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Cosmic strings are linear concentrations of energy that form whenever phase transitions in the early universe break axial symmetries as originally shown by Kibble. They are the result of frustrated order in the quantum fields responsible…
This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em…
The article studies the extension of the internal spaces of fermion and boson second quantized fields, described by the superposition of odd (for fermions) and even (for bosons) products of the operators $\gamma^ {a}$, to strings and odd…
String theory is the leading contemporary framework to explore the synthesis of quantum mechanics with gravity. String phenomenology aims to study string theory while maintaining contact with observational data. The fermionic $Z_2\times…
A first-quantized string (and membrane) theory is developed here by using a general wave function of the string (and membrane), analogously to the first-quantized quantum theory of a point particle. From the general wave function of the…
The main thesis of this paper deals with the interactions of a set of fermions which are described by one basic type of bilinear interactions,two symmetric semiobjects,three embedded shells and four fundamental (strong)…
The results obtained on the particle mixing in Quantum Field Theory are reviewed. The Quantum Field Theoretical formulation of fermion and boson mixed fields is analyzed in detail and new oscillation formulas exhibiting corrections with…
Using E-strings, we can analyze not only six-dimensional superconformal field theories but also probe vacua of non-perturabative heterotic string. We study strings made of D3-branes wrapped on various two-cycles in the global F-theory…
A phenomenologically successful two-component hadronic duality picture led to Veneziano's amplitude, the fundamental first step to string theory. This picture is briefly recalled and its two components are identified as the open strings…
The emerging study of fractons, a new type of quasi-particle with restricted mobility, has motivated the construction of several classes of interesting continuum quantum field theories with novel properties. One such class consists of…
We consider a composite particle formed by two fermions or two bosons. We discover that composite behavior is deeply related to the quantum entanglement between the constituent particles. By analyzing the properties of creation and…
In the model every quark or lepton is identified with a quartet of four "more elementary" particles. One particle in a quartet is a massive spin-0 boson and other three particles are massless spin-1/2 fermions.
As of today there exist consistent, gauge-invariant string field theories describing all string theories: bosonic open and closed strings, open superstrings, heterotic strings and type II strings. The construction of these theories require…
We review efforts in string model building, focusing on the heterotic orbifold compactifications. We survey how one can, starting from an explicit string theory, obtain models which resemble Nature. These models exhibit the standard model…
This chapter is an introduction to the Free Fermionic Formulation of String Theory, with emphasis on heterotic model building. After a brief review of bosonization in two dimensional conformal field theories, we discuss how internal bosonic…
A string field theory of (p,q) minimal superstrings is constructed with the free-fermion realization of 2-component KP (2cKP) hierarchy, starting from 2-cut ansatz of two-matrix models. Differential operators of 2cKP hierarchy are…
We introduce a concise quantum operator formula for bosonization in which the Lie group structure appears in a natural way. The connection between fermions and bosons is found to be exactly the connection between Lie group elements and the…
A low energy string theory should reduce to an ordinary quantum field theory, but in reality the structures of the two are so different as to make the equivalence obscure. The string formalism is more symmetrical between the spacetime and…
Two-dimensional fermionic string theory is shown to have a structure of topological model, which is isomorphic to a tensor product of two topological ghost systems independent of each other. One of them is identified with $c=1$ bosonic…
A new way of computing scattering amplitudes in a certain very important QFT (N=4 SYM) has recently been developed, in which an algebraic structure called the positive Grassmannian plays a very important role. The mathematics of the…