Non-Abelian chiral gauge theories in two dimensions

An anomalous multiflavor chiral theory, with the gauge group SU(N), is studied using non-Abelian bosonization. The theory can be made gauge invariant by introducing Wess-Zumino fields and it is particularly simple if the Jackiw-Rajaraman parameter equals 2. In the strong-coupling limit, the low-energy effective theory only contains light unconfined fermions which interact weakly.

On the Epistemology of Narrative Theory: Narratology and Other Theories of Fictional Narrative

In this article, I propose to analyze narrative theory from an epistemological standpoint. To do so, I will draw upon both Genettian narratology and what I would call, following Shigeyuki Kuroda, “non-communicational” theories of fictional narrative. In spite of their very unequal popularity, I consider these theories as objective, or, in other words, as debatable and ripe for rational analyses; one can choose between them. The article is made up of three parts. The first part concerns the object of narrative theory, or the narrative as a constructed object, both in narratology (where narrative is likened to a narrative discourse) and in non-communicational narrative theories (where fictional narrative and discourse are mutually exclusive categories). The second part takes up the question of how the claims of these theories do or do not lend themselves to falsification. In particular, Gérard Genette’s claim that “every narrative is, explicitly or not, ‘in the first person’”, will be considered, through the lens of Ann Banfield’s theory of free indirect style. In the third part the reductionism of narrative theory will be dealt with. This leads to a reflection on the role of narrative theory in the analysis of fictional narratives.

On the alleged equivalence of certain field theories

Abstract. We critically examine some recent claims that certain field theories with and without boson kinetic energy terms are equivalent. We point out that the crucial element in these claims is the finiteness or otherwise of the boson wavefunction renormalisation constant. We show that when this constant is finite, the equivalence proof offered in the literature fails in a direct way. When the constant is divergent, the claimed equivalence is only a consequence of improper use of divergent quantities.

Poincaré invariance of anomalous gauge theories

We establish the Poincaré invariance of anomalous gauge theories in two dimensions, for both the Abelian and non-Abelian cases, in the canonical Hamiltonian formalism. It is shown that, despite the noncovariant appearance of the constraints of these theories, Poincaré generators can be constructed which obey the correct algebra and yield the correct transformations in the constrained space.

Spin and mass content of linearized Poincaré gauge theories

A unified gauge theory of massless and massive spin-2 fields is of considerable current interest. The Poincaré gauge theories with quadratic Lagrangian are linearized, and the conditions on the parameters are found which will lead to viable linear theories with massive gauge particles. As well as the 2+ massless gravitons coming from the translational gauge potential, the rotational gauge potentials, in the linearized limit, give rise to 2+ and 2− particles of equal mass, as well as a massive pseudoscalar.

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.

Witten index of supersymmetric chiral theories

The Witten index can be defined in many supersymmetric theories by formulating them in the space-time R×S3. If the index is nonzero for any value of the radius of S3, it can be shown that the theory does not break supersymmetry in Minkowski space. This approach rules out supersymmetry breaking in a large class of models, chiral and otherwise. The index arguments are consistent with previous instanton calculations which indicate supersymmetry breaking in certain theories.

Solitons of Coupled Scalar Field Theories in Two Dimensions

This work offers a method for finding some exact soliton solutions to coupled relativistic scalar field theories in 1+1 dimensions. The method can yield static solutions as well as quasistatic "charged" solutions for a variety of Lagrangians. Explicit solutions are derived as examples. A particularly interesting class of solutions is nontopological without being either charged or time dependent.

Path integral quantisation of topological field theories

Conditions for quantum topological invariance of classically topological field theories in the path integral formulation are discussed. Both the three-dimensional Chern-Simons system and a Witten-type topological field theory are shown to satisfy these conditions.

Mean-field theories of Hubbard and t-J models

We report novel results obtained for the Hubbard and t-J models by various mean-field approximations.

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.

Euclideanization, topological theories, higher dimensions and all that

It is shown that the euclideanized Yukawa theory, with the Dirac fermion belonging to an irreducible representation of the Lorentz group, is not bounded from below. A one parameter family of supersymmetric actions is presented which continuously interpolates between the N = 2 SSYM and the N = 2 supersymmetric topological theory. In order to obtain a theory which is bounded from below and satisfies Osterwalder-Schrader positivity, the Dirac fermion should belong to a reducible representation of the Lorentz group and the scalar fields have to be reinterpreted as the extra components of a higher dimensional vector field.