The mass term in non-Abelian gauge field dynamics on matrix D-branes and T-duality in the $\sigma$-model approach

Abstract

The formal extension of the T-duality rules for open strings from Abelian to non-Abelian gauge field background leads in a well known manner to the notion of matrix valued D-brane position. The application of this concept to the non-Abelian gauge field RG $\beta$-function of the corresponding $\sigma$-model yields a mass term in the gauge field dynamics on the matrix D-brane. The direct calculation in a corresponding D-brane model does $not$ yield such a mass term, if the Dirichlet boundary condition is implemented as a constraint on the integrand in the defining functional integral. However, the mass term arises in the direct calculation for a D-brane model with dynamically realized boundary condition.

13 pages, Latex, some typos corrected

References in corpus (2)

• D-branes and Matrix Theory in Curved Space
• Matrix Sigma-models for Multi D-brane Dynamics

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