Giant gravitons in AdS 5 × S 5 , and its orbifolds, have a dual field theory representation as states created by chiral primary operators. We argue that these operators are not single-trace operators in the conformal field theory, but rather are determinants and subdeterminants of scalar fields; the stringy exclusion principle applies to these operators. Evidence for this identification comes from three sources: (a) topological considerations in orbifolds, (b) computation of protected correlators using free field theory and (c) a Matrix model argument. The last argument applies to AdS 7 × S 4 and the dual (2, 0) theory, where we use algebraic aspects of the fuzzy 4-sphere to compute the expectation value of a giant graviton operator along the Coulomb branch of the theory.

We present new rolling tachyon solutions describing the classical decay of Dbranes. Our methods are simpler than those appearing in recent works, yet our results are exact in classical string theory. The role of pressure in the decay is studied using tachyon profiles with spatial variation. In this case the final state involves an array of codimension one D-branes rather than static, pressureless tachyon matter.

Exploiting insights on strings moving in pp-wave backgrounds, we show how open strings emerge from N = 4 SU(N) Yang-Mills theory as fluctuations around certain states carrying R-charge of order N . These states are dual to spherical D3-branes of AdS 5 × S 5 and we reproduce the spectrum of small fluctuations of these states from Yang-Mills theory. We discuss the emergence of the G 2 light degrees of freedom expected when G such D3-branes nearly coincide. The open strings running between the branes can be quantized easily in a Penrose limit of the spacetime. Taking the corresponding large charge limit of the Yang-Mills theory, we reproduce the open string worldsheets and their spectra from field theory degrees of freedom.

We construct new topological theories related to sigma models whose target space is a seven dimensional manifold of G 2 holonomy. We define a new type of topological twist and identify the BRST operator and the physical states. Unlike the more familiar six dimensional case, our topological model is defined in terms of conformal blocks and not in terms of local operators of the original theory. We also present evidence that one can extend this definition to all genera and construct a seven-dimensional topological string theory. We compute genus zero correlation functions and relate these to Hitchin's functional for three-forms in seven dimensions. Along the way we develop the analogue of special geometry for G 2 manifolds. When the seven dimensional topological twist is applied to the product of a Calabi-Yau manifold and a circle, the result is an interesting combination of the six dimensional A-and B-models.

We explore bosonic strings and Type II superstrings in the simplest time dependent backgrounds, namely orbifolds of Minkowski space by time reversal and some spatial reflections. We show that there are no negative norm physical excitations. However, the contributions of negative norm virtual states to quantum loops do not cancel, showing that a ghost-free gauge cannot be chosen. The spectrum includes a twisted sector, with strings confined to a "conical" singularity which is localized in time. Since these localized strings are not visible to asymptotic observers, interesting issues arise regarding unitarity of the Smatrix for scattering of propagating states. The partition function of our model is modular invariant, and for the superstring, the zero momentum dilaton tadpole vanishes. Many of the issues we study will be generic to time-dependent cosmological backgrounds with singularities localized in time, and we derive some general lessons about quantizing strings on such spaces.