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Register a new userNonabelian gauge field dynamics on matrix D-branes
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Authors
H. Dorn
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We construct a calculational scheme for handling the matrix ordering problems connected with the appearance of D-brane positions taking values in the same Lie algebra as the nonabelian gauge field living on the D-brane. The formalism is based on the use of an one-dimensional auxiliary field living on the boundary of the string world sheet and taking care of the order of the matrix valued fields. The resulting system of equations of motion for both the gauge field and the D-brane position is derived in lowest order of the $alpha$ -expansion.
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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.
This paper shows how to construct anomaly free world sheet actions in string theory with $D$-branes. Our method is to use Deligne cohomology and bundle gerbe theory to define geometric objects which are naturally associated to $D$-branes and connections on them. The holonomy of these connections can be used to cancel global anomalies in the world sheet action.
We give the nonabelian extension of the newly discovered N = (2, 2) two-dimensional vector multiplets. These can be used to gauge symmetries of sigma models on generalized Kahler geometries. Starting from the transformation rule for the nonabelian case we find covariant derivatives and gauge covariant field-strengths and write their actions in N = (2, 2) and N = (1, 1) superspace.
Closed string field theory is constructed by stochastically quantizing a matrix model for Polyakov loops that describes phases of a large N gauge theory at finite temperature. Coherent states in this string field theory describes winding string condensation which has been expected to cause a topology change from thermal AdS geometry to AdS-Schwarzschild black hole geometry. D-branes in this closed string field theory is also discussed. Slightly extended version of a talk given at CosPA 2007, Nov.13-15, Taipei, Taiwan.
We discuss T-duality for open strings in general background fields both in the functional integral formulation as well as in the language of canonical transformations. The Dirichlet boundary condition in the dual theory has to be treated as a constraint on the functional integration. Furthermore, we give meaning to the notion of matrix valued string end point position in the presence of nonabelian gauge field background.
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