### Abstract

A strict positivity of the ground-state energy is a necessary and sufficient condition for spontaneous supersymmetry breaking. This ground-state energy may be directly determined from the expectation value of the Hamiltonian in the functional integral, defined with an antiperiodic temporal boundary condition for all fermionic variables. We propose to use this fact to observe the dynamical spontaneous supersymmetry breaking in Euclidean lattice simulations. If a lattice formulation possesses a manifestly preserved fermionic symmetry, there exists a natural choice of a Hamiltonian operator that is consistent with a topological nature of the Witten index. We numerically confirm the validity of our idea in models of supersymmetric quantum mechanics. We further examine the possibility of dynamical supersymmetry breaking in the two-dimensional N = (2, 2) super Yang-Mills theory with the gauge group SU(2), for which the Witten index is unknown. Although statistical errors are still large, we do not observe positive ground-state energy, at least within one standard deviation. This prompts us to draw a different conclusion from a recent conjectural claim that supersymmetry is dynamically broken in this system.

Original language | English |
---|---|

Pages (from-to) | 797-827 |

Number of pages | 31 |

Journal | Progress of Theoretical Physics |

Volume | 119 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 1 2008 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)

### Cite this

*Progress of Theoretical Physics*,

*119*(5), 797-827. https://doi.org/10.1143/PTP.119.797

**Observing dynamical supersymmetry breaking with euclidean lattice simulations.** / Kanamori, Issaku; Sugino, Fumihiko; Suzuki, Hiroshi.

Research output: Contribution to journal › Article

*Progress of Theoretical Physics*, vol. 119, no. 5, pp. 797-827. https://doi.org/10.1143/PTP.119.797

}

TY - JOUR

T1 - Observing dynamical supersymmetry breaking with euclidean lattice simulations

AU - Kanamori, Issaku

AU - Sugino, Fumihiko

AU - Suzuki, Hiroshi

PY - 2008/5/1

Y1 - 2008/5/1

N2 - A strict positivity of the ground-state energy is a necessary and sufficient condition for spontaneous supersymmetry breaking. This ground-state energy may be directly determined from the expectation value of the Hamiltonian in the functional integral, defined with an antiperiodic temporal boundary condition for all fermionic variables. We propose to use this fact to observe the dynamical spontaneous supersymmetry breaking in Euclidean lattice simulations. If a lattice formulation possesses a manifestly preserved fermionic symmetry, there exists a natural choice of a Hamiltonian operator that is consistent with a topological nature of the Witten index. We numerically confirm the validity of our idea in models of supersymmetric quantum mechanics. We further examine the possibility of dynamical supersymmetry breaking in the two-dimensional N = (2, 2) super Yang-Mills theory with the gauge group SU(2), for which the Witten index is unknown. Although statistical errors are still large, we do not observe positive ground-state energy, at least within one standard deviation. This prompts us to draw a different conclusion from a recent conjectural claim that supersymmetry is dynamically broken in this system.

AB - A strict positivity of the ground-state energy is a necessary and sufficient condition for spontaneous supersymmetry breaking. This ground-state energy may be directly determined from the expectation value of the Hamiltonian in the functional integral, defined with an antiperiodic temporal boundary condition for all fermionic variables. We propose to use this fact to observe the dynamical spontaneous supersymmetry breaking in Euclidean lattice simulations. If a lattice formulation possesses a manifestly preserved fermionic symmetry, there exists a natural choice of a Hamiltonian operator that is consistent with a topological nature of the Witten index. We numerically confirm the validity of our idea in models of supersymmetric quantum mechanics. We further examine the possibility of dynamical supersymmetry breaking in the two-dimensional N = (2, 2) super Yang-Mills theory with the gauge group SU(2), for which the Witten index is unknown. Although statistical errors are still large, we do not observe positive ground-state energy, at least within one standard deviation. This prompts us to draw a different conclusion from a recent conjectural claim that supersymmetry is dynamically broken in this system.

UR - http://www.scopus.com/inward/record.url?scp=49749093149&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49749093149&partnerID=8YFLogxK

U2 - 10.1143/PTP.119.797

DO - 10.1143/PTP.119.797

M3 - Article

AN - SCOPUS:49749093149

VL - 119

SP - 797

EP - 827

JO - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 5

ER -