Vacuum Structures of Supersymmetric Yang-Mills Theories in $1+1$ Dimensions

Hodaka Oda; Norisuke Sakai; Tadakatsu Sakai

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Vacuum Structures of Supersymmetric Yang-Mills Theories in $1+1$ Dimensions

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arxiv hep-th/9606157 v4 pith:NW4JQ54H submitted 1996-06-25 hep-th

Hodaka Oda , Norisuke Sakai , Tadakatsu Sakai This is my paper

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abstract

Vacuum structures of supersymmetric (SUSY) Yang-Mills theories in $1+1$ dimensions are studied with the spatial direction compactified. SUSY allows only periodic boundary conditions for both fermions and bosons. By using the Born-Oppenheimer approximation for the weak coupling limit, we find that the vacuum energy vanishes, and hence the SUSY is unbroken. Other boundary conditions are also studied, especially the antiperiodic boundary condition for fermions which is related to the system in finite temperatures. In that case we find for gaugino bilinears a nonvanishing vacuum condensation which indicates instanton contributions.

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