451 research outputs found
Oscillator Representation of the BCFT Construction of D-branes in Vacuum String Field Theory
Starting from the boundary CFT definition for the D-branes in vacuum string
field theory (VSFT) given in hep-th/0105168, we derive the oscillator
expression for the D24-brane solution in the VSFT on D25-brane. We show that
the state takes the form of a squeezed state, similar to the one found directly
in terms of the oscillators and reported in hep-th/0102112. Both the solutions
are actually one parameter families of solutions. We also find numerical
evidence that at least for moderately large values of the parameter in
the oscillator construction the two families of solutions are same under a
suitable redefinition of the parameter. Finally we generalize the method to
computing the oscillator expression for a D-brane solution with constant gauge
field strength turned on along the world volume.Comment: Latex, 43 pages, 3 figures, references adde
Quantum Query Complexity of Multilinear Identity Testing
Motivated by the quantum algorithm in \cite{MN05} for testing commutativity
of black-box groups, we study the following problem: Given a black-box finite
ring where is an additive
generating set for and a multilinear polynomial over
also accessed as a black-box function (where we allow the
indeterminates to be commuting or noncommuting), we study the
problem of testing if is an \emph{identity} for the ring . More
precisely, the problem is to test if for all .
We give a quantum algorithm with query complexity assuming . Towards a lower bound,
we also discuss a reduction from a version of -collision to this problem.
We also observe a randomized test with query complexity and constant
success probability and a deterministic test with query complexity.Comment: 12 page
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