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After an introduction into the subject we show how one constructs a canonical formalism in space-time noncommutative theories which allows to define the notion of first-class constraints and to analyse gauge symmetries. We use this…
In these notes the exact renormalization group formulation of the scalar theory is briefly reviewed. This regularization scheme is then applied to supersymmetric theories. In case of a supersymmetric gauge theory it is also shown how to…
We study the non-linear background field redefinitions arising at the quantum level in a spontaneously broken effective gauge field theory. The non-linear field redefinitions are crucial for the symmetric (i.e. fulfilling all the relevant…
This thesis is almost entirely devoted to studying string theory backgrounds characterized by simple geometrical and integrability properties. The archetype of this type of system is given by Wess-Zumino-Witten models, describing string…
String field theory is a candidate for a full non-perturbative definition of string theory. We aim to define string field theory on a space-time lattice to investigate its behaviour at the quantum level. Specifically, we look at string…
A method of constructing a canonical gauge invariant quantum formulation for a non-gauge classical theory depending on a set of parameters is advanced and then applied to the theory of closed bosonic string interacting with massive…
A recently proposed connection between closed string field and an open Wilson line defined on an arbitrary contour is further explored here. We suggest that reparametrization invariance of a Wilson line is the principle which determines the…
We define string geometry: spaces of superstrings including the interactions, their topologies, charts, and metrics. Trajectories in asymptotic processes on a space of strings reproduce the right moduli space of the super Riemann surfaces…
We summarize exact solutions of closed superstrings in a constant magnetic field, from a view point of the regularization criterion. Some models will be excluded according to this criterion. The spectrum-generating algebra is also…
We construct and fully characterize a scalar boundary conformal field theory on a triangulated Riemann surface. The results are analyzed from a string theory perspective as tools to deal with open/closed string dualities.
Let $X$ be a smooth projective variety of dimension $n\geq 2$. It is shown that a finite configuration of points on $X$ subject to certain geometric conditions possesses rich inner structure. On the mathematical level this inner structure…
The worldline formalism provides an alternative to Feynman diagrams in the construction of amplitudes and effective actions that shares some of the superior properties of the organization of amplitudes in string theory. In particular, it…
The well known string solution to Bethe ansatz equations is shown to be inconsistent in its widely accepted form. A valid refinement demanding higher order corrections in subsequent roots is identified. A new alternative string solution is…
The random percolation model can be viewed as the dual of a well defined confining gauge theory; since this theory, having no Monte Carlo dynamics at all, is simple to simulate, it is possible to study the properties of the flux tube with…
We consider gauge theories in a String Field Theory-inspired formalism. The constructed algebraic operations lead in particular to homotopy algebras of the related BV theories. We discuss invariant description of the gauge fixing procedure…
Using the renormalization-group formalism, a sigma model of a special type- in which the metric and the dilaton depend explicitly on one of the string coordinates only-is investigated near two dimensions. It is seen that dilatonic gravity…
We classify almost all classical string configurations, considered in the framework of the semi-classical limit of the string/gauge theory duality. Then, we describe a procedure for obtaining the conserved quantities and the exact classical…
We present a formulation of coherent states as of consistent quantum description of classical configurations in the BRST-invariant quantization of electrodynamics. The quantization with proper gauge-fixing is performed on the vacuum of the…
The Hamiltonian description of classical gauge theories is a very well studied subject. The two best known approaches, namely the covariant and canonical Hamiltonian formalisms have received a lot of attention in the literature. However, a…
Brane systems provide a large class of gauge theories that arise in string theory. This paper demonstrates how such brane systems fit with a somewhat exotic geometric object, called the affine Grassmannian. This gives a strong motivation to…