David Berenstein has written a fresh new paper on the geometry of giant gravitons. Essentially, he begins by studying N=4 SYM and a Z/2 orbifold, building giant graviton states with their collective coordinates, attaching strings to them and computing the energies of the strings as functions of the collective coordinates. At the end of the computations it is found that the contribution to the mass of the strings stretched between the giants (at one loop order in the field theory) is a distance squared in the collective coordinate geometry.
The procedure makes contact with the D-brane description, where one can associate the masses to the Higgs mechanism associated to breaking an enhanced gauge symmetry of coincident D-branes down to a diagonal group when the branes are separated. This Higgsed gauge symmetry is the emergent gauge symmetry, realized in terms of collective coordinates of D-branes.
Rolf Schimmrigk's new paper on the arxiv demonstrates that the Omega-motives of
exactly solvable mirror pairs of Calabi-Yau threefolds are isomorphic, as expected by mirror symmetry since the L-functions of the Omega-motives of such pairs are predicted to be identical.
String theory suggests a relation between two-dimensional conformal field theory and the geometry of Calabi-Yau varieties. This comes in the form of relating automorphic forms derived from pure or mixed motives that arise in Calabi-Yau varieties to modular forms that come from Kac-Moody algebras on the worldsheet. Such relations allow an arithmetic link between the spacetime and worldsheet theory, giving a means to pass from the extra-dimensional geometry to the worldsheet and back.
In the framework of M-theory, it would be of interest to generalize the Calabi-Yau results to G2 manifolds and other higher dimensional compactification spaces.
Seth Lloyd gave a talk on quantum computation with closed time like curves (CTCs), Nov. 4th 2010. He begins in a light manner with examples of the many worlds vs consistent history perspectives and moves on to considering sending qubits through projective CTCs. The talk ends with an experiment that is post-selectively equivalent to a projective CTC circuit.
Following the work of Rolf Schimmrgk, it is tempting to try to piece together the "big picture", in relating motives to black holes and emergent spacetime. In the 10D stringy picture, one considers automorphic forms on the worldsheet and constructs the Calabi-Yau varieties induced by those automorphic forms. One can also consider black holes with Siegal form partition function (modular form) and ask if the form is associated to (motives of) a compactified geometry. This is the essence of the stringy extension of the geometric Langland's program.
Hence, the "big question", in quantum gravity, is can one always re-construct spacetime geometries from number theory information? More examples are needed, but there are tantalizing hints coming from supergravity and topological string theory.