Related papers: Hyperbolic band theory through Higgs bundles
The celebrated holographic duality posits a correspondence between a quantum gravity in a bulk spacetime and a quantum field theory (QFT) defined on its lower-dimensional boundary. This duality not only offers deep insights into the…
Topological photonics is developed based on the analogy of Schr\"{o}dinger equation which is mathematically reduced to a standard eigenvalue equation. Notably, several photonic systems are beyond the standard topological band theory as they…
This paper examines frameworks and phenomenology of ultrarelativistic Higgs vacuum bubble collisions in a first-order phase transition associated with the Standard Model Higgs field in the early Universe. Such collisions act as a cosmic…
This thesis was motivated by a desire to understand the natural geometry of hyperbolic monopole moduli spaces. We take two approaches. Firstly we develop the twistor theory of singular hyperbolic monopoles and use it to study the geometry…
In algebraic quantum field theory the spacetime manifold is replaced by a suitable base for its topology ordered under inclusion. We explain how certain topological invariants of the manifold can be computed in terms of the base poset. We…
We consider the moduli space of polystable $L$-twisted $G$-Higgs bundles over a compact Riemann surface $X$, where $G$ is a real reductive Lie group, and $L$ is a holomorphic line bundle over $X$. Evaluating the Higgs field at a basis of…
We give an overview of the work of Corlette, Donaldson, Hitchin and Simpson leading to the non-abelian Hodge theory correspondence between representations of the fundamental group of a surface and the moduli space of Higgs bundles. We then…
The moduli space of stable Higgs bundles of degree $0$ is equipped with the hyperk\"ahler metric, called the Hitchin metric. On the locus where the spectral curves are smooth, there is the hyperk\"ahler metric called the semi-flat metric,…
The discovery of the Standard Model Higgs boson opens up a range of speculative cosmological scenarios, from the formation of structure in the early universe immediately after the big bang, to relics from the electroweak phase transition…
We define and study the existence of very stable Higgs bundles on Riemann surfaces, how it implies a precise formula for the multiplicity of the very stable components of the global nilpotent cone and its relationship to mirror symmetry.…
This article presents a number of technical tools and results that may be instrumental to discern the nature of the Higgs particle. In scenarios where an additional strongly interacting sector is present in the electroweak theory resulting…
Hyperbolic space is quickly gaining traction as a promising geometry for hierarchical and robust representation learning. A core open challenge is the development of a mathematical formulation of hyperbolic neural networks that is both…
We study Nahm transformation for parabolic Higgs bundles on the projective line \PP^1, with logarithmic singularities on a finite set P. Such a Higgs bundle can be given by its spectral data: a Hirzebruch surface Z together with a coherent…
Quantum cluster theories are a set of approaches for the theory of correlated and disordered lattice systems, which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a…
An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…
We extend the notion of topologically protected semi-metallic band crossings to hyperbolic lattices in a negatively curved plane. Because of their distinct translation group structure, such lattices are associated with a high-dimensional…
We examine brane-world scenarios in which all the observed Standard Model particles reside on a brane but the Higgs is an elementary extra-dimensional scalar in the bulk. We show that, for codimension 2 branes, often-neglected interactions…
We set up a BNR correspondence for moduli spaces of Higgs bundles over a curve with a parabolic structure over any algebraically closed field. This leads to a concrete description of generic fibers of the associated strongly parabolic…
The Hubbard model, which augments independent-electron band theory with a single parameter to describe electron-electron correlations, is widely regarded to be the `standard model' of condensed matter physics. The model has been remarkably…
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits…