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1 
Aspects of SU(24) symmetric field theories and the LinMaldacena geometriesvan Anders, Greg 11 1900 (has links)
Gauge/gravity duality is an important tool for learning about strongly coupled gauge theories. This thesis explores a set of examples of this duality in which the field theories have SU(24) supersymmetry and discrete sets of vacuum solutions. Specifically, we use the duality to propose Lagrangian definitions of type IIA Little String Theory on S⁵ as doublescaling limits of the PlaneWave Matrix Model, maximally supersymmetric YangMills theory
on R x S² and N=4 supersymmetric YangMills theory on R×S³/Zk. We find the supergravity solutions dual to generic vacua of the PlaneWave Matrix Model and maximally supersymmetric YangMills theory on R×S².
We use the supergravity duals to calculate new instanton amplitudes for the PlaneWave Matrix Model at strong coupling. Finally, we study a natural coarsegraining of the vacua, and find that the associated geometries are singular. We define an entropy functional that vanishes for regular geometries, is nonzero for singular geometries, and is maximized by the thermal state.

2 
Aspects of SU(24) symmetric field theories and the LinMaldacena geometriesvan Anders, Greg 11 1900 (has links)
Gauge/gravity duality is an important tool for learning about strongly coupled gauge theories. This thesis explores a set of examples of this duality in which the field theories have SU(24) supersymmetry and discrete sets of vacuum solutions. Specifically, we use the duality to propose Lagrangian definitions of type IIA Little String Theory on S⁵ as doublescaling limits of the PlaneWave Matrix Model, maximally supersymmetric YangMills theory
on R x S² and N=4 supersymmetric YangMills theory on R×S³/Zk. We find the supergravity solutions dual to generic vacua of the PlaneWave Matrix Model and maximally supersymmetric YangMills theory on R×S².
We use the supergravity duals to calculate new instanton amplitudes for the PlaneWave Matrix Model at strong coupling. Finally, we study a natural coarsegraining of the vacua, and find that the associated geometries are singular. We define an entropy functional that vanishes for regular geometries, is nonzero for singular geometries, and is maximized by the thermal state.

3 
Aspects of SU(24) symmetric field theories and the LinMaldacena geometriesvan Anders, Greg 11 1900 (has links)
Gauge/gravity duality is an important tool for learning about strongly coupled gauge theories. This thesis explores a set of examples of this duality in which the field theories have SU(24) supersymmetry and discrete sets of vacuum solutions. Specifically, we use the duality to propose Lagrangian definitions of type IIA Little String Theory on S⁵ as doublescaling limits of the PlaneWave Matrix Model, maximally supersymmetric YangMills theory
on R x S² and N=4 supersymmetric YangMills theory on R×S³/Zk. We find the supergravity solutions dual to generic vacua of the PlaneWave Matrix Model and maximally supersymmetric YangMills theory on R×S².
We use the supergravity duals to calculate new instanton amplitudes for the PlaneWave Matrix Model at strong coupling. Finally, we study a natural coarsegraining of the vacua, and find that the associated geometries are singular. We define an entropy functional that vanishes for regular geometries, is nonzero for singular geometries, and is maximized by the thermal state. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

4 
Disorder in holographic field theories : inhomogeneous geometries, momentum relaxation and SYK modelsLoureiro, Bruno January 2018 (has links)
Holographic dualities are now an established tool in the study of universal properties of strongly coupled field theories. Yet, theories without translational symmetry are still poorly understood in this context. In this dissertation, we investigate three new approaches to this challenging problem. The first part of the dissertation concerns a class of phenomenological holographic models in which momentum relaxation can be achieved without breaking translational symmetry in the dual geometry. In particular, we focus on an example in which the dual geometry is similar to antide Sitter (AdS) BransDicke theory. We study the thermodynamic and transport properties of the model and show that for strong momentum relaxation and low temperatures the model has insulatorlike behaviour. In the second part, we go beyond the effective description and consider holographic theories which explicitly break translational symmetry. From the perspective of gravity, these theories translate to geometries that vary explicitly in the boundary spacelike coordinates. We refer to these geometries as 'inhomogeneous' and investigate two approaches to study them. The first is motivated by the question: "what happens to a homogeneous geometry when coupled with a field varying randomly in space?". Starting from an AdS geometry at zero or finite temperature, we show that a spatially varying random Maxwell potential drives the dual field theory to a nontrivial infrared fixed point characterised by an emerging scale invariance. Thermodynamic and transport properties of this disordered ground state are also discussed. The second is motivated by the complementary question: "how does a random geometry affect a probe field?". In the weak disorder limit, we show that disorder induces an additional powerlaw decay in the dual correlation functions. For certain choices of geometry profile, this contribution becomes dominant in the infrared, indicating the breaking of perturbation theory and the possible existence of a phase transition induced by disorder. The third and last part of this dissertation switches from the gravity to the field theoretical side of the duality. We discuss the SachdevYeKitaev (SYK) model, a disordered manybody model with distinctive black holelike properties. We provide analytical and numerical evidence that these holographic properties are robust against a natural onebody deformation for a finite range of parameters. Outside this interval, this system undergoes a chaoticintegrable transition.

