TY - JOUR

T1 - Two-dimensional N ≤ (2,2) super Yang-Mills theory on computer

AU - Suzuki, Hiroshi

PY - 2007/9/1

Y1 - 2007/9/1

N2 - We carry out preliminary numerical study of Sugino's lattice formulation [1, 2] of the two-dimensional ≤ (2,2) super Yang-Mills theory (2d ≤ (2,2) SYM) with the gauge group SU(2). The effect of dynamical fermions is included by re-weighting a quenched ensemble by the pfaffian factor. It appears that the complex phase of the pfaffian due to lattice artifacts and flat directions of the classical potential are not problematic in Monte Carlo simulation. Various one-point supersymmetric Ward-Takahashi (WT) identities are examined for lattice spacings up to a ≤ 0.5/g with the fixed physical lattice size L ≤ 4.0/g, where g denotes the gauge coupling constant in two dimensions. WT identities implied by an exact fermionic symmetry of the formulation are confirmed in fair accuracy and, for most of these identities, the quantum effect of dynamical fermions is clearly observed. For WT identities expected only in the continuum limit, the results seem to be consistent with the behavior expected from supersymmetry, although we do not see clear distintion from the quenched simulation. We measure also the expectation values of renormalized gauge-invariant bi-linear operators of scalar fields.

AB - We carry out preliminary numerical study of Sugino's lattice formulation [1, 2] of the two-dimensional ≤ (2,2) super Yang-Mills theory (2d ≤ (2,2) SYM) with the gauge group SU(2). The effect of dynamical fermions is included by re-weighting a quenched ensemble by the pfaffian factor. It appears that the complex phase of the pfaffian due to lattice artifacts and flat directions of the classical potential are not problematic in Monte Carlo simulation. Various one-point supersymmetric Ward-Takahashi (WT) identities are examined for lattice spacings up to a ≤ 0.5/g with the fixed physical lattice size L ≤ 4.0/g, where g denotes the gauge coupling constant in two dimensions. WT identities implied by an exact fermionic symmetry of the formulation are confirmed in fair accuracy and, for most of these identities, the quantum effect of dynamical fermions is clearly observed. For WT identities expected only in the continuum limit, the results seem to be consistent with the behavior expected from supersymmetry, although we do not see clear distintion from the quenched simulation. We measure also the expectation values of renormalized gauge-invariant bi-linear operators of scalar fields.

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U2 - 10.1088/1126-6708/2007/09/052

DO - 10.1088/1126-6708/2007/09/052

M3 - Article

AN - SCOPUS:34948890459

VL - 2007

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 9

M1 - 052

ER -