| Summary: | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2008. === Includes bibliographical references (p. 179-194). === At present, there are no non-perturbative analytic methods available for investigating gauge theories at large couplings. Consequently, it is desirable to explore more avenues to gain qualitative and quantitative insights. The gauge/gravity (AdS/CFT) correspondences provides a unique opportunity to study gauge theories both at finite and zero temperatures in the strong coupling regime, potentially leading to insights into QCD. In this regime, where both the 't Hooft coupling and the number of colors is large, the dynamics of the gauge theory is described by super gravity solutions, which describe the low-energy limit of systems of D-branes. In this dissertation, I use the AdS/CFT correspondence to study the dispersion relations of mesons in a particular hot, strongly coupled, supersymmetric gauge theory plasma. This plasma arises by placing a probe D7-brane in the near-horizon geometry of non-extremal D3-branes. I find the large momentum dispersion relations of scalar mesons and extract from them their limiting velocity vo, which depends only on the ratio of the temperature to the quark mass. I use vo to find that the temperature above which no meson bound states with velocity v exist is Tdiss(V) - (1 - v2)1/4Tdiss(v = 0). This agrees with results inferred indirectly via analysis of the screening length between a static quark and anti quark in a moving plasma. Although these calculations are not done in QCD, I argue that the qualitative features of my results may apply to bottomonium and charmonium mesons propagating in the strongly coupled QCD plasma. To aid further investigations of the effect of fundamental matter on hot gauge theory plasmas I find the non-extremal, localized D2/D6-brane solution in its linear limit. Pursuing a different direction, I consider a stack of N D3-branes and M D5-branes wrapped at the apex of a cone over Sasaki- Einstein spaces yp,q. Replacing the D-branes by their fluxes, I construct asymptotic solutions for all p and q in the form of warped products of the cone and R" 3. These theories are not conformal, and the solutions describe cascading renormalization group flows. === by Qudsia Jabeen Ejaz. === Ph.D.
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