5 
Wilson loops and their gravity duals in AdS_4/CFT_3Farquet, Daniel January 2015 (has links)
In the first part of this thesis, we study the duality of Wilson loops and M2branes in AdS<sub>4</sub>/CFT<sub>3</sub>. We focus on supersymmetric Mtheory solutions on AdS<sub>4</sub>xY<sub>7</sub> that have a superconformal dual description on S<sup>3</sup> = ?AdS<sup>4</sup>. We will find that the Hamiltonian function h<sub>M</sub> for the Mtheory circle plays an important role in the duality. We show that an M2brane wrapping the Mtheory circle is supersymmetric precisely at the critical points of h<sub>M</sub>, and moreover the value of this function at those points determines the M2brane actions. Such a configuration determines the holographic dual of a Wilson loop for a Hopf circle in S<sup>3</sup>. We find agreement in large classes of examples between the Wilson loop and its dual M2brane and also that the image h<sub>M</sub>(Y<sub>7</sub>) determines the range of support of the eigenvalues in the dual large N matrix model, with the critical points of h<sub>M</sub> mapping to points where the derivative of the eigenvalue density is discontinuous. We will then move away from the threesphere and construct gravity duals to a broad class of N=2 supersymmetric gauge theories defined on a general class of threemanifold geometries. The gravity backgrounds are based on Euclidean selfdual solutions to fourdimensional gauged supergravity. As well as constructing new examples, we prove in general that for solutions defined on the fourball the gravitational free energy depends only on the supersymmetric Killing vector. Our result agrees with the large N limit of the free energy of the dual gauge theory, computed using localisation. This constitutes an exact check of the gauge/gravity correspondence for a very broad class of gauge theories defined on a general class of background threemanifold geometries. To further verify that our gravitational backgrounds are indeed dual to field theories on their boundaries, we compute Wilson loops and their M2brane duals in this general setting. We find that the Wilson loop is given by a simple closed formula which depends on the background geometry only through the supersymmetric Killing vector field. The supergravity dual M2brane precisely reproduces this large N field theory result. This constitutes a further check of AdS<sub>4</sub>/CFT<sub>3</sub> for a very broad class of examples.

6 
Duality symmetries in stringinspired supergravity: Tdualities and the gauge/gravity correspondenceWhiting, Catherine Ann 01 May 2015 (has links)
Motivated by the AdS/CFT correspondence, new supersymmetric solutions to Type IIB and Type IIA supergravity are presented. These solutions contain $AdS_5$ or $AdS_4$ factors and are generated using Tduality symmetries of supergravity. The technique used to generate these solutions consists of performing a series of nonAbelian and Abelian Tdualities, sometimes with coordinate shifts inbetween, to FreundRubin type seed backgrounds. An added bonus of the gauge fixing procedure inherent in nonAbelian TDuality is the freedom to generate backgrounds with extra free parameters, some examples of which are presented. Aspects of the dual field theories of these new solutions are analyzed using holography techniques. The supersymmetry of these new backgrounds is also discussed.
In addition to supergravity backgrounds with AdS, the study of generalized CalabiYau manifolds in the context of flux compactifications is briefly reviewed. The particular case of the resolved cone over $Y^{p,q}$ and its admission of generalized SU(3) structure solutions is examined. Contrary to geometries with $AdS$ factors, whose field theory duals are conformal field theories, these types of geometries can be phenomenologically interesting to study, as their gauge theory duals are minimally supersymmetric and confining, thus they could someday help aid our understanding of stronglycoupled QCD (Quantum Chromodynamics).

7 
Applications of the holographic principle in string theoryButton, Bradly Kevin 01 July 2014 (has links)
The holographic principle has become an extraordinary tool in theoretical physics, most notably in the form of the AntideSitter Conformal Field Theory (AdS/CFT) correspondence, in which classical gravitational degrees of freedom in Ndimensions are related quantum field theory degrees of freedom in N − 1 dimensions in the limit of a large number of fields. Here we present an account of the AdS/CFT correspondence, also known as the gauge/gravity duality, from its origins in the large N 'tHooft expansion, up to Maldacena's proposal that type IIB string theory in the presences of Dbranes at low energy is dual to an N = 4, d = 4, U(N) super YangMills on AdS5 × S5 . We begin with an extensive review of (super)string theory including Dbranes. We then present the general formulation of the AdS/CFT in the supergravity background of AdS5 × S5 , along with several examples of how it is used in terms of the identification of bulk fields with operators on the bound ary of a CFT. We move on to discuss two applications of the gauge/gravity duality. The first is the application of the holographic gauge/gravity correspondence to the QCDkstring. The second applies the AdS/CFT formalism to a Kerr black hole solution embedded in 10dimensional heterotic sting theory. These two applications of the holographic gauge/gravity duality comprise the original work presented here. We follow with summaries and discussions of the background material, the original work, and future investigations.

