RECORD
Families index theory for Overlap lattice Dirac operator. I
High Energy Physics - Lattice · Submitted 20 Sep 2001
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our main result is a formula for the topological charge (integrated Chern character) of the index bundle over even-dimensional spheres in the orbit space.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
The index bundle of the Overlap lattice Dirac operator over the orbit space of lattice gauge fields is introduced and studied. Obstructions to the vanishing of gauge anomalies in the Overlap formulation of lattice chiral gauge theory have a natural description in this context. Our main result is a formula for the topological charge (integrated Chern character) of the index bundle over even-dimensional spheres in the orbit space. It reduces under suitable conditions to the topological charge of the usual (continuum) index bundle in the classical continuum limit (this is announced and sketched here; the details will be given in a forthcoming paper). Thus we see that topology of the index bundle of the Dirac operator over the gauge field orbit space can be captured in a finite-dimensional lattice setting.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The index bundle of the Overlap lattice Dirac operator over the orbit space of lattice gauge fields is introduced and studied. | contribution 0.99 | 0.83 | 0.05 | asserted 1.00 |
| s1 | Obstructions to the vanishing of gauge anomalies in the Overlap formulation of lattice chiral gauge theory have a natural description in this context. | interpretation 0.76 | 0.27 | 0.03 | asserted 1.00 |
| s2 | Our main result is a formula for the topological charge (integrated Chern character) of the index bundle over even-dimensional spheres in the orbit space. | result 0.99 | 0.94 | 0.97 | asserted 1.00 |
| s3 | It reduces under suitable conditions to the topological charge of the usual (continuum) index bundle in the classical continuum limit (this is announced and sketched here; the details will be given in a forthcoming paper). | future work 0.65 | 0.47 | 0.05 | asserted 0.76 |
| s4 | Thus we see that topology of the index bundle of the Dirac operator over the gauge field orbit space can be captured in a finite-dimensional lattice setting. | interpretation 1.00 | 0.77 | 0.22 | asserted 0.97 |
What was examined, and what was not
- arXiv listing abstract v4
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
The index bundle of the Overlap lattice Dirac operator over the orbit space of lattice gauge fields is introduced and studied. Obstructions to the vanishing of gauge anomalies in the Overlap formulation of lattice chiral gauge theory have a natural description in this context. Our main result is a formula for the topological charge (integrated Chern character) of the index bundle over even-dimensional spheres in the orbit space. It reduces under suitable conditions to the topological charge of the usual (continuum) index bundle in the classical continuum limit (this is announced and sketched here; the details will be given in a forthcoming paper). Thus we see that topology of the index bundle of the Dirac operator over the gauge field orbit space can be captured in a finite-dimensional lattice setting.
Human review
How the literature uses it
4 arXiv papers cite this in 4 sentences
Papers citing it · 1 sentence without a confident label
Cites it as background 3 papers
-
It is well known that the existence of gauge anomaly in chiral theories is deeply connected to the topology of the gauge field configuration space (for a discussion in the continuum, see [ref] , while for lattice overlap work, see [ref] , [ref] , [ref] ).
Lattice chirality and the decoupling of mirror fermions · Anomaly cancellation and smoothness: the Wilson line background · 0.99
-
The $Ind( D)$ is a powerful topological quantity that has been used for diverse purposes [ref] - [ref] ; see also [ref] and refs therein for other applications; it gives a rigorous explanation of the origin of chiral anomalies and constitutes an alternative approach to the perturbative method based on computing radiative corrections to describe $Ψ̅γ^μΨA_μ$ interactions in QFT$_1+2$ where the topological Chern-Simons gauge theory emerges as a 1-loop correction of the gauge field propagator [ref] .
Topological Aspects of Fermions on Hyperdiamond · Introduction · 0.87
-
There is a significant amount of literature [ref] on many aspects of the expression ([ref]) that will not be discussed here.
Chiral Lattice Gauge Theories Via Mirror-Fermion Decoupling: A Mission (im)Possible? · Ginsparg-Wilson fermions: an elegant solution · 0.99
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.