Influence of topology on the scale setting

Recently a new method to set the scale in lattice gauge theories, based on the gradient flow generated by the Wilson action, has been proposed, and the systematic errors of the new scales t0 and w0 have been investigated by various groups. The Wilson flow provides also an interesting alternative smoothing procedure particularly useful for the measurement of the topological charge as a pure gluonic observable. We show the viability of this method for N=1 supersymmetric Yang-Mills theory by analysing the configurations produced by the DESY-Muenster Collaboration. The relation between the scale and the topological charge has been investigated showing a strong correlation. We have found that the scale has a linear dependence on the topological charge, the slope of which increases decreasing the volume and the gluino mass. Moreover we have investigated this dependence as a function of the reference parameter used to define the scale: the tuning of this parameter turns out to be fundamental for a more reliable scale setting. Similar conclusions hold for the Sommer parameter r0.

Gravidade de Lovelock e a correspondência AdS/CFT

A correspondência AdS/CFT é uma notável ferramenta no estudo de teorias de gauge fortemente acopladas que podem ser mapeadas em uma descrição gravitacional dual fracamente acoplada. A correspondência é melhor entendida no limite em que ambos $N$ e $\\lambda$, o rank do grupo de gauge e o acoplamento de \'t Hooft da teoria de gauge, respectivamente, são infinitos. Levar em consideração interações com termos de curvatura de ordem superior nos permite considerar correções de $\\lambda$ finito. Por exemplo, a primeira correção de acoplamento finito para supergravidade tipo IIB surge como um termo de curvatura com forma esquemática $\\alpha\'^3 R^4$. Neste trabalho investigamos correções de curvatura no contexto da gravidade de Lovelock, que é um cenário simples para investigar tais correções pois as suas equações de movimento ainda são de segunda ordem em derivadas. Esse cenário também é particularmente interessante do ponto de vista da correspondência AdS/CFT devido a sua grande classe de soluções de buracos negros assintoticamente AdS. Consideramos um sistema de gravidade AdS-axion-dilaton em cinco dimensões com um termo de Gauss-Bonnet e encontramos uma solução das equações de movimento, o que corresponde a uma black brane exibindo uma anisotropia espacial, onde a fonte da anisotropia é um campo escalar linear em uma das coordenadas espaciais. Estudamos suas propriedades termodinâmicas e realizamos a renormalização holográfica usando o método de Hamilton-Jacobi. Finalmente, usamos a solução obtida como dual gravitacional de um plasma anisotrópico fortemente acoplado com duas cargas centrais independentes, $a eq c$. Calculamos vários observáveis relevantes para o estudo do plasma, a saber, a viscosidade de cisalhamento sobre densidade de entropia, a força de arrasto, o parâmetro de jet quenching, o potencial entre um par quark-antiquark e a taxa de produção de fótons.

Applications of Quantum Field Theory, From the Formal to the Phenomenological

Thesis (Ph.D.)--University of Washington, 2016-06

Quantum Space-Time and Noncommutative Gauge Field Theories

Arguments arising from quantum mechanics and gravitation theory as well as from string theory, indicate that the description of space-time as a continuous manifold is not adequate at very short distances. An important candidate for the description of space-time at such scales is provided by noncommutative space-time where the coordinates are promoted to noncommuting operators. Thus, the study of quantum field theory in noncommutative space-time provides an interesting interface where ordinary field theoretic tools can be used to study the properties of quantum spacetime. The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative space-time is the apparent loss of Lorentz invariance that has been addressed in different ways in the literature. One recently developed approach is to eliminate the Lorentz violating effects by integrating over the parameter of noncommutativity. Fundamental properties of such theories are investigated in this thesis. Another issue addressed is model building, which is difficult in the noncommutative setting due to severe restrictions on the possible gauge symmetries imposed by the noncommutativity of the space-time. Possible ways to relieve these restrictions are investigated and applied and a noncommutative version of the Minimal Supersymmetric Standard Model is presented. While putting the results obtained in the three original publications into their proper context, the introductory part of this thesis aims to provide an overview of the present situation in the field.

Gauge Field Theories, Quantum Space-Time and Some Applications

In this thesis, the possibility of extending the Quantization Condition of Dirac for Magnetic Monopoles to noncommutative space-time is investigated. The three publications that this thesis is based on are all in direct link to this investigation. Noncommutative solitons have been found within certain noncommutative field theories, but it is not known whether they possesses only topological charge or also magnetic charge. This is a consequence of that the noncommutative topological charge need not coincide with the noncommutative magnetic charge, although they are equivalent in the commutative context. The aim of this work is to begin to fill this gap of knowledge. The method of investigation is perturbative and leaves open the question of whether a nonperturbative source for the magnetic monopole can be constructed, although some aspects of such a generalization are indicated. The main result is that while the noncommutative Aharonov-Bohm effect can be formulated in a gauge invariant way, the quantization condition of Dirac is not satisfied in the case of a perturbative source for the point-like magnetic monopole.

Gauge-invariant reformulation of theories with second-class constraints

Given a classical dynamical theory with second-class constraints, it is sometimes possible to construct another theory with first-class constraints, i.e., a gauge-invariant one, which is physically equivalent to the first theory. We identify some conditions under which this may be done, explaining the general principles and working out several examples. Field theoretic applications include the chiral Schwinger model and the non-linear sigma model. An interesting connection with the work of Faddeev and Shatashvili is pointed out.

