RECORD
Current algebras from QP-manifolds in general dimensions
Mathematical Physics · Submitted 1 Aug 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim A large class of current algebras with and without anomalous terms (central extensions) are constructed from the above structure.
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
We propose a new unified formulation of the current algebra theory in general dimensions in terms of supergeometry. We take a QP-manifold, i.e. a differential graded (dg) symplectic manifold, as a fundamental framework. A Poisson bracket in a current algebra is constructed by the so called derived bracket of the graded Poisson structure induced from the above QP-structure. By taking a canonical transformation on a QP-manifold, correct anomalous terms in physical theories are derived. A large class of current algebras with and without anomalous terms (central extensions) are constructed from the above structure. Moreover, using this formulation, a new class of current algebras related higher structures are systematically obtained.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We propose a new unified formulation of the current algebra theory in general dimensions in terms of supergeometry. | contribution 1.00 | 0.92 | 0.35 | asserted 0.96 |
| s1 | We take a QP-manifold, i.e. a differential graded (dg) symplectic manifold, as a fundamental framework. | method 0.82 | 0.59 | 0.07 | asserted 0.99 |
| s2 | A Poisson bracket in a current algebra is constructed by the so called derived bracket of the graded Poisson structure induced from the above QP-structure. | method 0.87 | 0.72 | 0.13 | asserted 1.00 |
| s3 | By taking a canonical transformation on a QP-manifold, correct anomalous terms in physical theories are derived. | result 0.46 | 0.84 | 0.11 | asserted 1.00 |
| s4 | A large class of current algebras with and without anomalous terms (central extensions) are constructed from the above structure. | result 0.72 | 0.91 | 0.25 | asserted 1.00 |
| s5 | Moreover, using this formulation, a new class of current algebras related higher structures are systematically obtained. | result 0.51 | 0.91 | 0.24 | asserted 1.00 |
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
We propose a new unified formulation of the current algebra theory in general dimensions in terms of supergeometry. We take a QP-manifold, i.e. a differential graded (dg) symplectic manifold, as a fundamental framework. A Poisson bracket in a current algebra is constructed by the so called derived bracket of the graded Poisson structure induced from the above QP-structure. By taking a canonical transformation on a QP-manifold, correct anomalous terms in physical theories are derived. A large class of current algebras with and without anomalous terms (central extensions) are constructed from the above structure. Moreover, using this formulation, a new class of current algebras related higher structures are systematically obtained.
Human review
References
How the literature uses it
4 arXiv papers cite this in 5 sentences
Papers citing it · 3 sentences without a confident label
Builds on it 1 paper
-
A “QP” approach to current algebras was also pursued by Ikeda and Xu [ref] , who constructed a current algebra in the special case where $ℳ$ is a shifted cotangent bundle of another graded manifold $ℳ'$: [equation] (We were also notified of reference [ref] in the same context, again for the cotangent case $ℳ=T^⋆[P]ℳ'$.) In our construction, we lift this restriction on $ℳ$.
Brane current algebras and generalised geometry from QP manifolds · Introduction and Discussion · 0.89
Cites it as background 1 paper
-
A twisted QP-manifold has some applications to physical theories such as the reduction of the AKSZ sigma models and the supergeometric construction of current algebras [ref] .
Compatible $E$-Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds · Twisting of homological functions and twisted QP-manifolds · 0.80
What it cites · 22 sentences without a confident label
Uses the method or tool of 3 papers
-
This derived bracket relation is translated on the mapping spaces following the AKSZ construction [ref] [ref] [ref] .
AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories · AKSZ-BFV Construction on a QP Pair · 0.97
-
This derived bracket relation is translated on the mapping spaces following the AKSZ construction [ref] [ref] [ref] .
The Geometry of the Master Equation and Topological Quantum Field Theory · AKSZ-BFV Construction on a QP Pair · 0.97
-
This derived bracket relation is translated on the mapping spaces following the AKSZ construction [ref] [ref] [ref] .
On the AKSZ formulation of the Poisson sigma model · AKSZ-BFV Construction on a QP Pair · 0.97
Compares with 3 papers
-
This coincides with the generalized current algebra in three dimensions in [ref] .
Current Algebras and QP Manifolds · Examples · 0.98
-
This coincides with the generalized current algebra described in [ref] .
Current Algebras and Differential Geometry · Examples · 0.98
-
= -_(n)(J_1J_2)|_cl (ϵϵ^') - 1/(n-1)! ∫_Σ_n d _(0) ^'_(0) J_(n)(G,B)J_(n)(G^',B^') d x^I ∧⋯∧d x^I_n-1, coincides with the generalized current algebra of the topological $n$-brane theory in [ref] .
From current algebras for p-branes to topological M-theory · Examples · 0.96
Cites as background 8 papers
-
A triple $(, ω, Q)$ is called a QP-manifold of degree $n$ and its structure is called a QP structure, if $ω$ and $Q$ are compatible, that is, $_Q ω=0$ [ref] . $Q$ is also called a homological vector field.
Geometry of Batalin-Vilkovisky quantization · Preliminary: QP Manifolds, Twisting and QP Pairs · 0.95
-
[ref] Let $(,{-,-}_s,α)$ be a QP manifold.
Canonical Functions and Differential Graded Symplectic Pairs in Supergeometry and AKSZ Sigma Models with Boundary · Preliminary: QP Manifolds, Twisting and QP Pairs · 0.90
-
and the AKSZ formalism [ref] [ref] [ref] [ref] .
The Geometry of the Master Equation and Topological Quantum Field Theory · Introduction · 0.99
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.