### Abstract

We compare N=2 strings and N=4 topological strings within the framework of the sigma model approach. Being classically equivalent on a flat background, the theories are shown to lead to different geometries when put in a curved space. In contrast with the well studied Kahler geometry characterizing the former case, in the latter case a manifold has to admit a covariantly constant holomorphic two-form in order to support an N =4 twisted supersymmetry. This restricts the holonomy group to be a subgroup of SU(1,1) and leads to a Ricci-flat manifold. We speculate that the N=4 topological formalism is an appropriate framework to smooth down ultraviolet divergences intrinsic to the N=2 theory.

Original language | English |
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Article number | 104026 |

Journal | Physical Review D |

Volume | 65 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2002 |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Mathematical Physics

### Cite this

*Physical Review D*,

*65*(10), [104026]. https://doi.org/10.1103/PhysRevD.65.104026

**Geometry of an N=4 twisted string.** / Bellucci, Stefano; Deriglazov, Alexei; Galajinsky, Anton.

Research output: Contribution to journal › Article

*Physical Review D*, vol. 65, no. 10, 104026. https://doi.org/10.1103/PhysRevD.65.104026

}

TY - JOUR

T1 - Geometry of an N=4 twisted string

AU - Bellucci, Stefano

AU - Deriglazov, Alexei

AU - Galajinsky, Anton

PY - 2002

Y1 - 2002

N2 - We compare N=2 strings and N=4 topological strings within the framework of the sigma model approach. Being classically equivalent on a flat background, the theories are shown to lead to different geometries when put in a curved space. In contrast with the well studied Kahler geometry characterizing the former case, in the latter case a manifold has to admit a covariantly constant holomorphic two-form in order to support an N =4 twisted supersymmetry. This restricts the holonomy group to be a subgroup of SU(1,1) and leads to a Ricci-flat manifold. We speculate that the N=4 topological formalism is an appropriate framework to smooth down ultraviolet divergences intrinsic to the N=2 theory.

AB - We compare N=2 strings and N=4 topological strings within the framework of the sigma model approach. Being classically equivalent on a flat background, the theories are shown to lead to different geometries when put in a curved space. In contrast with the well studied Kahler geometry characterizing the former case, in the latter case a manifold has to admit a covariantly constant holomorphic two-form in order to support an N =4 twisted supersymmetry. This restricts the holonomy group to be a subgroup of SU(1,1) and leads to a Ricci-flat manifold. We speculate that the N=4 topological formalism is an appropriate framework to smooth down ultraviolet divergences intrinsic to the N=2 theory.

UR - http://www.scopus.com/inward/record.url?scp=0037053119&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037053119&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.65.104026

DO - 10.1103/PhysRevD.65.104026

M3 - Article

VL - 65

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 10

M1 - 104026

ER -