String Theory Seminar
Thursday, November 13, 2003, 4:00 pm, 277 Phillips Hall, String Theory
Seminar at UNC
Koenraad Schalm (Columbia
University),
Non-abelian
D0-branes in curved space: From matrix-valued
diffeomorphisms to a geometric Myers effect
When N D0-branes, pointlike solitons in
string theory, are superposed,
the qualitative effect is to promote the fields in
the single brane
low-energy effective action to N x N matrix-valued fields. These
fluctuations correspond to the D0-branes collective
coordinates and it
prompts the question how to couple this system to
gravity. We'll
investigate the characteristics of {\em
matrix-valued} diffeomorphisms
qualitatively and quantitatively. Inspired by string
theory effective
actions, we translate diffeomorphism invariance into
the constraint of
base-point
independence for normal coordinate systems. This
base-point independence is analogous to the shift
symmetry in the
Yang-Mills background field method. We construct a
normal coordinate based
algorithm to impose base-point independence order by
order and explicitly
determine the effective action to order 6 in
fluctuations. We show that
the resultant action, including novel potential
terms absent for abelian
diffeomorphisms, obeys the requirements of
D-geometry, including
geodesic-masses for off-diagonal fluctuations and
consistency with
T-duality. We conclude with a demonstration that the
oft used symmetrized
trace approximation equals that of linearized
gravity up to
two-derivatives, and that the novel terms imposed by
base-point-independence indicate that a
gravitational Myers effect --- the
existence of a stable N D0-brane collective state ---
ought to be
present in negatively curved spacetimes.