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Register a new userOn T-duality for open strings in general abelian and nonabelian gauge field backgrounds
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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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This contribution gives in sigma-model language a short review of recent work on T-duality for open strings in the presence of abelian or non-abelian gauge fields. Furthermore, it adds a critical discussion of the relation between RG beta-functions and the Born-Infeld action in the case of a string coupled to a D-brane.
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.
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.
We consider gauge theories with scalar matter with and without supersymmetry at nonzero chemical potential. It is argued that a chemical potential plays a role similar to the FI term. We analyze theory at weak coupling regime at large chemical potential and argue that it supports nonabelian non-BPS strings. Worldsheet theory on the nonabelian string in a dense matter is briefly discussed.
We study semiclassical string solutions that live on white regions of the LLM plane for a generic LLM geometry. These string excitations are labelled by conserved charges E, J and S and are thus holographically dual to operators in the SL(2) sector of N = 4 super-Yang Mills made up of covariant derivatives acting on complex scalar fields Z. On the other hand, the LLM geometry itself is dual to an operator consisting of O(N^2) Z-fields so that the operators dual to our solutions, containing both the stringy excitation and background, are non-planar. In an appropriate short string limit we argue that the string solution we find should be dual to a localised SL(2) excitation in the gauge theory language. This allows us to perform a non-trivial check of the recent proposal that the dynamics of localised excitations should be identical, up to a rescaling of the t Hooft coupling, to the dynamics of those same excitations in the AdS5xS5 background
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