R-Symmetries and Curvature Constraints in A-Twisted Heterotic Landau–Ginzburg Models
In this paper, we discuss various aspects of a class of A-twisted heterotic Landau–Ginzburg models on a Kähler variety <i>X</i>. We provide a classification of the R-symmetries in these models which allow the A-twist to be implemented, focusing on the case in which the gauge bundle is ei...
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MDPI AG
2023-08-01
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| Online Access: | https://www.mdpi.com/2571-712X/6/3/47 |
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| author | Richard S. Garavuso |
| author_facet | Richard S. Garavuso |
| author_sort | Richard S. Garavuso |
| collection | DOAJ |
| description | In this paper, we discuss various aspects of a class of A-twisted heterotic Landau–Ginzburg models on a Kähler variety <i>X</i>. We provide a classification of the R-symmetries in these models which allow the A-twist to be implemented, focusing on the case in which the gauge bundle is either a deformation of the tangent bundle of <i>X</i> or a deformation of a sub-bundle of the tangent bundle of <i>X</i>. Some anomaly-free examples are provided. The curvature constraint imposed by supersymmetry in these models when the superpotential is not holomorphic is reviewed. Constraints of this nature have been used to establish properties of analogues of pullbacks of Mathai–Quillen forms which arise in the correlation functions of the corresponding A-twisted or B-twisted heterotic Landau–Ginzburg models. The analogue most relevant to this paper is a deformation of the pullback of a Mathai–Quillen form. We discuss how this deformation may arise in the class of models studied in this paper. We then comment on how analogues of pullbacks of Mathai–Quillen forms not discussed in previous work may be obtained. Standard Mathai–Quillen formalism is reviewed in an appendix. We also include an appendix which discusses the deformation of the pullback of a Mathai–Quillen form. |
| first_indexed | 2024-03-10T22:18:01Z |
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| id | doaj.art-0aed63a9ff07493cbbb0e18c6558600c |
| institution | Directory Open Access Journal |
| issn | 2571-712X |
| language | English |
| last_indexed | 2024-03-10T22:18:01Z |
| publishDate | 2023-08-01 |
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| spelling | doaj.art-0aed63a9ff07493cbbb0e18c6558600c2023-11-19T12:21:26ZengMDPI AGParticles2571-712X2023-08-016374676110.3390/particles6030047R-Symmetries and Curvature Constraints in A-Twisted Heterotic Landau–Ginzburg ModelsRichard S. Garavuso0Department of Physical Sciences, Kingsborough Community College, The City University of New York, 2001 Oriental Boulevard, Brooklyn, NY 11235-2398, USAIn this paper, we discuss various aspects of a class of A-twisted heterotic Landau–Ginzburg models on a Kähler variety <i>X</i>. We provide a classification of the R-symmetries in these models which allow the A-twist to be implemented, focusing on the case in which the gauge bundle is either a deformation of the tangent bundle of <i>X</i> or a deformation of a sub-bundle of the tangent bundle of <i>X</i>. Some anomaly-free examples are provided. The curvature constraint imposed by supersymmetry in these models when the superpotential is not holomorphic is reviewed. Constraints of this nature have been used to establish properties of analogues of pullbacks of Mathai–Quillen forms which arise in the correlation functions of the corresponding A-twisted or B-twisted heterotic Landau–Ginzburg models. The analogue most relevant to this paper is a deformation of the pullback of a Mathai–Quillen form. We discuss how this deformation may arise in the class of models studied in this paper. We then comment on how analogues of pullbacks of Mathai–Quillen forms not discussed in previous work may be obtained. Standard Mathai–Quillen formalism is reviewed in an appendix. We also include an appendix which discusses the deformation of the pullback of a Mathai–Quillen form.https://www.mdpi.com/2571-712X/6/3/47heterotic Landau–Ginzburg modelsMathai–Quillen formsR-symmetriessupersymmetry and dualitytopological field theories |
| spellingShingle | Richard S. Garavuso R-Symmetries and Curvature Constraints in A-Twisted Heterotic Landau–Ginzburg Models Particles heterotic Landau–Ginzburg models Mathai–Quillen forms R-symmetries supersymmetry and duality topological field theories |
| title | R-Symmetries and Curvature Constraints in A-Twisted Heterotic Landau–Ginzburg Models |
| title_full | R-Symmetries and Curvature Constraints in A-Twisted Heterotic Landau–Ginzburg Models |
| title_fullStr | R-Symmetries and Curvature Constraints in A-Twisted Heterotic Landau–Ginzburg Models |
| title_full_unstemmed | R-Symmetries and Curvature Constraints in A-Twisted Heterotic Landau–Ginzburg Models |
| title_short | R-Symmetries and Curvature Constraints in A-Twisted Heterotic Landau–Ginzburg Models |
| title_sort | r symmetries and curvature constraints in a twisted heterotic landau ginzburg models |
| topic | heterotic Landau–Ginzburg models Mathai–Quillen forms R-symmetries supersymmetry and duality topological field theories |
| url | https://www.mdpi.com/2571-712X/6/3/47 |
| work_keys_str_mv | AT richardsgaravuso rsymmetriesandcurvatureconstraintsinatwistedheteroticlandauginzburgmodels |