This thesis describes a geometric approach to integrable systems. In the first part we describe the geometry of Drinfeld--Sokolov integrable hierarchies including the corresponding tau-functions. Motivated by a relation between Drinfeld--Sokolov hierarchies and certain physical partition functions, we define a dispersionless limit of Drinfeld--Sokolov systems. We introduce a class of solutions which we call string solutions and prove that the tau-functions of string solutions satisfy Virasoro constraints generalizing those familiar from two-dimensional quantum gravity. In the second part we explain how procedures of Hamiltonian and quasi-Hamiltonian reductions in symplectic geometry arise naturally in the context of shifted symplectic structures. All constructions that appear in quasi-Hamiltonian reduction have a natural interpretation in terms of the classical Chern-Simons theory that we explain. As an application, we construct a prequantization of character stacks purely locally. / text

6d (2, 0) theory on M5 branes is investigated by considering its KK modes on a 2d space. Selecting KK modes on different 2d spaces amounts to choosing different set of selfdual strings as the perturbative degrees of freedom thus will give the 6d theories related to each other by U-duality. The 4d effective theory for the KK modes is studied via the M5-D3 duality. Except for the (p, q) open strings, which is the KK mode arising from the selfdual strings, the 3-string junction should also be added since it is the bound state of the (p, q) open strings. The quantization of the 3-string junctions gives the fields, which, when lifted to 6d, may account for the conformal anomaly of the 6d (2, 0) theory. The interaction between the open strings and the 3-string junctions is also considered. The Lagrangian and the corresponding N=4 supersymmetry transformation is obtained up to some additional terms to be added. Although the original 6d (2, 0) theory is not constructed directly, the 4d effective theory for the KK modes gives an equivalent description, from which the 6d S-matrix can be calculated.

Thesis (Ph. D.)--University of California, San Diego, 2009. / Title from first page of PDF file (viewed September 17, 2009). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 444-468).

A "Geometrodynamical Analog to Electric Charge" (or "p-charge") is defined (as in the earlier paper by Unruh, [Gen. Rel. and Grav., 2, (1971), pp 27-33 ] to be the period on a p-cycle (p = 1, 2, or 3) of a p-form which is constructed out of only the Riemann tensor or its derivatives. A previously-unpublished proof by Unruh is briefly summarized which proves that no non-zero p-charges can exist on a completely unrestricted metric field. The metric field is then constrained to obey Einstein's equations for empty space, and sets of linearly-independent, purely-gravitational p-forms are analyzed to determine if p-charges can be defined under these conditions. A scheme is developed, based on the spin-tensor representation of the gravitational field, to generate complete sets of such p-forms, arid calculate their derivatives, with a symbolic-manipulation computer program. It is shown that no gravitational p-forms that are linear combinations of less than five Riemann tensors and less than nine derivatives will result in p-charges. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Please note: this work is indefinitely embargoed in OpenBU. No public access is forecasted. To request private access, please click on the lock icon and fill out the appropriate web form. / Based on a qualitative study on the new development of Presbyterianism in China, this thesis explores the urban and rational side of Chinese Christianity, so as to open an empirical window on meso-level social change in urban China. From an empirical perspective, although the organizational form of the Presbyterian Church in China and its scope are still in the fledging stage, the discursive practices and the institutional and coalition building of Chinese Presbyterians fit into the profile of a social movement. This preliminary data collected so far examines the emerging Protestant elites and their role in the precarious civil society of today’s China. On the normative side, these Chinese Presbyterians articulate a strong political theology that blends the Anabaptist and the reformed theologies. In addition, the institutional and the missional tension of this movement is also under examination. In the end, this project is an experiment that tests the commensurability between theology and social sciences, especially the viability of theologically engaged ethnography. / 2031-01-01

Using the AdS/CFT correspondence, we study the anisotropic transport properties of both supersymmetric and non-supersymmetric matter fields on (2+1)-dimensional defects coupled to a (3+1)-dimensional N=4 SYM "heat bath". We address on the one hand the purely conformal defect where the only non-vanishing background field that we turn on is a "topological", parameter parametrizing the impact on the bulk. On the other hand we also address the case of a finite external background magnetic field, finite net charge density and finite mass. We find in the purely conformal limit that the system possesses a conduction threshold given by the wave number of the perturbation and that the charge transport arises from a quasiparticle spectrum which is consistent with an intuitive picture where the defect acquires a finite width in the direction of the SYM bulk. We also examine finite-coupling modifications arising from higher derivative interactions in the probe brane action. In the case of finite density, mass and magnetic field, our results generalize the conformal case. We discover at high frequencies a spectrum of quasiparticle resonances due to the magnetic field and finite density and at small frequencies a Drude-like expansion around the DC limit. Both of these regimes display many generic features and some features that we attribute to strong coupling, such as a minimum DC conductivity and an unusual behavior of the "cyclotron" and plasmon frequencies, which become correlated to the resonances found in the conformal case. We further study the hydrodynamic regime and the relaxation properties, in which the system displays a set of different possible transitions to the collisionless regime. The mass dependence can be cast in two regimes: a generic relativistic behavior dominated by the UV and a non-linear hydrodynamic behavior dominated by the IR. In the massless case, we also extend earlier results to find an interesting duality under the transformation of the conductivity and the exchange of density and magnetic field. Furthermore, we look at the thermodynamics and the phase diagram, which reproduces general features found earlier in 3+1 dimensional systems and demonstrates stability in the relevant phase.

