No abstract

We study a non-supersymmetric E 8 × E 8 compactification of M-theory on S 1 /Z 2 , related to the supersymmetric E 8 × E 8 theory by a chirality flip at one of the boundaries. This system represents an M-theory analog of the D-brane anti-D-brane systems of string theory.Alternatively, this compactification can be viewed as a model of supersymmetry breaking in the "brane-world" approach to phenomenology. We calculate the Casimir energy of the system at large separations, and show that there is an attractive Casimir force between the E 8 and E 8 boundary. We predict that a tachyonic instability develops at separations of order the Planck scale, and discuss the possibility that the M-theory fivebrane might appear as a topological defect supported by the E 8 × E 8 system. Finally, we analyze the eventual fate of the configuration, in the semiclassical approximation at large separations:the two ends of the world annihilate by nucleating wormholes between the two boundaries.

We consider the set of controlled time-dependent backgrounds of general relativity and string theory describing "bubbles of nothing", obtained via double analytic continuation of black hole solutions. We analyze their quantum stability, uncover some novel features of their dynamics, identify their causal structure and observables, and compute their particle production spectrum. We present a general relation between squeezed states, such as those arising in cosmological particle creation, and nonlocal theories on the string worldsheet. The bubble backgrounds have various aspects in common with de Sitter space, Rindler space, and moving mirror systems, but constitute controlled solutions of general relativity and string theory with no external forces. They provide a useful theoretical laboratory for studying issues of observables in systems with cosmological horizons, particle creation, and time-dependent string perturbation theory.

We construct a string theory realization of the 4+1d quantum Hall effect recently discovered by Zhang and Hu. The string theory picture contains coincident D4branes forming an S 4 and having D0-branes (i.e. instantons) in their world-volume. The charged particles are modelled as string ends. Their configuration space approaches in the large n limit a CP 3 , which is an S 2 fibration over S 4 , the extra S 2 being made out of the Chan-Paton degrees of freedom. An alternative matrix theory description involves the fuzzy S 4 . We also find that there is a hierarchy of quantum Hall effects in odd-dimensional spacetimes, generalizing the known cases in 2 + 1d and 4 + 1d.

We study string theory on a non-singular time-dependent orbifold of flat space, known as the 'null-brane'. The orbifold group, which involves only spacelike identifications, is obtained by a combined action of a null Lorentz transformation and a constant shift in an extra direction. In the limit where the shift goes to zero, the geometry of this orbifold reproduces an orbifold with a light-like singularity, which was recently studied by Liu, Moore and Seiberg (hep-th/0204168). We find that the backreaction on the geometry due to a test particle can be made arbitrarily small, and that there are scattering processes which can be studied in the approximation of a constant background. We quantize strings on this orbifold and calculate the torus partition function. We construct a basis of states on the smooth orbifold whose tree level string interactions are nonsingular. We discuss the existence of physical modes in the singular orbifold which resolve the singularity. We also describe another way of making the singular orbifold smooth which involves a sandwich pp-wave.