Suppressions and cascades : insights from gauge/gravity dualities

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 supergravity 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 =2)1/4Tdiss(v 0). This agrees with results inferred indirectly via analysis of the screening length between a static quark and antiquark 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"13 . These theories are not conformal, and the solutions describe cascading renormalization group flows. Thesis Supervisor: Hong Liu Title: Associate Professor Acknowledgments I dedicate this dissertation to the memory of my Mother-in-law, Maan ji. Without her love, support, and trust I never would have made it this far. I am greatly indebted to my advisor Hong Liu for all he has taught me with profound patience, kindness and diligence. His guidance has had a profound impact on my development as a physicist. It is a privilege for me to thank Krishna Rajagopal from whom I have learned much about research and writing. I would also like to thank Edward Farhi for his guidance and support throughout my time here as a graduate student. It is an honor for me to acknowledge my friend and collaborator Thomas Faulkner for all his help, support and very useful discussions while working together and otherwise. I would also like to express my gratitude to Chris P. Herzog, Igor R. Klebanov and Urs A. Wiedemann for all they have taught me during my collaboration with them. With deep gratitude, I would like to acknowledge my academic advisor John Negele for his help and advice in navigating my journey here at MIT as well as for being available to help and offer his support whenever I requested it. I would also like to thank all my friend in Women in Physics and CTP for their support and companionship, especially Bonna Newman, Jessie Shelton, Carlos Nufiez, Guido Festuccia, Mauro Brigante and Sean P. Robinson. Last but not least, I would like to thank Ejaz Nasser for all his love, support and patience, without which this work would never have been completed, and my friend and mentor, Pervez Hoodbhoy for all he has taught and shared with me. Overview of the Gauge/Gravity Correspondence Introduction . AdS5 x S5 and A = 4 SYM . A Review of Field Theory Models for Quarkonia in QGP Calculating the Screening Length using AdS/CFT . Adding Flavors using the Probe Approximation . 1.5. 1 D7-brane Embedding at Zero Temperature . 1.5. 2 D7-brane Embedding at Finite Temperature . 2 A Limiting Velocity for Quarkonium Propagation in a Strongly Coupled Plasma via AdS/CFT 2.