• Corpus ID: 246996925

Categorical symmetries of T-duality

  title={Categorical symmetries of T-duality},
  author={Konrad Waldorf},
Topological T-duality correspondences are higher categorical objects that can be classified by a strict Lie 2-group. In this article we compute the categorical automorphism group of this 2-group; hence, the higher symmetries of topological T-duality. We prove that the categorical automorphism group is a non-central categorical extension of the integral split pseudo-orthogonal group. We show that its splits over several subgroups, and that its k-invariant is 2-torsion. 
1 Citations
Non-Geometric T-Duality as Higher Groupoid Bundles with Connections
We describe T-duality between general geometric and non-geometric backgrounds as higher groupoid bundles with connections. Our description extends the previous observation by Nikolaus and Waldorf


On the Topology of T-Duality
We study a topological version of the T-duality relation between pairs consisting of a principal U(1)-bundle equipped with a degree-three integral cohomology class. We describe the homotopy type of a
Higher Geometry for Non-geometric T-Duals
We investigate topological T-duality in the framework of non-abelian gerbes and higher gauge groups. We show that this framework admits the gluing of locally defined T-duals, in situations where no
T-duality for torus bundles with H-fluxes via noncommutative topology, II: the high-dimensional case and the T-duality group
We use noncommutative topology to study T-duality for principal torus bundles with H-flux. We characterize precisely when there is a "classical" T-dual, i.e., a dual bundle with dual H-flux, and when
Categorical tori
We give explicit and elementary constructions of the categorical extensions of a torus by the circle and discuss an application to loop group extensions. Examples include maximal tori of simple and
T-Duality for Torus Bundles with H-Fluxes via Noncommutative Topology
It is known that the T-dual of a circle bundle with H-flux (given by a Neveu-Schwarz 3-form) is the T-dual circle bundle with dual H-flux. However, it is also known that torus bundles with H-flux do
Differentiable Cohomology of Gauge Groups
We give a definition of differentiable cohomology of a Lie group G (possibly infinite-dimensional) with coefficients in any abelian Lie group. This differentiable cohomology maps both to the
In string theory, the concept of T-duality between two principal Tn-bundles E and E over the same base space B, together with cohomology classes h ∈ H3(E,ℤ) and ĥ ∈ H3(E,ℤ), has been introduced. One
We recall and partially expand four versions of smooth, non-abelian gerbes: Cech cocycles, classifying maps, bundle gerbes, and principal 2-bundles. We prove that all these four versions are
Central extensions of smooth 2–groups and a finite-dimensional string 2–group
We provide a model of the String group as a central extension of finite-dimensional 2‐groups in the bicategory of Lie groupoids, left-principal bibundles, and bibundle maps. This bicategory is a
On mysteriously missing T-duals, H-flux and the T-duality group
A general formula for the topology and H-flux of the T-duals of type II string theories with H-flux on toroidal compactifications is presented here. It is known that toroidal compactifications with