O(a) improvement of 2D N=(2,2) lattice SYM theory

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  • Hanada, Masanori
    Yukawa Institute for Theoretical Physics, Kyoto University・The Hakubi Center for Advanced Research, Kyoto University・Department of Physics, University of Colorado
  • Kadoh, Daisuke
    Hiyoshi Departments of Physics, and Research and Education Center for Natural Sciences, Keio University
  • Matsuura, So
    Hiyoshi Departments of Physics, and Research and Education Center for Natural Sciences, Keio University
  • Sugino, Fumihiko
    Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS), Seoul
  • 花田, 政範

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  • <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>a</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> improvement of 2D <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> lattice SYM theory

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We perform a tree-level O(a) improvement of two-dimensional N=(2, 2) supersymmetric Yang–Mills theory on the lattice, motivated by the fast convergence in numerical simulations. The improvement respects an exact supersymmetry Q which is needed for obtaining the correct continuum limit without a parameter fine tuning. The improved lattice action is given within a milder locality condition in which the interactions are decaying as the exponential of the distance on the lattice. We also prove that the path-integral measure is invariant under the improved Q-transformation.

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