TY - JOUR

T1 - Ferrara-Zumino supermultiplet and the energy-momentum tensor in the lattice formulation of 4D N=1 SYM

AU - Suzuki, Hiroshi

N1 - Funding Information:
I would like to thank Michael G. Endres, Kazuo Fujikawa, Yoshio Kikukawa, Martin Lüscher, Yusuke Taniguchi and Naoto Yokoi for enlightening discussions. Some part of this work was carried out during the YITP workshop on “Field Theory and String Theory” ( YITP-W-12-05 ) and I would like to thank the Yukawa Institute for Theoretical Physics at Kyoto University for the hospitality. This work is supported in part by a Grant-in-Aid for Scientific Research , nos. 22340069 and 23540330 .

PY - 2013/3/11

Y1 - 2013/3/11

N2 - It is well-known that Noether currents in the classical four-dimensional N=1 supersymmetric Yang-Mills theory (4D N=1 SYM), i.e., the U(1)A current, the supersymmetry (SUSY) current and the energy-momentum tensor, form a multiplet under SUSY, called the Ferrara-Zumino supermultiplet. Inspired by this structure, we define the energy-momentum tensor in the lattice formulation of 4D N=1 SYM by a renormalized super transformation of a lattice SUSY current. By using a renormalized SUSY Ward-Takahashi relation, the energy-momentum tensor so constructed is shown to be conserved in the quantum continuum limit. Our construction of the energy-momentum tensor is very explicit and usable in non-perturbative numerical simulations.

AB - It is well-known that Noether currents in the classical four-dimensional N=1 supersymmetric Yang-Mills theory (4D N=1 SYM), i.e., the U(1)A current, the supersymmetry (SUSY) current and the energy-momentum tensor, form a multiplet under SUSY, called the Ferrara-Zumino supermultiplet. Inspired by this structure, we define the energy-momentum tensor in the lattice formulation of 4D N=1 SYM by a renormalized super transformation of a lattice SUSY current. By using a renormalized SUSY Ward-Takahashi relation, the energy-momentum tensor so constructed is shown to be conserved in the quantum continuum limit. Our construction of the energy-momentum tensor is very explicit and usable in non-perturbative numerical simulations.

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U2 - 10.1016/j.nuclphysb.2012.11.023

DO - 10.1016/j.nuclphysb.2012.11.023

M3 - Article

AN - SCOPUS:84870799165

SN - 0550-3213

VL - 868

SP - 459

EP - 475

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 2

ER -