Using the AdS/CFT correspondence, we study the anisotropic transport properties of both supersymmetric and non-supersymmetric matter fields on (2+1)-dimensional defects coupled to a (3+1)-dimensional N=4 SYM "heat bath". We address on the one hand the purely conformal defect where the only non-vanishing background field that we turn on is a "topological", parameter parametrizing the impact on the bulk. On the other hand we also address the case of a finite external background magnetic field, finite net charge density and finite mass. We find in the purely conformal limit that the system possesses a conduction threshold given by the wave number of the perturbation and that the charge transport arises from a quasiparticle spectrum which is consistent with an intuitive picture where the defect acquires a finite width in the direction of the SYM bulk. We also examine finite-coupling modifications arising from higher derivative interactions in the probe brane action. In the case of finite density, mass and magnetic field, our results generalize the conformal case. We discover at high frequencies a spectrum of quasiparticle resonances due to the magnetic field and finite density and at small frequencies a Drude-like expansion around the DC limit. Both of these regimes display many generic features and some features that we attribute to strong coupling, such as a minimum DC conductivity and an unusual behavior of the "cyclotron" and plasmon frequencies, which become correlated to the resonances found in the conformal case. We further study the hydrodynamic regime and the relaxation properties, in which the system displays a set of different possible transitions to the collisionless regime. The mass dependence can be cast in two regimes: a generic relativistic behavior dominated by the UV and a non-linear hydrodynamic behavior dominated by the IR. In the massless case, we also extend earlier results to find an interesting duality under the transformation of the conductivity and the exchange of density and magnetic field. Furthermore, we look at the thermodynamics and the phase diagram, which reproduces general features found earlier in 3+1 dimensional systems and demonstrates stability in the relevant phase.

Aiming at a systematic inclusion of pseudoscalar and vector mesons as active degrees of freedom in an effective Lagrangian, studies have been performed in this thesis concerning the foundations of such an effective Lagrangian as well as tree-level and beyond-tree-level calculations. Hereby, vector mesons are described by antisymmetric tensor fields. First, an existing power counting scheme for both pseudoscalar and vector mesons is extended to include the pseudoscalar-meson singlet in a systematic way. Based on this, tree-level calculations are carried out which are in good agreement with the available experimental data and several processes are predicted. In particular, the ω-π0 transition form factor is in better agreement with experimental data than the prediction done in the vector-meson-dominance model. Furthermore, a Lagrangian with vector mesons is used together with the leading contributions of chiral perturbation theory in order to calculate tree-level reactions in the sector of odd intrinsic parity. It turns out that both the Lagrangian with vector mesons and the Lagrangian of chiral perturbation theory are needed to describe experimental data. Additionally, a feasibility check for one-loop calculations with pseudoscalar and vector mesons in the loop is performed. Thereby, only a limited number of interaction terms in the Lagrangian with vector mesons is used. The results are used to both renormalise the low-energy constants of chiral perturbation theory up to chiral order Q4 and to determine the influence of loops with vector mesons on masses and decay constants of pseudoscalar mesons.

No description available.

The discovery of integrability in planar N=4 super Yang-Mills and ABJM has enabled a precise study of AdS/CFT. In the past decade integrability has been successfully applied to the spectrum of anomalous dimensions, which can now be obtained at any value of the coupling. However, in order to solve conformal field theories one also needs to understand their structure constants. Recently, there has been great progress in this direction with the all-loop proposal of Basso, Komatsu and Vieira. But there is still much to understand, as it is not yet possible to use that formalism to find structure constants of short operators at strong coupling. It is important to study wrapping corrections and resum them as the TBA did for the spectrum. It is also crucial to obtain perturbative data that can be used to check if the all-loop proposal is correct or if there are new structures that need to be unveiled. In this thesis we compute several structure constants of short operators at strong coupling, including the structure constant of Konishi with half-BPS operators. Still at strong coupling, we find a relation between the building blocks of superstring amplitudes and the tensor structures allowed by conformal symmetry. We also consider the case of extremal correlation functions and the relation of their poles to mixing with double-trace operators. We also study three-point functions at weak coupling. We take the OPE limit in a four-point function of half-BPS operators in order to shed some light on the structure of five-loop wrapping corrections of the Hexagon form factors. Finally, we take the first steps in the generalization of the Hexagon programme to other theories. We find the non-extremal setup in ABJM and the residual symmetry that it preserves, which we use to fix the two-particle form factor and constrain the four-particle hexagon. Finally, we find that the Watson equations hint at a dressing phase that needs to be further investigated.