32,405 research outputs found
pp Wave Big Bangs: Matrix Strings and Shrinking Fuzzy Spheres
We find pp wave solutions in string theory with null-like linear dilatons.
These provide toy models of big bang cosmologies. We formulate Matrix String
Theory in these backgrounds. Near the big bang ``singularity'', the string
theory becomes strongly coupled but the Yang-Mills description of the matrix
string is weakly coupled. The presence of a second length scale allows us to
focus on a specific class of non-abelian configurations, viz. fuzzy cylinders,
for a suitable regime of parameters. We show that, for a class of pp waves,
fuzzy cylinders which start out big at early times dynamically shrink into
usual strings at sufficiently late times.Comment: 29 pages, ReVTeX and AMSLaTeX. 4 Figures. v2: Typo corrected and
reference adde
Unsharp Degrees of Freedom and the Generating of Symmetries
In quantum theory, real degrees of freedom are usually described by operators
which are self-adjoint. There are, however, exceptions to the rule. This is
because, in infinite dimensional Hilbert spaces, an operator is not necessarily
self-adjoint even if its expectation values are real. Instead, the operator may
be merely symmetric. Such operators are not diagonalizable - and as a
consequence they describe real degrees of freedom which display a form of
"unsharpness" or "fuzzyness". For example, there are indications that this type
of operators could arise with the description of space-time at the string or at
the Planck scale, where some form of unsharpness or fuzzyness has long been
conjectured.
A priori, however, a potential problem with merely symmetric operators is the
fact that, unlike self-adjoint operators, they do not generate unitaries - at
least not straightforwardly. Here, we show for a large class of these operators
that they do generate unitaries in a well defined way, and that these operators
even generate the entire unitary group of the Hilbert space. This shows that
merely symmetric operators, in addition to describing unsharp physical
entities, may indeed also play a r{\^o}le in the generation of symmetries, e.g.
within a fundamental theory of quantum gravity.Comment: 23 pages, LaTe
ABJM Baryon Stability and Myers effect
We consider magnetically charged baryon vertex like configurations in AdS^4 X
CP^3 with a reduced number of quarks l. We show that these configurations are
solutions to the classical equations of motion and are stable beyond a critical
value of l. Given that the magnetic flux dissolves D0-brane charge it is
possible to give a microscopical description in terms of D0-branes expanding
into fuzzy CP^n spaces by Myers dielectric effect. Using this description we
are able to explore the region of finite 't Hooft coupling.Comment: 29 pages, Latex; minor changes; version to appear in JHE
Fuzzy Spheres in pp Wave Matrix String Theory
The behaviour of matrix string theory in the background of a type IIA pp wave
at small string coupling, g_s << 1, is determined by the combination M g_s
where M is a dimensionless parameter proportional to the strength of the
Ramond-Ramond background. For M g_s << 1, the matrix string theory is
conventional; only the degrees of freedom in the Cartan subalgebra contribute,
and the theory reduces to copies of the perturbative string. For M g_s >> 1,
the theory admits degenerate vacua representing fundamental strings blown up
into fuzzy spheres with nonzero lightcone momenta. We determine the spectrum of
small fluctuations around these vacua. Around such a vacuum all N-squared
degrees of freedom are excited with comparable energies. The spectrum of masses
has a spacing which is independent of the radius of the fuzzy sphere, in
agreement with expected behaviour of continuum giant gravitons. Furthermore,
for fuzzy spheres characterized by reducible representations of SU(2) and
vanishing Wilson lines, the boundary conditions on the field are characterized
by a set of continuous angles which shows that generically the blown up strings
do not ``close''.Comment: 45 pages REVTeX 4 and AMSLaTeX. 1 figure. v2: references added.
Figure redrawn using LaTe
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