-state situation rather than a system in equilibrium. We conjecture a definition of thermodynamic free energy for this steady-state phase and using this proposal we study the detailed phase structure when both electric and magnetic fields are present in two representative configurations: mutually perpendicular and parallel. / text

We report on the first systematic study of correlation functions in N=4 super Yang-Mills theory using integrability techniques. In particular, we show how to compute three- and four- point functions of single-trace gauge-invariant operators at tree level in the SU(2) sector of the theory. Using the AdS/CFT correspondence, the correlation functions that we compute can be thought of as the joining or splitting of strings moving in AdS5 × S5. We show that when one (two) of the operators in the three-(four-)point function are taken to be small BPS operators, our weak coupling results match perfectly with the strong coupling results in the Frolov-Tseytlin limit. We conclude by presenting some results that will be needed to extend the methods presented in this thesis beyond the SU(2) sector of N=4 super Yang-Mills.

Over the past decade, the AdS/CFT correspondence has proven to be a remarkable tool to study various properties of strongly coupled field theories. In the context of the holography, Ryu and Takayanagi have proposed an elegant method to calculate entanglement entropy for these field theories. In this thesis, we use this holographic entanglement entropy to study a candidate c-theorem and entanglement entropy for singular surfaces. We use holographic entanglement entropy for strip geometry and construct a candidate c-function in arbitrary dimensions. For holographic theories dual to Einstein gravity, this c-function is shown to decrease monotonically along RG flows. A sufficient condition required for this monotonic flow is that the stress tensor of the matter fields driving the holographic RG flow must satisfy the null energy condition over the holographic surface used to calculate the entanglement entropy. In the case where the bulk theory is described by Gauss-Bonnet gravity, the latter condition alone is not sufficient to establish the monotonic flow of the c-function. We also observe that for certain holographic RG flows, the entanglement entropy undergoes a ‘phase transition’ as the size of the system grows and as a result, evolution of the c-function may exhibit a discontinuous drop. Then, we turn towards studying the holographic entanglement entropy for regions with a singular boundary in higher dimensions. Here, we find that various singularities make new universal contributions. When the boundary CFT has an even spacetime dimension, we find that the entanglement entropy of a conical surface contains a term quadratic in the logarithm of the UV cut-off. In four dimensions, the coefficient of this contribution is proportional to the central charge c. A conical singularity in an odd number of spacetime dimensions contributes a term proportional to the logarithm of the UV cut-off. We also study the entanglement entropy for various boundary surfaces with extended singularities. In these cases, extended singularities contribute through new linear or quadratic terms in logarithm only when the locus of the singularity is even dimensional and curved.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第22992号 / 理博第4669号 / 新制||理||1670(附属図書館) / 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 高柳 匡, 教授 青木 慎也, 教授 田中 貴浩 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

We employ the AdS/CFT correspondence and hydrodynamics to analyze the transport properties of \(2+1\) dimensional electron fluids. In this way, we use theoretical methods from both condensed matter and high-energy physics to derive tangible predictions that are directly verifiable in experiment. The first research topic we consider is strongly-coupled electron fluids. Motivated by early results by Gurzhi on the transport properties of weakly coupled fluids, we consider whether similar properties are manifest in strongly coupled fluids. More specifically, we focus on the hydrodynamic tail of the Gurzhi effect: A decrease in fluid resistance with increasing temperature