D-branes and short distances in string theory

Abstract

We study the behavior of D-branes at distances far shorter than the string length scale l s .We argue that short-distance phenomena are described by the IR behavior of the Dbrane world-volume quantum theory. This description is valid until the brane motion becomes relativistic. At weak string coupling g s this corresponds to momenta and energies far above string scale. We use 0-brane quantum mechanics to study 0-brane collisions and find structure at length scales corresponding to the eleven-dimensional Planck lengths l s ) and to the radius of the eleventh dimension in M-theory (R 11 ∼ g s l s ). We use 0-branes to probe non-trivial geometries and topologies at sub-stringy scales. We study the 0-brane 4-brane system, calculating the 0-brane moduli space metric, and find the bound state at threshold, which has characteristic size l 11 P . We examine the blowup of an orbifold and are able to resolve the resulting S 2 down to size l 11 P . A 0-brane with momentum approaching 1/R 11 is able to explore a larger configuration space in which the blowup is embedded. Analogous phenomena occur for small instantons. We finally turn to 1-branes and calculate the size of a bound state to be ∼ g

Fuzzy sphere dynamics and non-abelian DBI in curved backgrounds

“…Inserting this into the equation of motion yields the solution 20) which we expect to provide a reasonable approximation as r → 0, and once again shows the increasing exponential dependence of the tachyon field. Again the contribution from the two charges can change the dynamics of the field, as described earlier.…”

On relativistic brane probes in singular spacetimes

“…Finally, according to the generic properties of D-brane probes [21,22], the resolution of the probe is ∼ v/c l s . From our analysis, it then follows that v/c → 1 as the brane probe approaches the singularity.…”

Branes and the gauge hierarchy

“…As a result, the quantum-corrected Lagrangian of the brane theory is obtained by evaluating these bulk backgrounds at the position of our world-brane. Note that this position is only defined within ∼ o(l s ), since at shorter distances the classical supergravity equations don't make sense [26]. The main message is that when d ⊥ = 2 we have a method for resumming the large logs which is equally-powerful as the renormalization-group equations in the case of renormalizable quantum field theory.…”