Related papers: Quantum Line Defects and Refined BPS Spectra
This paper is based on my talk at ICM on recent progress in a number of classical problems of linear algebra and representation theory, based on new approach, originated from geometry of stable bundles and geometric invariant theory.
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
We work in the reduced SU(N,K) modular category as constructed recently by Blanchet. We define spin type and cohomological refinements of the Turaev-Viro invariants of closed oriented 3-manifolds and give a formula relating them to…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
Quantum embedding theories are promising approaches to investigate strongly-correlated electronic states of active regions of large-scale molecular or condensed systems. Notable examples are spin defects in semiconductors and insulators. We…
We construct explicit BPS and non-BPS solutions of the Yang-Mills equations on noncommutative spaces R^{2n}_theta x G/H which are manifestly G-symmetric. Given a G-representation, by twisting with a particular bundle over G/H, we obtain a…
The half-BPS Wilson line operators in the irreducible representations labeled by the Young diagrams for $\mathcal{N}=4$ $U(N)$ super Yang-Mills theory have gravity dual descriptions. When the number $k$ of boxes of the diagram grows as…
Gromov-Witten invariants of weighted projective planes and Euler characteristics of moduli spaces of representations of bipartite quivers are related via the tropical vertex, a group of formal automorphisms of a torus. On the Gromov-Witten…
We propose a modified mode-expansion of the bulk fields in a BPS domain wall background to obtain the effective theory on the wall. The broken SUSY is nonlinearly realized on each mode defined by our mode-expansion. Our work clarifies a…
We formulate a mathematical setup for computational neural networks using noncommutative algebras and near-rings, in motivation of quantum automata. We study the moduli space of the corresponding framed quiver representations, and find…
Quantum light is described not only by a quantum state but also by the shape of the electromagnetic modes on which the state is defined. Optical precision measurements often estimate a ``mode parameter'' that determines properties such as…
We define a refined topological vertex which depends in addition on a parameter, which physically corresponds to extending the self-dual graviphoton field strength to a more general configuration. Using this refined topological vertex we…
Supersymmetric D-branes supported on the complex two-dimensional base $S$ of the local Calabi-Yau threefold $K_S$ are described by semi-stable coherent sheaves on $S$. Under suitable conditions, the BPS indices counting these objects (known…
Matrix Product States (MPS) are a particular type of one dimensional tensor network states, that have been applied to the study of numerous quantum many body problems. One of their key features is the possibility to describe and encode…
We exactly evaluate the partition function (index) of N=4 supersymmetric quiver quantum mechanics in the Higgs phase by using the localization techniques. We show that the path integral is localized at the fixed points, which are obtained…
We consider line defects with large quantum numbers in conformal field theories. First, we consider spin impurities, both for a free scalar triplet and in the Wilson-Fisher $O(3)$ model. For the free scalar triplet, we find a rich phase…
We explore connections between three structures associated with the cohomology of the moduli of 1-dimensional stable sheaves on $\mathbb{P}^2$: perverse filtrations, tautological classes, and refined BPS invariants for local $\mathbb{P}^2$.…
Quantum defect embedding theory (QDET) is a many-body embedding method designed to describe condensed systems with correlated electrons localized within a given region of space, for example spin defects in semiconductors and insulators.…
BPS coherent states closely resemble semiclassical states and they have gravity dual descriptions in terms of semiclassical geometries. The half BPS coherent states have been well studied, however less is known about quarter BPS coherent…
We study Gromov-Witten invariants of a rational elliptic surface using holomorphic anomaly equation in [HST1](hep-th/9901151). Formulating invariance under the affine $E_8$ Weyl group symmetry, we determine conjectured invariants, the…