Related papers: Phase Transitions and Moduli Space Topology
We revisit the duality between heterotic string theory compactified on K3 x T^2 and type IIA compactified on a Calabi-Yau threefold X in the hypermultiplet sector. We derive an explicit map between the field variables of the respective…
It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n> 1. Recently the physical meaning of these higher categorical…
The standard formulation of gauge theories results from the Lagrangian (functional integral) quantization of classical gauge theories. A more intrinsic qunantum theoretical access in the spirit of Wigner's representation theory shows that…
One of the important characteristics of topological phases of matter is the topology of the underlying manifold on which they are defined. In this paper, we present the sensitivity of such phases of matter to the underlying topology, by…
This thesis is broadly split into two parts. In the first part, simple state sum models for minimally coupled fermion and scalar fields are constructed on a $1$-manifold. The models are independent of the triangulation and give the same…
Using the complex Klein-Gordon field as a model, we quantize the quaternionic scalar field in the real Hilbert space. The lagrangian formulation has accordingly been obtained, as well as the hamiltonian formulation, and the energy and…
We briefly review the advanced mathematical language of fiber bundle structures and how they can be used to classify two-level quantum systems based on the analysis of the topological properties of their sets of state vectors. The…
The relation between thermodynamic phase transitions in classical systems and topology changes in their state space is discussed for systems in which equivalence of statistical ensembles does not hold. As an example, the spherical model…
I present a new class of topological string theories, and discuss them in two dimensions as candidates for the string description of large-$N$ QCD. The starting point is a new class of topological sigma models, whose path integral is…
A system of functional equations relating the Euler characteristics of moduli spaces of stable representations of quivers and the Euler characteristics of (Hilbert scheme-type) framed versions of quiver moduli is derived. This is applied to…
We analyze global aspects of the moduli space of K\"ahler forms for $N$=(2,2) conformal $\sigma$-models. Using algebraic methods and mirror symmetry we study extensions of the mathematical notion of length (as specified by a K\"ahler…
We construct 3-dimensional once-Extended Topological Quantum Field Theories (ETQFTs for short) out of (possibly non-semisimple) modular categories, and we explicitly identify linear categories and functors in their image. The circle…
Quantum field theory can be physically regularized by modularizing it on several levels of aggregation. Since computation is already thoroughly modularized, physical experiments are treated here as quantum relativistic cellular computations…
We analyze the global theory of boundary conditions for a constrained quantum system with classical configuration space a compact Riemannian manifold $M$ with regular boundary $\Gamma=\partial M$. The space $\CM$ of self-adjoint extensions…
We propose a topological paradigm in alterfold topological quantum field theory to explore various concepts, including modular invariants, $\alpha$-induction and connections in Morita contexts within a modular fusion category of non-zero…
Topologically non trivial effects appearing in the discussion of duality transformations in higher genus manifolds are discussed in a simple example, and their relation with the properties of Topological Field Theories is established.
We develop a general framework for the description of anomalies using extended functorial field theories extending previous work by Freed and Monnier. In this framework, anomalies are described by invertible field theories in one dimension…
We construct matter field theories in ``theory space'' that are fractal, and invariant under geometrical renormalization group (RG) transformations. We treat in detail complex scalars, and discuss issues related to fermions, chirality, and…
We provide a description of phase transitions at finite temperature in strongly coupled field theories using holography. For this purpose, we introduce a general class of gravity duals to superconducting theories that exhibit various types…
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…