Born-Infeld Action in String Theory

Abstract: In this thesis I present applications of the Born-Infeld action to the description of D-branes, mostly in the context of type IIB string theory. First I present the Callan-Maldacena construction of a fundamental string attached to a threebrane, whereby the string is made out of the wrapped brane. This interpretation withstands a rather detailed scrutiny, including the magnitude of the static tension and of the B-I charge; and Polchinski's mixed Dirichlet/Neumann boundary conditions for small perturbations of the string. The latter arise dynamically from the full non-linear equations of motion. Also, the Born-Infeld charge is shown to produce the correct form of dipole radiation under the influence of harmonic oscillations of the string. The second part comprises of the application of these ideas to the AdS/CFT correspondence. Using the essentially non-perturbative nature of the B-I action we were able to construct in the near-horizon geometry of N D3-branes the color-singlet baryon vertex of the SU(N) gauge theory as a fivebrane wrapped on the $S^5$ sphere, with B-I strings playing the role of the quarks. Also, in the asymptotically flat background we obtain a smooth classical description of the Hanany-Witten phenomenon. In the case of non-extremal background we construct baryons of the three-dimensional non-supersymmetric theory, the low energy dynamics of which was conjectured to be equivalent to ordinary QCD. Our approach allows to exhibit confining properties of color flux tubes, i.e. the dependence of the tension of the flux tube on its color content. We do this by building an extended baryon, where a fraction $\nu$ of the total of N quarks is removed to a finite distance.