Gravitação quadrática em (2 + 1)D com e sem termo topológico de Chern-Simons

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

O espaço-tempo não comutativo em Teoria Quântica de Campos, Matéria Condensada Mole e Física Biológica

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Eletrodinâmica de ordem superior em (2+1)D

Pós-graduação em Física - IFT

Soluções do tipo vórtice em um modelo de Maxwell-Chern-Simons-Higgs com campos de Gauge distintos

Pós-graduação em Física - FEG

Soluções tipo vórtex em teorias de gauge Chern-Simons-Maxwell-Higgs

Pós-graduação em Física - IFT

Four-dimensional current algebra from Chern-Simons theory

We study an abelian Chern-Simons theory on a five-dimensional manifold with boundary. We find it to be equivalent to a higher-derivative generalization of the abelian Wess-Zumino-Witten model on the boundary. It contains a U(1) current algebra with an operational extension.

Supersymmetric Chern-Simons theories with vector matter

In this paper we discuss SU(N) Chern-Simons theories at level k with both fermionic and bosonic vector matter. In particular we present an exact calculation of the free energy of the N = 2 supersymmetric model (with one chiral field) for all values of the `t Hooft coupling in the large N limit. This is done by using a generalization of the standard Hubbard-Stratanovich method because the SUSY model contains higher order polynomial interactions.

Supersymmetry of classical solutions in Chern-Simons higher spin supergravity

We construct and study classical solutions in Chern-Simons supergravity based on the superalgebra sl(N vertical bar N = 1). The algebra for the N = 3 case is written down explicitly using the fact that it arises as the global part of the super conformal W-3 superalgebra. For this case we construct new classical solutions and study their supersymmetry. Using the algebra we write down the Killing spinor equations and explicitly construct the Killing spinor for conical defects and black holes in this theory. We show that for the general sl(N|N - 1) theory the condition for the periodicity of the Killing spinor can be written in terms of the products of the odd roots of the super algebra and the eigenvalues of the holonomy matrix of the background. Thus the supersymmetry of a given background can be stated in terms of gauge invariant and well defined physical observables of the Chern-Simons theory. We then show that for N >= 4, the sl(N|N - 1) theory admits smooth supersymmetric conical defects.

Chern-Simons vortices and holography

In this paper, based on the AdS(4)/CFT3 duality, we have explored the precise connection between the abelian Chern-Simons (CS) Higgs model in (2 + 1) dimensions to that with its dual gravitational counterpart living in one higher dimension. It has been observed that theU(1) current computed at the boundary of the AdS(4) could be expressed as the local function of the vortex solution that has the remarkable structural similarity to that with the Ginzburg-Landau (GL) type local expression for the current associated with the Maxwell-CS type vortices in (2 + 1) dimensions. In order to explore this duality a bit further we have also computed the coherence length as well as the magnetic penetration depth associated with these vortices. Finally using the knowledge of both the coherence length as well as the magnetic penetration depth we have computed the Ginzburg-Landau coefficient for the Maxwell-CS type vortices in (2 + 1) dimensions.

3D gravity, Chern-Simons and higher spins: A mini introduction

We give a review on (a) elements of (2 + 1)-dimensional gravity, (b) some aspects of its relation to Chern-Simons theory, (c) its generalization to couple higher spins, and (d) cosmic singularity resolution as an application in the context of flat space higher spin theory. A knowledge of the Einstein-Hilbert action, classical non-Abelian gauge theory and some (negotiable amount of) maturity are the only pre-requisites.

