Modelos de Schwinger, Thirring e Kondo à temperatura finita: um estudo

Pós-graduação em Física - IFT

Construção exata de sólitons de Hopf

Pós-graduação em Física - IFT

Twinlike models for kinks and compactons in flat and warped spacetime

This work deals with the presence of twinlike models in scalar field theories. We show how to build distinct scalar field theories having the same extended solution, with the same energy density and linear stability. Here, however, we start from a given but generalized scalar field theory, and we construct the corresponding twin model, which also engenders generalized dynamics. We investigate how the twinlike models arise in both flat and curved spacetimes. In the curved spacetime, we consider a braneworld model with the warp factor controlling the spacetime geometry with a single extra dimension of infinite extent. In particular, we study linear stability in both flat and curved spacetimes, and in the case of curved spacetime-in both the gravity and the scalar field sectors-for the two braneworld models. DOI: 10.1103/PhysRevD.86.125021

Integral form of Yang-Mills equations and its gauge invariant conserved charges

Despite the fact that the integral form of the equations of classical electrodynamics is well known, the same is not true for non-Abelian gauge theories. The aim of the present paper is threefold. First, we present the integral form of the classical Yang-Mills equations in the presence of sources and then use it to solve the long-standing problem of constructing conserved charges, for any field configuration, which are invariant under general gauge transformations and not only under transformations that go to a constant at spatial infinity. The construction is based on concepts in loop spaces and on a generalization of the non-Abelian Stokes theorem for two-form connections. The third goal of the paper is to present the integral form of the self-dual Yang-Mills equations and calculate the conserved charges associated with them. The charges are explicitly evaluated for the cases of monopoles, dyons, instantons and merons, and we show that in many cases those charges must be quantized. Our results are important in the understanding of global properties of non-Abelian gauge theories.

The r-matrix of the Alday-Arutyunov-Frolov model

We investigate the classical integrability of the Alday-Arutyunov-Frolov model, and show that the Lax connection can be reduced to a simpler 2 x 2 representation. Based on this result, we calculate the algebra between the L-operators and find that it has a highly non-ultralocal form. We then employ and make a suitable generalization of the regularization technique proposed by Mail let for a simpler class of non-ultralocal models, and find the corresponding r- and s-matrices. We also make a connection between the operator-regularization method proposed earlier for the quantum case, and the Mail let's symmetric limit regularization prescription used for non-ultralocal algebras in the classical theory.

The concept of quasi-integrability for modified non-linear Schrodinger models

We consider modifications of the nonlinear Schrodinger model (NLS) to look at the recently introduced concept of quasi-integrability. We show that such models possess an in finite number of quasi-conserved charges which present intriguing properties in relation to very specific space-time parity transformations. For the case of two-soliton solutions where the fields are eigenstates of this parity, those charges are asymptotically conserved in the scattering process of the solitons. Even though the charges vary in time their values in the far past and the far future are the same. Such results are obtained through analytical and numerical methods, and employ adaptations of algebraic techniques used in integrable field theories. Our findings may have important consequences on the applications of these models in several areas of non-linear science. We make a detailed numerical study of the modified NLS potential of the form V similar to (vertical bar psi vertical bar(2))(2+epsilon), with epsilon being a perturbation parameter. We perform numerical simulations of the scattering of solitons for this model and find a good agreement with the results predicted by the analytical considerations. Our paper shows that the quasi-integrability concepts recently proposed in the context of modifications of the sine-Gordon model remain valid for perturbations of the NLS model.

A Skyrme-like model with an exact BPS bound

We propose a new Skyrme-like model with fields taking values on the sphere S3 or, equivalently, on the group SU(2). The action of the model contains a quadratic kinetic term plus a quartic term which is the same as that of the Skyrme-Faddeev model. The novelty of the model is that it possess a first order Bogomolny type equation whose solutions automatically satisfy the second order Euler-Lagrange equations. It also possesses a lower bound on the static energy which is saturated by the Bogomolny solutions. Such Bogomolny equation is equivalent to the so-called force free equation used in plasma and solar Physics, and which possesses large classes of solutions. An old result due to Chandrasekhar prevents the existence of finite energy solutions for the force free equation on the entire three- dimensional space R3. We construct new exact finite energy solutions to the Bogomolny equations for the case where the space is the three-sphere S3, using toroidal like coordinates.

