30,177 research outputs found
Higher Dimensional Geometries from Matrix Brane constructions
Matrix descriptions of even dimensional fuzzy spherical branes in
Matrix Theory and other contexts in Type II superstring theory reveal, in the
large limit, higher dimensional geometries , which have an
interesting spectrum of harmonics and can be up to 20 dimensional,
while the spheres are restricted to be of dimension less than 10. In the case
, the matrix description has two dual field theory formulations. One
involves a field theory living on the non-commutative coset which
is a fuzzy fibre bundle over a fuzzy . In the other, there is a U(n)
gauge theory on a fuzzy with instantons. The two
descriptions can be related by exploiting the usual relation between the fuzzy
two-sphere and U(n) Lie algebra. We discuss the analogous phenomena in the
higher dimensional cases, developing a relation between fuzzy
cosets and unitary Lie algebras.Comment: 28 pages (Harvmac big) ; version 2 : minor typos fixed and ref. adde
Large-small dualities between periodic collapsing/expanding branes and brane funnels
We consider space and time dependent fuzzy spheres arising in
intersections in IIB string theory and collapsing D(2p)-branes in
IIA string theory.
In the case of , where the periodic space and time-dependent solutions
can be described by Jacobi elliptic functions, there is a duality of the form
to which relates the space and time dependent solutions.
This duality is related to complex multiplication properties of the Jacobi
elliptic functions. For funnels, the description of the periodic space
and time dependent solutions involves the Jacobi Inversion problem on a
hyper-elliptic Riemann surface of genus 3. Special symmetries of the Riemann
surface allow the reduction of the problem to one involving a product of genus
one surfaces. The symmetries also allow a generalisation of the to duality. Some of these considerations extend to the case of the
fuzzy .Comment: Latex, 50 pages, 2 figures ; v2 : a systematic typographical error
corrected + minor change
Domain walls between gauge theories
Noncommutative U(N) gauge theories at different N may be often thought of as
different sectors of a single theory: the U(1) theory possesses a sequence of
vacua labeled by an integer parameter N, and the theory in the vicinity of the
N-th vacuum coincides with the U(N) noncommutative gauge theory. We construct
noncommutative domain walls on fuzzy cylinder, separating vacua with different
gauge theories. These domain walls are solutions of BPS equations in gauge
theory with an extra term stabilizing the radius of the cylinder. We study
properties of the domain walls using adjoint scalar and fundamental fermion
fields as probes. We show that the regions on different sides of the wall are
not disjoint even in the low energy regime -- there are modes penetrating from
one region to the other. We find that the wall supports a chiral fermion zero
mode. Also, we study non-BPS solution representing a wall and an antiwall, and
show that this solution is unstable. We suggest that the domain walls emerge as
solutions of matrix model in large class of pp-wave backgrounds with
inhomogeneous field strength. In the M-theory language, the domain walls have
an interpretation of a stack of branes of fingerstall shape inserted into a
stack of cylindrical branes.Comment: Final version; minor corrections; to appear in Nucl.Phys.
- âŠ