Topics In Conformal Field Theory And String Theory

<p>The Standard Model is a remarkably successful theory. It is a quantum theory describing the electromagnetic weak and the strong interactions in nature. Its biggest shortcoming lies in its inability to describe gravity in the quantum regime. Furthermore the con-stituents of dark matter and their interactions remain poorly understood making it clear that there is much physics beyond Standard Model. String theory has the promise to pro-vide a quantum theory of gravity unifying all forces of nature [1-4]. It is a theory of interacting strings and other extended objects like D-branes. Its spectrum always con-tains a massless spin-2 state whose low energy interactions are as in general relativity. String perturbation theory is known to be ultraviolet ���nite. At present the most promis-ing direction to connect string theory with nature is by compactifying ten dimensional string theories on six dimensional Calabi-Yau manifolds. Much progress has taken place in this direction and this remains an active area of research. Furthermore the techniques of perturbative quantum ���eld theory fail in the case of strong interactions (QCD) at low energies. However a close cousin of QCD i.e. N = 4 supersymmetric Yang-Mills theory in four dimensions at strong coupling can be understood via its string theory dual due to a mathematical correspondence [5 6]. This has given hope that string theory can shed light on strong dynamics.</p>