18 research outputs found
A Lorentz invariant doubled worldsheet theory
We propose a Lorentz invariant version of Tseytlin's doubled worldsheet
theory that makes T-duality covariance of the string manifest. This theory can
be derived as a gauge fixed version of Buscher's gauging procedure, in which
the left-over gauge field component acts as a Lagrange multiplier. This
description can naturally account for fractional linear O(D,D) transformations
of the metric and b-field. It is capable of describing non-geometric
backgrounds; geometric and non-geometric fluxes are encoded in the doubled
anti-symmetric tensor field strength.Comment: 4 pages LaTeX, no figures, discussion of path integral quantization
include
Renormalization of a Lorentz invariant doubled worldsheet theory
Manifestly T-duality covariant worldsheet string models can be constructed by
doubling the coordinate fields. We describe the underlying gauge symmetry of a
recently proposed Lorentz invariant doubled worldsheet theory that makes half
of the worldsheet degrees of freedom redundant. By shifting the Lagrange
multiplier, that enforces the gauge fixing condition, the worldsheet action can
be cast into various guises. We investigate the renormalization of this theory
using a non-linear background / quantum split by employing a normal coordinate
expansion adapted to the gauge-fixed theory. The propagator of the doubled
coordinates contains a projection operator encoding that half of them do not
propagate. We determine the doubled target space equations of motion by
requiring one-loop Weyl invariance. Some of them are generalizations of the
conventional sigma model beta-functions, while others seem to be novel to the
doubled theory: In particular, a dilaton equation seems related to the strong
constraint of double field theory. However, the other target space field
equations are not identical to those of double field theory.Comment: 32 pages; v2: motivation and discussion expanded, references adde
(Non-)commutative closed string on T-dual toroidal backgrounds
In this paper we investigate the connection between (non-)geometry and
(non-)commutativity of the closed string. To this end, we solve the classical
string on three T-dual toroidal backgrounds: a torus with H-flux, a twisted
torus and a non-geometric background with Q-flux. In all three situations we
work under the assumption of a dilute flux and consider quantities to linear
order in the flux density. Furthermore, we perform the first steps of a
canonical quantization for the twisted torus, to derive commutators of the
string expansion modes. We use them as well as T-duality to determine, in the
non-geometric background, a commutator of two string coordinates, which turns
out to be non-vanishing. We relate this non-commutativity to the closed string
boundary conditions, and the non-geometric Q-flux.Comment: 47 pages; published versio
Non-Geometric Fluxes in Supergravity and Double Field Theory
In this paper we propose ten-dimensional realizations of the non-geometric
fluxes Q and R. In particular, they appear in the NSNS Lagrangian after
performing a field redefinition that takes the form of a T-duality
transformation. Double field theory simplifies the computation of the field
redefinition significantly, and also completes the higher-dimensional picture
by providing a geometrical role for the non-geometric fluxes once the winding
derivatives are taken into account. The relation to four-dimensional gauged
supergravities, together with the global obstructions of non-geometry, are
discussed.Comment: 43 page
Generalized geometry, calibrations and supersymmetry in diverse dimensions
We consider type II backgrounds of the form R^{1,d-1} x M^{10-d} for even d,
preserving 2^{d/2} real supercharges; for d = 4, 6, 8 this is minimal
supersymmetry in d dimensions, while for d = 2 it is N = (2,0) supersymmetry in
two dimensions. For d = 6 we prove, by explicitly solving the Killing-spinor
equations, that there is a one-to-one correspondence between background
supersymmetry equations in pure-spinor form and D-brane generalized
calibrations; this correspondence had been known to hold in the d = 4 case.
Assuming the correspondence to hold for all d, we list the calibration forms
for all admissible D-branes, as well as the background supersymmetry equations
in pure-spinor form. We find a number of general features, including the
following: The pattern of codimensions at which each calibration form appears
exhibits a (mod 4) periodicity. In all cases one of the pure-spinor equations
implies that the internal manifold is generalized Calabi-Yau. Our results are
manifestly invariant under generalized mirror symmetry.Comment: 28 pages, 1 tabl