Aspects of Integrability in Gauge/String Correspondence

In this thesis, we present our work about some generalisations of ideas, techniques and physical interpretations typical for integrable models to one of the most outstanding advances in theoretical physics of nowadays: the AdS/CFT correspondences. We have undertaken the problem of testing this conjectured duality under various points of view, but with a clear starting point - the integrability - and with a clear ambitious task in mind: to study the finite-size effects in the energy spectrum of certain string solutions on a side and in the anomalous dimensions of the gauge theory on the other. Of course, the final desire woul be the exact comparison between these two faces of the gauge/string duality. In few words, the original part of this work consists in application of well known integrability technologies, in large parte borrowed by the study of relativistic (1+1)-dimensional integrable quantum field theories, to the highly non-relativisic and much complicated case of the thoeries involved in the recent conjectures of AdS5/CFT4 and AdS4/CFT3 corrspondences. In details, exploiting the spin chain nature of the dilatation operator of N = 4 Super-Yang-Mills theory, we concentrated our attention on one of the most important sector, namely the SL(2) sector - which is also very intersting for the QCD understanding - by formulating a new type of nonlinear integral equation (NLIE) based on a previously guessed asymptotic Bethe Ansatz. The solutions of this Bethe Ansatz are characterised by the length L of the correspondent spin chain and by the number s of its excitations. A NLIE allows one, at least in principle, to make analytical and numerical calculations for arbitrary values of these parameters. The results have been rather exciting. In the important regime of high Lorentz spin, the NLIE clarifies how it reduces to a linear integral equations which governs the subleading order in s, o(s0). This also holds in the regime with L ! 1, L/ ln s finite (long operators case). This region of parameters has been particularly investigated in literature especially because of an intriguing limit into the O(6) sigma model defined on the string side. One of the most powerful methods to keep under control the finite-size spectrum of an integrable relativistic theory is the so called thermodynamic Bethe Ansatz (TBA). We proposed a highly non-trivial generalisation of this technique to the non-relativistic case of AdS5/CFT4 and made the first steps in order to determine its full spectrum - of energies for the AdS side, of anomalous dimensions for the CFT one - at any values of the coupling constant and of the size. At the leading order in the size parameter, the calculation of the finite-size corrections is much simpler and does not necessitate the TBA. It consists in deriving for a nonrelativistc case a method, invented for the first time by L¨uscher to compute the finite-size effects on the mass spectrum of relativisic theories. So, we have formulated a new version of this approach to adapt it to the case of recently found classical string solutions on AdS4 × CP3, inside the new conjecture of an AdS4/CFT3 correspondence. Our results in part confirm the string and algebraic curve calculations, in part are completely new and then could be better understood by the rapidly evolving developments of this extremely exciting research field.

Die Rolle von Hopfkategorien und Operaden in störungstheoretischen Quantenfeldtheorien

Die Vorhersagen störungstheoretischer Quantenfeldtheorienzeigen eine gute Übereinstimmung mit experimentellgemessenen Werten. Bei diesen störungstheoretischenBerechnungen treten allerdings Ultraviolettdivergenzen auf,die keine physikalische Interpretation der Ergebnisseermöglichen. Durch Renormierung dieser Theorien erhält manjedoch berechnbare Ergebnisse mit hoher experimentellerVorhersagekraft. Der Renormierungsvorgang kann durch eineHopfalgebra, die sogenannte 'Hopfalgebra der Wurzelbäume',beschrieben werden.Die vorliegende Arbeit leistet einen Beitrag für weitereUntersuchungen dieser Hopfalgebrenstruktur und Bestimmungneuer mathematischer Methoden zur Beschreibung desRenormierungsvorgangs. Dazu wird die algebraische Strukturvon Renormierung aus der Sicht der Kategorientheorie und derTheorie von Operaden untersucht.Aus Sicht der Kategorientheorie lassen sich die den Renormierungsprozess beschreibenden mathematischen Größen ineiner Kategorie zusammenfassen. Eine additive Strukturermöglicht dabei die Berücksichtigung beliebigerRenormierungsschemata. Auf dieser Kategorie kann einassoziativitätsverletzendes Produkt definiert werden, wobeidie Verletzung durch einen sogenannten 'Assoziator'kontrolliert werden kann. Die Struktur wird auf die einerHopfkategorie erweitert, so daß eine kategorientheoretischeUntersuchung des Renormierungsprozesses ermöglicht wird.Diese Hopfkategorie wird aus Sicht von Renormierunginterpretiert, wobei Beispielrechnungen die definierteStruktur verdeutlichen.Aus algebraischer Sicht kann aufgrund der graphischenDarstellung des Operadenproduktes eine Bijektivität zwischenWurzelbäumen und Operaden gezeigt werden. Auf diesenOperaden kann wiederum eine Hopfalgebrenstruktur definiertwerden. Beispiele verdeutlichen diese Bijektivität.

