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General Two-Dimensional Supergravity from Poisson Superalgebras

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M. Ertl, W. Kummer, T. Strobl

High Energy Physics - Theory · Submitted 21 Dec 2000

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

The authors' main claim This provides a supersymmetrization of any generalized dilaton gravity theory or of any theory with an action being an (essentially) arbitrary function of curvature and torsion.

how it is stated · asserted 0.97 read the record →

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arXiv IDhep-th/0012219 (version 1)
Pith IDUK7HVSDX, Pith's permanent record of this paper and its review
CitationM. Ertl, T. Strobl, W. Kummer. "General Two-Dimensional Supergravity from Poisson Superalgebras." arXiv:hep-th/0012219 (2000). https://pith.science/paper/UK7HVSDX
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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.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,461 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.61 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.42 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We provide the geometric actions for most general N=1 supergravity in two spacetime dimensions. Our construction implies an extension to arbitrary N. This provides a supersymmetrization of any generalized dilaton gravity theory or of any theory with an action being an (essentially) arbitrary function of curvature and torsion. Technically we proceed as follows: The bosonic part of any of these theories may be characterized by a generically nonlinear Poisson bracket on a three-dimensional target space. In analogy to a given ordinary Lie algebra, we derive all possible N=1 extensions of any of the given Poisson (or W-) algebras. Using the concept of graded Poisson Sigma Models, any extension of the algebra yields a possible supergravity extension of the original theory, local Lorentz and super-diffeomorphism invariance follow by construction. Our procedure automatically restricts the fermionic extension to the minimal one; thus local supersymmetry is realized on-shell. By avoiding a superfield approach we are also able to circumvent in this way the introduction of constraints and their solution. For many well-known dilaton theories different supergravity extensions are derived. In generic cases their field equations are solved explicitly.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We provide the geometric actions for most general N=1 supergravity in two spacetime dimensions. contribution 0.93 0.95 0.64 asserted 1.00
s1 Our construction implies an extension to arbitrary N. interpretation 0.94 0.81 0.15 asserted 0.94
s2 This provides a supersymmetrization of any generalized dilaton gravity theory or of any theory with an action being an (essentially) arbitrary function of curvature and torsion. interpretation 0.84 0.78 0.37 asserted 0.97
s3 Technically we proceed as follows: The bosonic part of any of these theories may be characterized by a generically nonlinear Poisson bracket on a three-dimensional target space. method 0.92 0.49 0.05 hedged possibility 0.97
s4 In analogy to a given ordinary Lie algebra, we derive all possible N=1 extensions of any of the given Poisson (or W-) algebras. method 0.98 0.92 0.07 asserted 1.00
s5 Using the concept of graded Poisson Sigma Models, any extension of the algebra yields a possible supergravity extension of the original theory, local Lorentz and super-diffeomorphism invariance follow by construction. method 0.92 0.78 0.25 asserted 0.77
s6 Our procedure automatically restricts the fermionic extension to the minimal one; thus local supersymmetry is realized on-shell. result 0.75 0.90 0.10 asserted 1.00
s7 By avoiding a superfield approach we are also able to circumvent in this way the introduction of constraints and their solution. method 0.79 0.90 0.04 asserted 0.94
s8 For many well-known dilaton theories different supergravity extensions are derived. result 0.54 0.94 0.08 asserted 1.00
s9 In generic cases their field equations are solved explicitly. result 0.93 0.91 0.07 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.54 · evidence from proof or derivation 1.00.

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  • 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

We provide the geometric actions for most general N=1 supergravity in two spacetime dimensions. Our construction implies an extension to arbitrary N. This provides a supersymmetrization of any generalized dilaton gravity theory or of any theory with an action being an (essentially) arbitrary function of curvature and torsion. Technically we proceed as follows: The bosonic part of any of these theories may be characterized by a generically nonlinear Poisson bracket on a three-dimensional target space. In analogy to a given ordinary Lie algebra, we derive all possible N=1 extensions of any of the given Poisson (or W-) algebras. Using the concept of graded Poisson Sigma Models, any extension of the algebra yields a possible supergravity extension of the original theory, local Lorentz and super-diffeomorphism invariance follow by construction. Our procedure automatically restricts the fermionic extension to the minimal one; thus local supersymmetry is realized on-shell. By avoiding a superfield approach we are also able to circumvent in this way the introduction of constraints and their solution. For many well-known dilaton theories different supergravity extensions are derived. In generic cases their field equations are solved explicitly.

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3 arXiv papers cite this in 13 sentences

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Papers whose main result relates to this one's

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Papers citing it · 9 sentences without a confident label

Uses its method or tool 1 paper
  • To deform the sCJT action [ref] to the most general 2d Carroll dilaton supergravity model, we express it as a gPSM (see, e.g., [ref] ) and then use the rigidity of gPSMs [ref] , which are 2d topological, non-linear gauge theories [ref] .

    Carroll dilaton supergravity in two dimensions · gPSM formulation · 0.93

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