Three-dimensional superconformal field theory, Chern-Simons theory, and their correspondence

In this thesis, we discuss 3d-3d correspondence between Chern-Simons theory and three-dimensional N = 2 superconformal field theory. In the 3d-3d correspondence proposed by Dimofte-Gaiotto-Gukov information of abelian flat connection in Chern-Simons theory was not captured. However, considering M-theory configuration giving the 3d-3d correspondence and also other several developments, the abelian flat connection should be taken into account in 3d-3d correspondence. With help of the homological knot invariants, we construct 3d N = 2 theories on knot complement in 3-sphere for several simple knots. Previous theories obtained by Dimofte-Gaiotto-Gukov can be obtained by Higgsing of the full theories. We also discuss the importance of all flat connections in the 3d-3d correspondence by considering boundary conditions in 3d N = 2 theories and 3-manifold.

非相对论Chern-Simons多涡旋解的拓扑结构(英文)

运用规范势分解理论研究了Jackiw-Pi模型中的自对偶方程,得到一个新的自对偶方程,发现了Chern-Simons多涡旋解与拓扑荷之间的联系。为了研究Jackiw-Pi模型多涡旋解的拓扑性质,构造了一个新的静态自对偶Chern-Simons多涡旋解,每个涡旋由5个实参数描述。2个实参量用来描述涡旋的位置,2个实参量用来描述涡旋的尺度和相位,还有一个实参量描述涡旋的荷。为了研究拓扑数对涡旋形状的影响,给出了具有不同拓扑数的多涡旋解。另外还研究了该涡旋解的磁通量的拓扑量子化。

SU(2)Chern-Simons涡旋解的拓扑结构

运用规范势分解理论研究了Dunne-Jackiw-Pi-Trugenberger模型中的自对偶方程,得到一个静态的自对偶Chern-Simons多涡旋解,每个涡旋由5个参数描述。发现了自对偶解与拓扑数之间的关系,而拓扑数由Brouwer度与Hopf指标确定。同时,也研究了该涡旋解的磁通量的拓扑量子化。

Vortices in (Abelian) Chern-Simons gauge theory

The vortex solutions of various classical planar field theories with (Abelian) Chern-Simons term are reviewed. Relativistic vortices, put forward by Paul and Khare, arise when the Abelian Higgs model is augmented with the Chern-Simons term. Adding a suitable sixth-order potential and turning off the Maxwell term provides us with pure Chern-Simons theory, with both topological and non-topological self-dual vortices, as found by Hong-Kim-Pac, and by Jackiw-Lee-Weinberg. The non-relativistic limit of the latter leads to non-topological Jackiw-Pi vortices with a pure fourth-order potential. Explicit solutions are found by solving the Liouville equation. The scalar matter field can be replaced by spinors, leading to fermionic vortices. Alternatively, topological vortices in external field are constructed in the phenomenological model proposed by Zhang-Hansson-Kivelson. Non-relativistic Maxwell-Chern-Simons vortices are also studied. The Schrodinger symmetry of Jackiw-Pi vortices, as well as the construction of some time-dependent vortices, can be explained by the conformal properties of non-relativistic space-time, derived in a Kaluza-Klein-type framework. (c) 2009 Elsevier B.V. All rights reserved.

规范势分解与Chern-Simons场中涡旋解的拓扑结构

本论文主要包括两部分内容，一部分简述了规范势的可分解理论，第二部分研究了Chern-Simons涡旋解的拓扑结构。讨论了SU(2)规范势分解的几何意义。提出了非对易规范势的可分解性，求出了非对易 群规范势用单位矢量场的分解以及规范平行条件下的规范场强。利用规范势分解理论和Ф-映射拓扑流理论分别研究了Jackiw-Pi模型和SU(2)Dunne-Jackiw-Pi-Trugenberger模型涡旋的拓扑结构，得到一个新的自对偶方程，发现了Chern-Simons多涡旋解与拓扑数之间的联系。我们构造了一个新的静态的自对偶Chern-Simons多涡旋解，每个涡旋由5个实参数描述。为了研究拓扑数对涡旋形状的影响，给出了具有不同拓扑数的多涡旋解，并绘出了涡旋密度的分布图。我们还研究了该涡旋解的磁通量的拓扑量子化