Complex higher spins, Weyl invariance and tractors

In this thesis work I analyze higher spin field theories from a first quantized perspective, finding in particular new equations describing complex higher spin fields on Kaehler manifolds. They are studied by means of worldline path integrals and canonical quantization, in the framework of supersymmetric spinning particle theories, in order to investigate their quantum properties both in flat and curved backgrounds. For instance, by quantizing a spinning particle with one complex extended supersymmetry, I describe quantum massless (p,0)-forms and find a worldline representation for their effective action on a Kaehler background, as well as exact duality relations. Interesting results are found also in the definition of the functional integral for the so called O(N) spinning particles, that will allow to study real higher spins on curved spaces. In the second part, I study Weyl invariant field theories by using a particular mathematical framework known as tractor calculus, that enable to maintain at each step manifest Weyl covariance.

Strongly correlated quantum gases in one dimension

In this work, we discuss some theoretical topics related to many-body physics in ultracold atomic and molecular gases. First, we present a comparison between experimental data and theoretical predictions in the context of quantum emulator of quantum field theories, finding good results which supports the efficiency of such simulators. In the second and third parts, we investigate several many-body properties of atomic and molecular gases confined in one dimension.

Top-quark pair production at hadron colliders

In this thesis we investigate several phenomenologically important properties of top-quark pair production at hadron colliders. We calculate double differential cross sections in two different kinematical setups, pair invariant-mass (PIM) and single-particle inclusive (1PI) kinematics. In pair invariant-mass kinematics we are able to present results for the double differential cross section with respect to the invariant mass of the top-quark pair and the top-quark scattering angle. Working in the threshold region, where the pair invariant mass M is close to the partonic center-of-mass energy sqrt{hat{s}}, we are able to factorize the partonic cross section into different energy regions. We use renormalization-group (RG) methods to resum large threshold logarithms to next-to-next-to-leading-logarithmic (NNLL) accuracy. On a technical level this is done using effective field theories, such as heavy-quark effective theory (HQET) and soft-collinear effective theory (SCET). The same techniques are applied when working in 1PI kinematics, leading to a calculation of the double differential cross section with respect to transverse-momentum pT and the rapidity of the top quark. We restrict the phase-space such that only soft emission of gluons is possible, and perform a NNLL resummation of threshold logarithms. The obtained analytical expressions enable us to precisely predict several observables, and a substantial part of this thesis is devoted to their detailed phenomenological analysis. Matching our results in the threshold regions to the exact ones at next-to-leading order (NLO) in fixed-order perturbation theory, allows us to make predictions at NLO+NNLL order in RG-improved, and at approximate next-to-next-to-leading order (NNLO) in fixed order perturbation theory. We give numerical results for the invariant mass distribution of the top-quark pair, and for the top-quark transverse-momentum and rapidity spectrum. We predict the total cross section, separately for both kinematics. Using these results, we analyze subleading contributions to the total cross section in 1PI and PIM originating from power corrections to the leading terms in the threshold expansions, and compare them to previous approaches. We later combine our PIM and 1PI results for the total cross section, this way eliminating uncertainties due to these corrections. The combined predictions for the total cross section are presented as a function of the top-quark mass in the pole, the minimal-subtraction (MS), and the 1S mass scheme. In addition, we calculate the forward-backward (FB) asymmetry at the Tevatron in the laboratory, and in the ttbar rest frames as a function of the rapidity and the invariant mass of the top-quark pair at NLO+NNLL. We also give binned results for the asymmetry as a function of the invariant mass and the rapidity difference of the ttbar pair, and compare those to recent measurements. As a last application we calculate the charge asymmetry at the LHC as a function of a lower rapidity cut-off for the top and anti-top quarks.

Search for Dark Matter in Events with a Hadronically Decaying W or Z Boson and Missing Transverse Momentum in pp Collisions at root s=8 TeV with the ATLAS Detector

A search is presented for dark matter pair production in association with a W or Z boson in pp collisions representing 20.3 fb(-1) of integrated luminosity at root s = 8 TeV using data recorded with the ATLAS detector at the Large Hadron Collider. Events with a hadronic jet with the jet mass consistent with a W or Z boson, and with large missing transverse momentum are analyzed. The data are consistent with the standard model expectations. Limits are set on the mass scale in effective field theories that describe the interaction of dark matter and standard model particles, and on the cross section of Higgs production and decay to invisible particles. In addition, cross section limits on the anomalous production of W or Z bosons with large missing transverse momentum are set in two fiducial regions.

Supersymmetric quantum mechanics on the lattice: I. Loop formulation

Simulations of supersymmetric field theories on the lattice with (spontaneously) broken supersymmetry suffer from a fermion sign problem related to the vanishing of the Witten index. We propose a novel approach which solves this problem in low dimensions by formulating the path integral on the lattice in terms of fermion loops. For N=2 supersymmetric quantum mechanics the loop formulation becomes particularly simple and in this paper – the first in a series of three – we discuss in detail the reformulation of this model in terms of fermionic and bosonic bonds for various lattice discretisations including one which is Q-exact.