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On the twisted chiral potential in 2d and the analogue of rigid special geometry for 4-folds
We discuss how to obtain an N=(2,2) supersymmetric SU(3) gauge theory in two dimensions via geometric engineering from a Calabi-Yau 4-fold and compute its non-perturbative twisted chiral potential. The relevant compact part of the 4-fold geometry consists of two intersecting P^1's fibered over...
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Lenguaje: | eng |
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1999
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Acceso en línea: | https://dx.doi.org/10.1088/1126-6708/1999/06/021 http://cds.cern.ch/record/386294 |
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author | Kaste, P |
author_facet | Kaste, P |
author_sort | Kaste, P |
collection | CERN |
description | We discuss how to obtain an N=(2,2) supersymmetric SU(3) gauge theory in two dimensions via geometric engineering from a Calabi-Yau 4-fold and compute its non-perturbative twisted chiral potential. The relevant compact part of the 4-fold geometry consists of two intersecting P^1's fibered over P^2. The rigid limit of the local mirror of this geometry is a complex surface that generalizes the Seiberg-Witten curve and on which there exist two holomorphic 2-forms. These stem from the same meromorphic 2-form as derivatives w.r.t. the two moduli, respectively. The middle periods of this meromorphic form give directly the twisted chiral potential. The explicit computation of these and of the four-point Yukawa couplings allows for a non-trivial test of the analogue of rigid special geometry for a 4-fold with several moduli. |
id | cern-386294 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 1999 |
record_format | invenio |
spelling | cern-3862942019-09-30T06:29:59Zdoi:10.1088/1126-6708/1999/06/021http://cds.cern.ch/record/386294engKaste, POn the twisted chiral potential in 2d and the analogue of rigid special geometry for 4-foldsParticle Physics - TheoryWe discuss how to obtain an N=(2,2) supersymmetric SU(3) gauge theory in two dimensions via geometric engineering from a Calabi-Yau 4-fold and compute its non-perturbative twisted chiral potential. The relevant compact part of the 4-fold geometry consists of two intersecting P^1's fibered over P^2. The rigid limit of the local mirror of this geometry is a complex surface that generalizes the Seiberg-Witten curve and on which there exist two holomorphic 2-forms. These stem from the same meromorphic 2-form as derivatives w.r.t. the two moduli, respectively. The middle periods of this meromorphic form give directly the twisted chiral potential. The explicit computation of these and of the four-point Yukawa couplings allows for a non-trivial test of the analogue of rigid special geometry for a 4-fold with several moduli.hep-th/9904218CERN-TH-99-114oai:cds.cern.ch:3862941999-05-03 |
spellingShingle | Particle Physics - Theory Kaste, P On the twisted chiral potential in 2d and the analogue of rigid special geometry for 4-folds |
title | On the twisted chiral potential in 2d and the analogue of rigid special geometry for 4-folds |
title_full | On the twisted chiral potential in 2d and the analogue of rigid special geometry for 4-folds |
title_fullStr | On the twisted chiral potential in 2d and the analogue of rigid special geometry for 4-folds |
title_full_unstemmed | On the twisted chiral potential in 2d and the analogue of rigid special geometry for 4-folds |
title_short | On the twisted chiral potential in 2d and the analogue of rigid special geometry for 4-folds |
title_sort | on the twisted chiral potential in 2d and the analogue of rigid special geometry for 4-folds |
topic | Particle Physics - Theory |
url | https://dx.doi.org/10.1088/1126-6708/1999/06/021 http://cds.cern.ch/record/386294 |
work_keys_str_mv | AT kastep onthetwistedchiralpotentialin2dandtheanalogueofrigidspecialgeometryfor4folds |