8,907 research outputs found
Frame-like Geometry of Double Field Theory
We relate two formulations of the recently constructed double field theory to
a frame-like geometrical formalism developed by Siegel. A self-contained
presentation of this formalism is given, including a discussion of the
constraints and its solutions, and of the resulting Riemann tensor, Ricci
tensor and curvature scalar. This curvature scalar can be used to define an
action, and it is shown that this action is equivalent to that of double field
theory.Comment: 35 pages, v2: minor corrections, to appear in J. Phys.
On supergravity solutions of space-like Dp-branes
Recently the time dependent solutions of type II supergravities in ,
with the metric having the symmetry have been
given by two groups (Chen-Gal'tsov-Gutperle (CGG), [hep-th/0204071] and
Kruczenski-Myers-Peet (KMP), [hep-th/0204144]). The supergravity solutions
correspond to space-like D-branes in type II string theory. While the CGG
solution is a four parameter solution, the KMP solution is a three parameter
solution and so in general they are different. This difference can be
attributed to the fact that unlike the CGG solution, KMP uses a specific
boundary condition for the metric and the dilaton field. It is shown that when
we impose the boundary conditions used in the KMP solution to the CGG solution
then both become three parameter solutions and they map to each other under a
coordinate transformation along with a Hodge duality of the field strength. We
also give the relations between the parameters characterizing the two
solutions.Comment: 14 pages, LaTeX, v2: minor corrections and a reference adde
The Signature Triality of Majorana-Weyl Spacetimes
Higher dimensional Majorana-Weyl spacetimes present space-time dualities
which are induced by the Spin(8) triality automorphisms. Different signature
versions of theories such as 10-dimensional SYM's, superstrings, five-branes,
F-theory, are shown to be interconnected via the S_3 permutation group.
Bilinear and trilinear invariants under space-time triality are introduced and
their possible relevance in building models possessing a space-versus-time
exchange symmetry is discussed. Moreover the Cartan's ``vector/chiral
spinor/antichiral spinor" triality of SO(8) and SO(4,4) is analyzed in detail
and explicit formulas are produced in a Majorana-Weyl basis. This paper is the
extended version of hep-th/9907148.Comment: 28 pages, LaTex. Extended version of hep-th/990714
Timelike Hopf Duality and Type IIA^* String Solutions
The usual T-duality that relates the type IIA and IIB theories compactified
on circles of inversely-related radii does not operate if the dimensional
reduction is performed on the time direction rather than a spatial one. This
observation led to the recent proposal that there might exist two further
ten-dimensional theories, namely type IIA^* and type IIB^*, related to type IIB
and type IIA respectively by a timelike dimensional reduction. In this paper we
explore such dimensional reductions in cases where time is the coordinate of a
non-trivial U(1) fibre bundle. We focus in particular on situations where there
is an odd-dimensional anti-de Sitter spacetime AdS_{2n+1}, which can be
described as a U(1) bundle over \widetilde{CP}^n, a non-compact version of CP^n
corresponding to the coset manifold SU(n,1)/U(n). In particular, we study the
AdS_5\times S^5 and AdS_7\times S^4 solutions of type IIB supergravity and
eleven-dimensional supergravity. Applying a timelike Hopf T-duality
transformation to the former provides a new solution of the type IIA^* theory,
of the form \widetilde{CP}^2\times S^1\times S^5. We show how the Hopf-reduced
solutions provide further examples of ``supersymmetry without supersymmetry.''
We also present a detailed discussion of the geometrical structure of the
Hopf-fibred metric on AdS_{2n+1}, and its relation to the horospherical metric
that arises in the AdS/CFT correspondence.Comment: Latex, 26 page
The many faces of OSp(1|32)
We show that the complete superalgebra of symmetries, including central
charges, that underlies F-theories, M-theories and type II string theories in
dimensions 12, 11 and 10 of various signatures correspond to rewriting of the
same OSp(1|32) algebra in different covariant ways. One only has to distinguish
the complex and the unique real algebra. We develop a common framework to
discuss all signatures theories by starting from the complex form of OSp(1|32).
Theories are distinguished by the choice of basis for this algebra. We
formulate dimensional reductions and dualities as changes of basis of the
algebra. A second ingredient is the choice of a real form corresponding to a
specific signature. The existence of the real form of the algebra selects
preferred spacetime signatures. In particular, we show how the real d=10 IIA
and IIB superalgebras for various signatures are related by generalized
T-duality transformations that not only involve spacelike but also timelike
directions. A third essential ingredient is that the translation generator in
one theory plays the role of a central charge operator in the other theory. The
identification of the translation generator in these algebras leads to the star
algebras of Hull, which are characterized by the fact that the positive
definite energy operator is not part of the translation generators. We apply
our results to discuss different T-dual pictures of the D-instanton solution of
Euclidean IIB supergravity.Comment: 30 pages, Latex, using lscape.st
Scale-Dependent Price Fluctuations for the Indian Stock Market
Classic studies of the probability density of price fluctuations for
stocks and foreign exchanges of several highly developed economies have been
interpreted using a {\it power-law} probability density function with exponent values , which are outside the
L\'evy-stable regime . To test the universality of this
relationship for less highly developed economies, we analyze daily returns for
the period Nov. 1994--June 2002 for the 49 largest stocks of the National Stock
Exchange which has the highest volume of trade in India. We find that
decays as an {\it exponential} function with a
characteristic decay scales for the negative tail and
for the positive tail, which is significantly different
from that observed for developed economies. Thus we conclude that the Indian
stock market may belong to a universality class that differs from those of
developed countries analyzed previously.Comment: 7 pages, 8 figure
Complexified sigma model and duality
We show that the equations of motion associated with a complexified
sigma-model action do not admit manifest dual SO(n,n) symmetry. In the process
we discover new type of numbers which we called `complexoids' in order to
emphasize their close relation with both complex numbers and matroids. It turns
out that the complexoids allow to consider the analogue of the complexified
sigma-model action but with (1+1)-worldsheet metric, instead of
Euclidean-worldsheet metric. Our observations can be useful for further
developments of complexified quantum mechanics.Comment: 15 pages, Latex, improved versio
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