8 
Holographic studies of thermal gauge theories with flavourThomson, Rowan January 2007 (has links)
The AdS/CFT correspondence and its extensions to more general gauge/gravity dualities have provided a powerful framework for the study of strongly coupled gauge theories. This thesis explores properties of a large class of thermal strongly coupled gauge theories using the gravity dual. In order to bring the holographic framework closer to Quantum Chromodynamics (QCD), we study theories with matter in the fundamental representation. In particular, we focus on the holographic dual of SU(Nc) supersymmetric
YangMills theory coupled to Nf<<Nc flavours of fundamental
matter at finite temperature, which is realised as Nf Dqbrane probes in the near horizon (black hole) geometry of Nc black Dpbranes.
We explore many aspects of these Dp/Dq brane systems, often focussing on the D3/D7 brane system which is dual to a four dimensional gauge theory.
We study the thermodynamics of the Dqbrane probes in the black hole geometry.
At low temperature, the branes sit outside the black hole and the meson spectrum is discrete and possesses a mass gap. As the temperature increases, the branes approach a critical solution. Eventually, they fall into the horizon and a phase transition occurs. At large Nc and large 't Hooft coupling, we show that this phase transition is always first order. We calculate the free energy, entropy and energy
densities, as well as the speed of sound in these systems. We compute the meson spectrum for brane embeddings outside the horizon and find that tachyonic modes appear where this phase is expected to be unstable from thermodynamic considerations.
We study the system at nonzero baryon density nb and find that there is a line of phase transitions for small nb, terminating at a critical point with finite nb.
We demonstrate that, to leading order in Nf/Nc,
the viscosity to entropy density ratio in these theories saturates the
conjectured universal bound.
Finally, we compute spectral functions and diffusion constants for fundamental matter in the high temperature phase of the D3/D7 theory.

9 
Holographic studies of thermal gauge theories with flavourThomson, Rowan January 2007 (has links)
The AdS/CFT correspondence and its extensions to more general gauge/gravity dualities have provided a powerful framework for the study of strongly coupled gauge theories. This thesis explores properties of a large class of thermal strongly coupled gauge theories using the gravity dual. In order to bring the holographic framework closer to Quantum Chromodynamics (QCD), we study theories with matter in the fundamental representation. In particular, we focus on the holographic dual of SU(Nc) supersymmetric
YangMills theory coupled to Nf<<Nc flavours of fundamental
matter at finite temperature, which is realised as Nf Dqbrane probes in the near horizon (black hole) geometry of Nc black Dpbranes.
We explore many aspects of these Dp/Dq brane systems, often focussing on the D3/D7 brane system which is dual to a four dimensional gauge theory.
We study the thermodynamics of the Dqbrane probes in the black hole geometry.
At low temperature, the branes sit outside the black hole and the meson spectrum is discrete and possesses a mass gap. As the temperature increases, the branes approach a critical solution. Eventually, they fall into the horizon and a phase transition occurs. At large Nc and large 't Hooft coupling, we show that this phase transition is always first order. We calculate the free energy, entropy and energy
densities, as well as the speed of sound in these systems. We compute the meson spectrum for brane embeddings outside the horizon and find that tachyonic modes appear where this phase is expected to be unstable from thermodynamic considerations.
We study the system at nonzero baryon density nb and find that there is a line of phase transitions for small nb, terminating at a critical point with finite nb.
We demonstrate that, to leading order in Nf/Nc,
the viscosity to entropy density ratio in these theories saturates the
conjectured universal bound.
Finally, we compute spectral functions and diffusion constants for fundamental matter in the high temperature phase of the D3/D7 theory.

10 
Black Holes And Their EntropyMei, Jianwei 2010 August 1900 (has links)
This dissertation covers two di erent but related topics: the construction of new
black hole solutions and the study of the microscopic origin of black hole entropy.
In the solution part, two di erent sets of new solutions are found. The rst
concerns a PlebanskiDemianski type solution in the vedimensional pure Einstein
gravity, and the second concerns a threecharge (two of which equal) tworotation
solution to the vedimensional maximal supergravity. Obtaining new and interesting
black hole solutions is an important and challenging task in studying general relativity
and its extensions. During the past decade, the solutions become even more important
because they might nd applications in the study of the gauge/gravity duality, which
is currently in the central stage of the quantum gravity research.
The Kerr/CFT correspondence is a recently propose example of the gauge/gravity
duality. In the entropy part, we explicitly show that the Kerr/CFT correspondence
can be applied to all known extremal stationary and axisymmetric black holes. We
improve over previous works in showing that this can be done in a general fashion,
rather than testing di erent solutions case by case. This e ort makes it obvious that
the common structure of the near horizon metric for all known extremal stationary
and axisymmetric black holes is playing a key role in the success of the Kerr/CFT
correspondence. The discussion is made possible by the identi cation of two general
ans atze that cover all such known solutions.

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