This talk surveys a broad range of applications of quantum field theory, as well as some recent developments. The stress is on the notion of effective field theories. Topics include implications of neutrino mass and a possible small value of sin(2β), supersymmetric extensions of the standard model, the use of field theory to understand fundamental issues in string theory (the problem of multipl...

We investigate nonperturbative effects in M -theory compactifications arising from wrapped membranes. In particular, we show that in d = 4,N = 1 compactifications along manifolds of G2 holonomy, membranes wrapped on rigid supersymmetric 3-cycles induce nonzero corrections to the superpotential. Thus, membrane instantons destabilize manyM -theory compactifications. Our computation shows that the...

We argue that it is possible to maintain both supersymmetry and integrability in the boundary tricritical Ising field theory. Indeed, we find two sets of boundary conditions and corresponding boundary perturbations which are both supersymmetric and integrable. The first set corresponds to a “direct sum” of two non-supersymmetric theories studied earlier by Chim. The second set corresponds to a ...

We present the one-loop scalar field effective potential for the N = 2 supersymmetric nonrelativistic self-interacting matter fields coupled to an Abelian Chern-Simons gauge field and for its generalization when bosonic matter fields are coupled to non-Abelian Chern-Simons field. In both models, Gauss’s law linearly relates the magnetic field to the matter field densities; hence, we also includ...

These are introductory lectures on the correspondence between SU(N) gauge theories and Superstring Theory in anti-de Sitter geometries (AdS). The subject combines a number of different topics, including supersymmetric field theory, classical and quantum physics of black holes, string theory, string dualities, conformal field theories (CFT), and quantum field theory in anti-de Sitter spaces. We ...

We study the cancellations among Feynman diagrams that implement the Ward and SlavnovTaylor identities corresponding to the conserved supersymmetry current in supersymmetric quantum field theories. In particular, we show that the Faddeev-Popov ghosts of gaugeand supersymmetries never decouple from the physical fields, even for abelian gauge groups. The supersymmetric Slavnov-Taylor identities p...

We consider N = 4 supersymmetric Yang-Mills theory formulated in terms of N = 2 superfields in harmonic superspace. Using the background field method we define manifestly gauge invariant and N = 2 supersymmetric effective action depending on N = 2 strength superfields and develop a general procedure for its calculation in one-loop approximation. Explicit form for this effective action is found ...

We propose the existence of a non-supersymmetric conformal field theory softly broken at the TeV scale as a new mechanism for solving the hierarchy problem. We find the imposition of conformal invariance to be very restrictive with many predictive consequences, including severe restrictions on the field content, the number of families as well as on the structure of inter-family Yukawa couplings...