### Abstract

We define supersymmetric Yang-Mills theory on an arbitrary 2D lattice (polygon decomposition) while preserving one supercharge. When a smooth Riemann surface ∑<inf>g</inf> with genus g emerges as an appropriate continuum limit of the generic lattice, the discretized theory becomes a topologically twisted N = (2, 2) supersymmetric Yang-Mills theory on ∑<inf>g</inf>. If we adopt the usual square lattice as a special case of the discretization, our formulation is identical with Sugino's lattice model. Although the tuning of parameters is generally required while taking the continuum limit, the number of necessary parameters is at most two because of the gauge symmetry and the supersymmetry. In particular, we do not need any fine-tuning if we arrange the theory so as to possess an extra global U(1) symmetry (U(1)<inf>R</inf> symmetry), which rotates the scalar fields.

Original language | English |
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Article number | 123B01 |

Journal | Progress of Theoretical and Experimental Physics |

Volume | 2014 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2014 Dec 4 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Progress of Theoretical and Experimental Physics*,

*2014*(12), [123B01]. https://doi.org/10.1093/ptep/ptu153

**Topologically twisted N = (2, 2) supersymmetric Yang-Mills theory on an arbitrary discretized Riemann surface.** / Matsuura, So; Misumi, Tatsuhiro; Ohta, Kazutoshi.

Research output: Contribution to journal › Article

*Progress of Theoretical and Experimental Physics*, vol. 2014, no. 12, 123B01. https://doi.org/10.1093/ptep/ptu153

}

TY - JOUR

T1 - Topologically twisted N = (2, 2) supersymmetric Yang-Mills theory on an arbitrary discretized Riemann surface

AU - Matsuura, So

AU - Misumi, Tatsuhiro

AU - Ohta, Kazutoshi

PY - 2014/12/4

Y1 - 2014/12/4

N2 - We define supersymmetric Yang-Mills theory on an arbitrary 2D lattice (polygon decomposition) while preserving one supercharge. When a smooth Riemann surface ∑g with genus g emerges as an appropriate continuum limit of the generic lattice, the discretized theory becomes a topologically twisted N = (2, 2) supersymmetric Yang-Mills theory on ∑g. If we adopt the usual square lattice as a special case of the discretization, our formulation is identical with Sugino's lattice model. Although the tuning of parameters is generally required while taking the continuum limit, the number of necessary parameters is at most two because of the gauge symmetry and the supersymmetry. In particular, we do not need any fine-tuning if we arrange the theory so as to possess an extra global U(1) symmetry (U(1)R symmetry), which rotates the scalar fields.

AB - We define supersymmetric Yang-Mills theory on an arbitrary 2D lattice (polygon decomposition) while preserving one supercharge. When a smooth Riemann surface ∑g with genus g emerges as an appropriate continuum limit of the generic lattice, the discretized theory becomes a topologically twisted N = (2, 2) supersymmetric Yang-Mills theory on ∑g. If we adopt the usual square lattice as a special case of the discretization, our formulation is identical with Sugino's lattice model. Although the tuning of parameters is generally required while taking the continuum limit, the number of necessary parameters is at most two because of the gauge symmetry and the supersymmetry. In particular, we do not need any fine-tuning if we arrange the theory so as to possess an extra global U(1) symmetry (U(1)R symmetry), which rotates the scalar fields.

UR - http://www.scopus.com/inward/record.url?scp=84928942038&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84928942038&partnerID=8YFLogxK

U2 - 10.1093/ptep/ptu153

DO - 10.1093/ptep/ptu153

M3 - Article

VL - 2014

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

SN - 2050-3911

IS - 12

M1 - 123B01

ER -