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Some Features of Blown-Up Nonlinear $\sigma$-Models

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H.B. Gao, H. Römer

High Energy Physics - Theory · Submitted 24 Jun 1994

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

The authors' main claim In terms of the gauged nonlinear $\sigma$-models, we describe some results and implications of solving the following problem: Given a smooth symplectic manifold as target space with a quasi-free Hamiltonian group action, perform the symplectic blowing up of the point singularity and identify the blow-up modes in the corresponding (gauged) $\sigma$-model.

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arXiv IDhep-th/9406165 (version 1)
Pith ID4GNULSHO, Pith's permanent record of this paper and its review
CitationH.B. Gao, H. R\"omer. "Some Features of Blown-Up Nonlinear $\sigma$-Models." arXiv:hep-th/9406165 (1994). https://pith.science/paper/4GNULSHO
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,083 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.07 · mentions code or data availability 0.01.

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

In terms of the gauged nonlinear $\sigma$-models, we describe some results and implications of solving the following problem: Given a smooth symplectic manifold as target space with a quasi-free Hamiltonian group action, perform the symplectic blowing up of the point singularity and identify the blow-up modes in the corresponding (gauged) $\sigma$-model. Both classical and quantum aspects of the construction are explained, along with illustrating examples from the toric projective space and the K\"ahler manifold. We also discuss related problems such as the origin of Mirror symmetry and the quantum cohomologies.(Talk to be given at ICHEP94, Glasgow, July 20-27.)

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 In terms of the gauged nonlinear $\sigma$-models, we describe some results and implications of solving the following problem: Given a smooth symplectic manifold as target space with a quasi-free Hamiltonian group action, perform the symplectic blowing up of the point singularity and identify the blow-up modes in the corresponding (gauged) $\sigma$-model. contribution 0.88 0.76 0.27 asserted 0.94
s1 Both classical and quantum aspects of the construction are explained, along with illustrating examples from the toric projective space and the K\"ahler manifold. contribution 0.77 0.76 0.09 asserted 0.99
s2 We also discuss related problems such as the origin of Mirror symmetry and the quantum cohomologies.(Talk to be given at ICHEP94, Glasgow, July 20-27.) contribution 0.80 0.42 0.06 asserted 0.68

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.94.

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Original abstract

In terms of the gauged nonlinear $\sigma$-models, we describe some results and implications of solving the following problem: Given a smooth symplectic manifold as target space with a quasi-free Hamiltonian group action, perform the symplectic blowing up of the point singularity and identify the blow-up modes in the corresponding (gauged) $\sigma$-model. Both classical and quantum aspects of the construction are explained, along with illustrating examples from the toric projective space and the K\"ahler manifold. We also discuss related problems such as the origin of Mirror symmetry and the quantum cohomologies.(Talk to be given at ICHEP94, Glasgow, July 20-27.)

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