Related papers: M-theoretic Genesis of Topological Phases

We construct a gauge fixed action for topological membranes on $G_2$-manifold such that its bosonic part is the standard membrane theory in a particular gauge. We prove that quantum mechanically the path-integral in this gauge localizes on…

We demonstrate the identification and classification of topological phase transitions from experimental data using Diffusion Maps: a nonlocal unsupervised machine learning method. We analyze experimental data from an optical system…

Bagger-Lambert-Gustavsson theory with infinite dimensional gauge group has been suggested to describe M5-brane as a condensation of multiple M2-branes. Here we perform a topological twisting of the Bagger-Lambert-Gustavsson theory. The…

We consider the topological and geometric structures associated with cohomological and homological objects in M-theory. For the latter, we have M2-branes and M5-branes, the analysis of which requires the underlying spacetime to admit a…

In recent years, attempts to generalize lattice gauge theories to model topological order have been carried out through the so called $2$-gauge theories. These have opened the door to interesting new models and new topological phases which…

This survey aims to provide a guide to the literature on topological 4-manifolds. Foundational theorems on 4-manifolds are stated, especially in the topological category. Precise references are given, with indications of the strategies…

Half-Heusler compounds are known for their various compositions and multifunctional properties including topological phases. In this study, we investigate the topological classification of this class of materials based on the ordering of…

The elsewhere surmised topological origin of phase transitions is given here new important evidence through the analytic study of an exactly solvable model for which both topology and thermodynamics are worked out. The model is a mean-field…

Meaningful topological invariants for mixed quantum states are challenging to identify as there is no unique way to define them, and most choices do not directly relate to physical observables. Here, we propose a simple pragmatic approach…

The discovery of topological phases in condensed matter systems has changed the modern conception of phases of matter. The global nature of topological ordering makes these phases robust and hence promising for applications. However, the…

This is the first part of a two-part work on a unified mathematical theory of gapped and gapless edges of 2d topological orders. We analyze all the possible observables on the 1+1D world sheet of a chiral gapless edge of a 2d topological…

One of the essential tasks in connectomics is the morphology analysis of neurons and organelles like mitochondria to shed light on their biological properties. However, these biological objects often have tangled parts or complex branching…

We study topological holography for 2+1-D gapped and gapless phases with generalized symmetries using tools from higher linear algebra and higher condensation theory. We focus on bosonic fusion 2-category symmetries, where the Symmetry…

We present a characterization of topological phases in photonic lattices. Our theory relies on a formal equivalence between the singular value decomposition of the non-Hermitian coupling matrix and the diagonalization of an effective…

In this paper we will present some ideas to use 3D topology for quantum computing extending ideas from a previous paper. Topological quantum computing used \textquotedblleft knotted\textquotedblright{} quantum states of topological phases…

We describe a class of parity- and time-reversal-invariant topological states of matter which can arise in correlated electron systems in 2+1-dimensions. These states are characterized by particle-like excitations exhibiting exotic braiding…

In spacetime dimensions of 4 (i.e., 3+1) and higher, topological orders exhibit spatially extended excitations like loops and membranes, which support diverse topological data characterizing braiding, fusion, and shrinking processes,…

We study the large $N$ expansion of twisted partition functions of 3d $\mathcal{N}=2$ superconformal field theories arising from $N$ M5-branes wrapped on a hyperbolic 3-manifold, $M_3$. Via the 3d-3d correspondence, the partition functions…

We construct a new class of topological surface defects in Chern-Simons theory with non-compact, non-Abelian gauge groups. These defects are characterized by isotropic subalgebras defined by solutions of the modified classical Yang-Baxter…

We propose a new theory to characterize equilibrium topological phase with non-equilibrium quantum dynamics by introducing the concept of high-order topological charges, with novel phenomena being predicted. Through a dimension reduction…