Consistent deformations of [p,p]-type gauge field theories

Using BRST-cohomological techniques, we analyze the consistent deformations of theories describing free tensor gauge fields whose symmetries are represented by Young tableaux made of two columns of equal length p, p > 1. Under the assumptions of locality and Poincaré invariance, we find that there is no consistent deformation of these theories that non-trivially modifies the gauge algebra and/or the gauge transformations. Adding the requirement that the deformation contains no more than two derivatives, the only possible deformation is a cosmological-constant-like term. © SISSA/ISAS 2004.

On anomalous U(1) gauge theory in four dimensions

We discuss the consistency, unitarity and Lorentz invariance of an anomalous U(1) gauge theory in four dimensions. Our analysis is based on an effective low-energy action valid in the chiral symmetry broken phase. The allegedly bad properties of anomalous theories (except non-renormalizability) are examined. It is shown that, in the low-energy context, the theory can be consistently and unitarily quantised, and is formally Lorentz covariant.

Supersymmetric Solution Of Gauge Hierarchy Problem

Some recent developments with respect to the resolution of the gauge hierarchy problem in grand unified theories by supersymmetry are presented. A general argument is developed to show how global supersymmetry maintains the stability of the different mass-scales under perturbative effects.

Noncommutative Quantum Field Theories and UV/IR Mixing

Our present-day understanding of fundamental constituents of matter and their interactions is based on the Standard Model of particle physics, which relies on quantum gauge field theories. On the other hand, the large scale dynamical behaviour of spacetime is understood via the general theory of relativity of Einstein. The merging of these two complementary aspects of nature, quantum and gravity, is one of the greatest goals of modern fundamental physics, the achievement of which would help us understand the short-distance structure of spacetime, thus shedding light on the events in the singular states of general relativity, such as black holes and the Big Bang, where our current models of nature break down. The formulation of quantum field theories in noncommutative spacetime is an attempt to realize the idea of nonlocality at short distances, which our present understanding of these different aspects of Nature suggests, and consequently to find testable hints of the underlying quantum behaviour of spacetime. The formulation of noncommutative theories encounters various unprecedented problems, which derive from their peculiar inherent nonlocality. Arguably the most serious of these is the so-called UV/IR mixing, which makes the derivation of observable predictions especially hard by causing new tedious divergencies, to which our previous well-developed renormalization methods for quantum field theories do not apply. In the thesis I review the basic mathematical concepts of noncommutative spacetime, different formulations of quantum field theories in the context, and the theoretical understanding of UV/IR mixing. In particular, I put forward new results to be published, which show that also the theory of quantum electrodynamics in noncommutative spacetime defined via Seiberg-Witten map suffers from UV/IR mixing. Finally, I review some of the most promising ways to overcome the problem. The final solution remains a challenge for the future.

Conformal invariance and scalar-tensor theories

A new generalisation of Einstein’s theory is proposed which is invariant under conformal mappings. Two scalar fields are introduced in addition to the metric tensor field, so that two special choices of gauge are available for physical interpretation, the ‘Einstein gauge’ and the ‘atomic gauge’. The theory is not unique but contains two adjustable parameters ζ anda. Witha=1 the theory viewed from the atomic gauge is Brans-Dicke theory (ω=−3/2+ζ/4). Any other choice ofa leads to a creation-field theory. In particular the theory given by the choicea=−3 possesses a cosmological solution satisfying Dirac’s ‘large numbers’ hypothesis.

Gauge-invariant reformulation of an anomalous gauge theory

An anomalous gauge theory can be reformulated in a gauge invariant way without any change in its physical content. This is demonstrated here for the exactly soluble chiral Schwinger model. Our gauge invariant version is very different from the Faddeev-Shatashvili proposal [L.D. Faddeev and S.L. Shatashvili, Theor. Math. Phys. 60 (1984) 206] and involves no additional gauge-group-valued fields. The status of the "gauge" A0=0 sometimes used in anomalous theories is also discussed and justified in our reformulation.

Hall viscosity to entropy ratio in higher derivative theories

In this paper based on the basic principles of gauge/gravity duality we compute the hall viscosity to entropy ratio in the presence of various higher derivative corrections to the dual gravitational description embedded in an asymptotically AdS(4) space time. As the first step of our analysis, considering the back reaction we impose higher derivative corrections to the abelian gauge sector of the theory where we notice that the ratio indeed gets corrected at the leading order in the coupling. Considering the probe limit as a special case we compute this leading order correction over the fixed background of the charged black brane solution. Finally we consider higher derivative (R-2) correction to the gravity sector of the theory where we notice that the above ratio might get corrected at the sixth derivative level.

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.

Spin three gauge theory revisited

We study the problem of consistent interactions for spin-3 gauge fields in flat spacetime of arbitrary dimension 3$">n>3. Under the sole assumptions of Poincaré and parity invariance, local and perturbative deformation of the free theory, we determine all nontrivial consistent deformations of the abelian gauge algebra and classify the corresponding deformations of the quadratic action, at first order in the deformation parameter. We prove that all such vertices are cubic, contain a total of either three or five derivatives and are uniquely characterized by a rank-three constant tensor (an internal algebra structure constant). The covariant cubic vertex containing three derivatives is the vertex discovered by Berends, Burgers and van Dam, which however leads to inconsistencies at second order in the deformation parameter. In dimensions 4$">n>4 and for a completely antisymmetric structure constant tensor, another covariant cubic vertex exists, which contains five derivatives and passes the consistency test where the previous vertex failed. © SISSA 2006.