36,562 research outputs found
T-Duality in Arbitrary String Backgrounds
T-Duality is a poorly understood symmetry of the space-time fields of string
theory that interchanges long and short distances. It is best understood in the
context of toroidal compactification where, loosely speaking, radii of the
torus are inverted. Even in this case, however, conventional techniques permit
an understanding of the transformations only in the case where the metric on
the torus is endowed with Abelian Killing symmetries. Attempting to apply these
techniques to a general metric appears to yield a non-local world-sheet theory
that would defy interpretation in terms of space-time fields. However, there is
now available a simple but powerful general approach to understanding the
symmetry transformations of string theory, which are generated by certain
similarity transformations of the stress-tensors of the associated conformal
field theories. We apply this method to the particular case of T-Duality and i)
rederive the known transformations, ii) prove that the problem of non-locality
is illusory, iii) give an explicit example of the transformation of a metric
that lacks Killing symmetries and iv) derive a simple transformation rule for
arbitrary string fields on tori.Comment: 25 pages, plain Tex, new references adde
Clustering Boolean Tensors
Tensor factorizations are computationally hard problems, and in particular,
are often significantly harder than their matrix counterparts. In case of
Boolean tensor factorizations -- where the input tensor and all the factors are
required to be binary and we use Boolean algebra -- much of that hardness comes
from the possibility of overlapping components. Yet, in many applications we
are perfectly happy to partition at least one of the modes. In this paper we
investigate what consequences does this partitioning have on the computational
complexity of the Boolean tensor factorizations and present a new algorithm for
the resulting clustering problem. This algorithm can alternatively be seen as a
particularly regularized clustering algorithm that can handle extremely
high-dimensional observations. We analyse our algorithms with the goal of
maximizing the similarity and argue that this is more meaningful than
minimizing the dissimilarity. As a by-product we obtain a PTAS and an efficient
0.828-approximation algorithm for rank-1 binary factorizations. Our algorithm
for Boolean tensor clustering achieves high scalability, high similarity, and
good generalization to unseen data with both synthetic and real-world data
sets
Self-similar equilibration of strongly interacting systems from holography
We study the equilibration of a class of far-from-equilibrium strongly
interacting systems using gauge/gravity duality. The systems we analyse are 2+1
dimensional and have a four dimensional gravitational dual. A prototype example
of a system we analyse is the equilibration of a two dimensional fluid which is
translational invariant in one direction and is attached to two different heat
baths with different temperatures at infinity in the other direction. We
realise such setup in gauge/gravity duality by joining two semi-infinite
asymptotically Anti-de Sitter (AdS) black branes of different temperatures,
which subsequently evolve towards equilibrium by emitting gravitational
radiation towards the boundary of AdS. At sufficiently late times the solution
converges to a similarity solution, which is only sensitive to the left and
right equilibrium states and not to the details of the initial conditions. This
attractor solution not only incorporates the growing region of equilibrated
plasma but also the outwardly-propagating transition regions, and can be
constructed by solving a single ordinary differential equation.Comment: 5 pages 3 figures. Published versio
An Infinite Dimensional Symmetry Algebra in String Theory
Symmetry transformations of the space-time fields of string theory are
generated by certain similarity transformations of the stress-tensor of the
associated conformal field theories. This observation is complicated by the
fact that, as we explain, many of the operators we habitually use in string
theory (such as vertices and currents) have ill-defined commutators. However,
we identify an infinite-dimensional subalgebra whose commutators are not
singular, and explicitly calculate its structure constants. This constitutes a
subalgebra of the gauge symmetry of string theory, although it may act on
auxiliary as well as propagating fields. We term this object a {\it weighted
tensor algebra}, and, while it appears to be a distant cousin of the
-algebras, it has not, to our knowledge, appeared in the literature before.Comment: 14 pages, Plain TeX, report RU93-8, CTP-TAMU-2/94, CERN-TH.7022/9
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