Vector fields on mapping spaces and a converse to the AKSZ construction

Theodore Th. Voronov

RECORD

Vector fields on mapping spaces and a converse to the AKSZ construction

Theodore Th. Voronov

Mathematical Physics · Submitted 27 Nov 2012

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this note, we show that the AKSZ setup and their main construction can be naturally recovered from the single requirement that the `difference' vector field arising on the mapping space be gradient (or Hamiltonian).

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

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

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,339 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.86 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

The well-known AKSZ construction (for Alexandrov--Kontsevich--Schwarz--Zaboronsky) gives an odd symplectic structure on a space of maps together with a functional $S$ that is automatically a solution for the classical master equation $(S,S)=0$. The input data required for the AKSZ construction consist of a volume element on the source space and a symplectic structure of suitable parity on the target space, both invariant under given homological vector fields on the source and target. In this note, we show that the AKSZ setup and their main construction can be naturally recovered from the single requirement that the `difference' vector field arising on the mapping space be gradient (or Hamiltonian). This can be seen as a converse statement for that of AKSZ. We include a discussion of properties of vector fields on mapping spaces.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The well-known AKSZ construction (for Alexandrov--Kontsevich--Schwarz--Zaboronsky) gives an odd symplectic structure on a space of maps together with a functional $S$ that is automatically a solution for the classical master equation $(S,S)=0$.	background 1.00	0.03	0.04	asserted 1.00
s1	The input data required for the AKSZ construction consist of a volume element on the source space and a symplectic structure of suitable parity on the target space, both invariant under given homological vector fields on the source and target.	background 1.00	0.04	0.03	asserted 1.00
s2	In this note, we show that the AKSZ setup and their main construction can be naturally recovered from the single requirement that the `difference' vector field arising on the mapping space be gradient (or Hamiltonian).	contribution 0.57	0.95	0.93	asserted 1.00
s3	This can be seen as a converse statement for that of AKSZ.	interpretation 0.99	0.67	0.23	asserted 0.77
s4	We include a discussion of properties of vector fields on mapping spaces.	contribution 0.99	0.83	0.03	asserted 0.68

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

The well-known AKSZ construction (for Alexandrov--Kontsevich--Schwarz--Zaboronsky) gives an odd symplectic structure on a space of maps together with a functional $S$ that is automatically a solution for the classical master equation $(S,S)=0$. The input data required for the AKSZ construction consist of a volume element on the source space and a symplectic structure of suitable parity on the target space, both invariant under given homological vector fields on the source and target. In this note, we show that the AKSZ setup and their main construction can be naturally recovered from the single requirement that the `difference' vector field arising on the mapping space be gradient (or Hamiltonian). This can be seen as a converse statement for that of AKSZ. We include a discussion of properties of vector fields on mapping spaces.

Human review

How Pith checks papers → · Full audit of this paper →

References

How the literature uses it

3 arXiv papers cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 4 sentences without a confident label

Uses its method or tool 1 paper

The construction is as follows (we use the exposition given in [ref] ).

Graded Geometry, $Q$-Manifolds, and Microformal Geometry · $Q$-structure on the space of maps. · 0.90

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.