THE MASS TERM IN NON-ABELIAN GAUGE FIELD-DYNAMICS ON MATRIX D-BRANES AND T-DUALITY IN THE SIGMA-MODEL APPROACH

The formal extension of the T-duality rules for open strings from Abel ian to non-Abelian gauge field background leads in a well known manner to the notion of matrix valued D-brane position. The application of t his concept to the non-Abelian gauge field RG beta-function of the cor responding sigma-model yields a mass term in the gauge field dynamics on the matrix D-brane. The direct calculation in a corresponding D-bra ne model does not yield such a mass term, if the Dirichlet boundary co ndition is implemented as a constraint on the integrand in the definin g functional integral. However, the mass term arises in the direct cal culation for a D-brane model with dynamically realized boundary condit ion.