due to the formation of a Poiseuille flow of electrons in the sample. We show that the hydrodynamic tail of the Gurzhi effect is also realized in strongly coupled and fully relativistic fluids, but with modified quantitative features. Namely, strongly-coupled fluids always exhibit a smaller resistance than weakly coupled ones and are, thus, far more efficient conductors. We also suggest that the coupling dependence of the resistance can be used to measure the coupling strength of the fluid. In view of these measurements, we provide analytical results for the resistance as a function of the shear viscosity over entropy density \(\eta/s\) of the fluid. \(\eta/s\) is itself a known function of the coupling strength in the weak and infinite coupling limits. In further analysis for strongly-coupled fluids, we propose a novel strongly coupled Dirac material based on a kagome lattice, Scandium-substituted Herbertsmithite (ScHb). The large coupling strength of this material, as well as its Dirac nature, provides us with theoretical and experimental access to non-perturbative relativistic and quantum critical physics. A highly suitable method for analyzing such a material's transport properties is the AdS/CFT correspondence. Concretely, using AdS/CFT we derive an estimate for ScHb's \(\eta/s\) and show that it takes a value much smaller than that observed in weakly coupled materials. In turn, the smallness of \(\eta/s\) implies that ScHb's Reynolds number, \(Re\), is large. In fact, \(Re\) is large enough for turbulence, the most prevalent feature of fluids in nature, to make its appearance for the first time in electronic fluids. Switching gears, we proceed to the second research topic considered in this thesis: Weakly coupled parity-breaking electron fluids. More precisely, we analyze the quantitative and qualitative changes to the classical Hall effect, for electrons propagating hydrodynamically in a lead. Apart from the Lorentz force, a parity-breaking fluid's motion is also impacted by the Hall-viscous force; the shear-stress force induced by the Hall-viscosity. We show that the interplay of these two forces leads to a hydrodynamic Hall voltage with non-linear dependence on the magnetic field. More importantly, the Lorentz and Hall-viscous forces become equal at a non-vanishing magnetic field, leading to a trivial hydrodynamic Hall voltage. Moreover, for small magnetic fields we provide analytic results for the dependence of the hydrodynamic Hall voltage on all experimentally-tuned parameters of our simulations, such as temperature and density. These dependences, along with the zero of the hydrodynamic Hall voltage, are distinct features of hydrodynamic transport and can be used to verify our predictions in experiments. Last but not least, we consider how a distinctly electronic property, spin, can be included into the hydrodynamic framework. In particular, we construct an effective action for non-dissipative spin hydrodynamics up to first order in a suitably defined derivative expansion. We also show that interesting spin-transport effects appear at second order in the derivative expansion. Namely, we show that the fluid's rotation polarizes its spin. This is the hydrodynamic manifestation of the Barnett effect and provides us with an example of hydrodynamic spintronics. To conclude this thesis, we discuss several possible extensions of our research, as well as proposals for research in related directions. / Wir verwenden die AdS/CFT-Korrespondenz und die Theorie der Hydrodynamik, um die Transporteigenschaften von \(2+1\)-dimensionalen Elektronisches Flüssigkeiten zu untersuchen. Somit nutzen wir sowohl theoretische Methoden der Fest\-körper\-physik als auch der Hochenergiephysik, um konkrete Vorhersagen zu treffen, die unmittelbar in Experimenten verifiziert werden können. Zunächst betrachten wir das Forschungsfeld der stark gekoppelten Elektronischen Flüssigkeiten. Motiviert durch die frühen Ergebnisse für die Transporteigenschaften schwach gekoppelter Flüssigkeiten von Gurzhi untersuchen wir, ob sich ähnliche Eigenschaften auch in stark gekoppelten Flüssigkei\-ten manifestieren. Dabei konzentrieren wir uns insbesondere auf den hydrodynamischen Teil des Gurzhi-Effekts, in