81 research outputs found
Classification of non-Riemannian doubled-yet-gauged spacetime
Assuming covariant fields as the `fundamental' variables,
Double Field Theory can accommodate novel geometries where a Riemannian metric
cannot be defined, even locally. Here we present a complete classification of
such non-Riemannian spacetimes in terms of two non-negative integers,
, . Upon these backgrounds, strings become
chiral and anti-chiral over and directions respectively, while
particles and strings are frozen over the directions. In
particular, we identify as Riemannian manifolds, as
non-relativistic spacetime, as Gomis-Ooguri non-relativistic string,
as ultra-relativistic Carroll geometry, and as Siegel's
chiral string. Combined with a covariant Kaluza-Klein ansatz which we further
spell, leads to Newton-Cartan gravity. Alternative to the conventional
string compactifications on small manifolds, non-Riemannian spacetime such as
, may open a new scheme of the dimensional reduction from ten to
four.Comment: 1+41 pages; v2) Refs added; v3) Published version; v4) Sign error in
(2.51) correcte
G<sub>2</sub>-structures and quantization of non-geometric M-theory backgrounds
We describe the quantization of a four-dimensional locally non-geometric
M-theory background dual to a twisted three-torus by deriving a phase space
star product for deformation quantization of quasi-Poisson brackets related to
the nonassociative algebra of octonions. The construction is based on a choice
of -structure which defines a nonassociative deformation of the addition
law on the seven-dimensional vector space of Fourier momenta. We demonstrate
explicitly that this star product reduces to that of the three-dimensional
parabolic constant -flux model in the contraction of M-theory to string
theory, and use it to derive quantum phase space uncertainty relations as well
as triproducts for the nonassociative geometry of the four-dimensional
configuration space. By extending the -structure to a -structure,
we propose a 3-algebra structure on the full eight-dimensional M2-brane phase
space which reduces to the quasi-Poisson algebra after imposing a particular
gauge constraint, and whose deformation quantisation simultaneously encompasses
both the phase space star products and the configuration space triproducts. We
demonstrate how these structures naturally fit in with previous occurences of
3-algebras in M-theory.Comment: 41 pages; v2: Final version published in JHE
Exotic branes in Exceptional Field Theory: E-7(7) and beyond
In recent years, it has been widely argued that the duality transformations
of string and M-theory naturally imply the existence of so-called `exotic
branes'---low codimension objects with highly non-perturbative tensions,
scaling as for . We argue that their intimate
link with these duality transformations make them an ideal object of study
using the general framework of Double Field Theory (DFT) and Exceptional Field
Theory (EFT)---collectively referred to as ExFT. Parallel to the theme of
dualities, we also stress that these theories unify known solutions in string-
and M-theory into a single solution under ExFT. We argue that not only is there
a natural unifying description of the lowest codimension objects, many of these
exotic states require this formalism as a consistent supergravity description
does not exist.Comment: 73 pages Latex, v2: citations added, some orbits correcte
Strings and branes are waves
We examine the equations of motion of double field theory and the duality
manifest form of M-theory. We show the solutions of the equations of motion
corresponding to null pp-waves correspond to strings or membranes from the
usual spacetime perspective. A Goldstone mode analysis of the null wave
solution in double field theory produces the equations of motion of the duality
manifest string.Comment: 31 pages, LaTex, v2 some typos corrected and refs adde
Global aspects of double geometry
We consider the concept of a generalised manifold in the O(d,d) setting,
i.e., in double geometry. The conjecture by Hohm and Zwiebach for the form of
finite generalised diffeomorphisms is shown to hold. Transition functions on
overlaps are defined. Triple overlaps are trivial concerning their action on
coordinates, but non-trivial on fields, including the generalised metric. A
generalised manifold is an ordinary manifold, but the generalised metric on the
manifold carries a gerbe structure. We show how the abelian behaviour of the
gerbe is embedded in the non-abelian T-duality group. We also comment on
possibilities and difficulties in the U-duality setting.Comment: 20 pp. v3: refs. added, discussion added on limitations of formalis
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