Related papers: Fields, Strings, Matrices and Symmetric Products
Recent years have seen noteworthy progress in the mathematical formulation of quantum field theory and perturbative string theory. We give a brief survey of these developments. It serves as an introduction to the more detailed collection…
We present an overview of the intimate relationship between string and D-brane dynamics, and the dynamics of gauge and gravitational fields in three spacetime dimensions. The successes, prospects and open problems in describing both…
I investigate two discrete models of random geometries, namely simplicial quantum gravity and quantum string theory. In four-dimensional simplicial quantum gravity, I show that the addition of matter gauge fields to the model is capable of…
These lecture notes provide a pedagogical introduction, with exercises, to the techniques used in attempts to construct vacua with stabilised moduli in string theory. The reader is only assumed to have a basic knowledge of general…
In certain backgrounds string theory exhibits quantum Hall-like behavior. These backgrounds provide an explicit realization of the effective non-commutative gauge theory description of the fractional quantum Hall effect (FQHE), and of the…
The worldsheet representation of the sum of the planar diagrams of scalar $\Phi^3$ field theory and ${\cal N}=0,1,2,4$ supersymmetric Yang-Mills theory is explained. This was a talk given to the Light Cone Workshop: Hadrons and Beyond, 5-9…
The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has…
We develop the idea for a new string field theory of ours that was proposed earlier in a very rudimentary form in a talk in the Symposium of Tohwa University [1]. The main point is to describe the system of strings in the Universe by means…
This paper fires the opening salvo in the systematic construction of the lattice-continuum correspondence, a precise dictionary that describes the emergence of continuum quantum theories from finite, nonperturbatively defined models…
This doctoral thesis focuses on the application of lattice techniques to study two separate topics: hadron interactions within quantum chromodynamics (QCD), and the emission of particles and gravitational waves (GWs) from cosmic string…
We show that the existence of string order in a given quantum state is intimately related to the presence of a local symmetry by proving that both concepts are equivalent within the framework of finitely correlated states. Once this…
The Swampland program aims to determine the constraints that an effective field theory must satisfy to be consistent with a UV embedding in a quantum gravity theory. Different proposals have been formulated in the form of Swampland…
We discuss the homological aspects of the connection between quantum string generating function and the formal power series associated to the dimensions of chains and homologies of suitable Lie algebras. Our analysis can be considered as a…
Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…
String-localized QFT allows to explain Standard Model interactions in an autonomous way, committed to quantum principles rather than a "gauge principle", thus avoiding an indefinite state space and compensating ghosts. The resulting…
We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two circles. The matrix quantum mechanics is…
These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…
This talk begins with some history and basic facts about string theory and its connections with strong interactions. Comparisons of stacks of Dirichlet branes with curved backgrounds produced by them are used to motivate the AdS/CFT…
In this talk I shall try to give an elementary introduction to certain areas of mathematical physics where the idea of moduli space is used to help solve problems or to further our understanding. In the wide area of gauge theory, I shall…
We propose a new approach to field theory on $\kappa$-Minkowski non-commutative space-time, a popular example of Lie-algebra space-time. Our proposal is essentially based on the introduction of a star product, a technique which is proving…