welchem der Widerstand der Flüssigkeit mit steigender Temperatur sinkt, weil sich im untersuchten Material ein Poiseuillefluss von Elektronen bildet. Wir zeigen, dass dieser hydrodynamische Teil des Gurzhi-Effekts auch in stark gekoppelten und vollständig relativistischen Flüssigkeiten realisiert ist, einige Eigenschaften sich hierbei aber quantitativ unterscheiden. Insbesondere zeigen stark gekoppelte Flüssigkeiten immer kleinere Widerstände als schwach gekoppelte, und sind damit wesentlich effektivere Leiter. Wir schlagen darüber hinaus vor, die Abhängigkeit des Widerstands von der Kopplung zu nutzen, um die Kopplungsstärke der Flüssigkeit zu messen. Für diese Messungen stellen wir analytische Ergebnisse bereit, welche den Widerstand als Funktion des Quotienten aus Scherviskosität und Entropiedichte \(\eta/s\) der Flüssigkeit ausdrücken. Dabei ist \(\eta/s\) selbst eine bekannte Funktion der Kopplungsstärke in den Grenzfällen schwacher und unendlich starker Kopplung. In einer weiteren Untersuchung stark gekoppelter Flüssigkeiten schlagen wir Scandium-substituiertes Herbertsmithit (ScHb) als neuartiges, stark gekoppeltes Diracmaterial vor, welches auf dem Kagome-Gitter basiert. Die hohe Kopplungsstärke und die Dirac-Eigenschaften dieses Materials vermitteln uns theoretischen und experimentellen Zugang zu nicht perturbativer relativistischer und quantenkritischer Physik. Um die Transporteigenschaften eines solchen Materials zu untersuchen, stellt die AdS/CFT-Korrespondenz eine hervorragend geeignete Methode dar. Konkret nutzen wir AdS/CFT, um eine Abschätzung von \(\eta/s\) in ScHb herzuleiten. Der so ermittelte Wert ist wesentlich kleiner als der entsprechende Messwert für schwach gekoppelte Materialien. Der kleine Wert von \(\eta/s\) wiederum impliziert, dass die Reynolds-Zahl \(Re\) in ScHb groß ist. Tatsächlich ist \(Re\) hinreichend groß, um erstmals Turbulenz in Elektronisches Flüssigkeiten beobachten zu können, ein Effekt, der auch in viele anderen Flüssigkeiten in der Natur vorkommt. Wir gehen zum zweiten Forschungsthema über, welches in der vorliegenden Arbeit besprochen wird: schwach gekoppelte, paritätsbrechende Elektronisches Flüssigkeiten. Wir betracthen die hydrodynamische Bewegung von Elektronen in einen zwei dimensionalen Kanal, und untersuchen die sich ergebenden quantitativen und qualitativen Änderungen gegenüber dem klassischen Hall-Effekt. Außer der Lorentzkraft ist die Bewegung einer paritätsbrechenden Flüss auch den Einflüssen der Hallviskositätskraft ausgesetzt, welche die von der Hall Viskosität induzierte Scherspannungskraft ist. Wir zeigen, dass das Wechselspiel dieser beiden Kräfte zu einer hydrodynamischen Hall-Spannung führt, die nicht linear vom magnetischen Feld abhängt. Noch wichtiger ist, dass Lorentz- sowie hallviskose Kraft für ein nicht verschwindendes Magnetfeld gleich werden und damit zu einer trivialen hydrodynamischen Hall-Spannung führen. Darüber hinaus geben wir für kleine Magnetfeldstärken analytische Ergebnisse an, die die Abhängigkeit der hydrodynamischen Hall-Spannung von allen experimentell festgelegten Parametern unserer Simulation, wie z.B. Temperatur und Dichte, beschreiben. Diese Abhängigkeiten sind zusammen mit der verschwindenden hydrodynamischen Hall-Spannung charakteristische Eigenschaften hydrodynamischen Transports und können daher verwendet werden, um unsere Vorhersagen experimentell zu verifizieren. Zu guter Letzt untersuchen wir, wie eine charakteristische Eigenschaft von Elektronen, der Spin, in die hydrodynamische Theorie einbezogen werden kann. Dazu konstruieren wir eine effektive Wirkung, die nicht dissipative Spin-Hydrodynamik bis zur ersten Ordnung in einer geeigneten Ableitungsentwicklung beschreibt. Wir zeigen darüber hinaus, dass in zweiter Ordnung dieser Entwicklung interessante Spin-Transporteffekte auftreten. Dabei stellt sich heraus, dass die Rotation der Flüssigkeit seinen Spin polarisiert. Dies ist die hydrodynamische Manifestation des Barnett-Effekts, die als Beispiel für hydrodynamische Spintronics dient. Zum Abschluss der vorliegenden Arbeit diskutieren wir mehrere mögliche Erweiterungen unserer Untersuchungen und unterbreiten Vorschläge für weitergehende Forschung in verschiedene Richtungen.