Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyperk\"{a}hler, Bi-hypercomplex, Generalized Hyperk\"{a}hler Structures
  and T-duality   We investigate comprehensive relations among T-duality, complex and
bi-hermitian structures $(J_+, J_-)$ in two-dimensional $\mathcal{N} =(2,2)$
sigma models with/without twisted chiral multiplets. The bi-hermitian
structures $(J_+,J_-)$ embedded in generalized K\"{a}hler structures
$(\mathcal{J}_+,\mathcal{J}_-)$ are organized into the algebra of the
tri-complex numbers. We newly write down an analogue of the Buscher rule by
which the T-duality transformation of the bi-hermitian and K\"{a}hler
structures are apparent. We also study the bi-hypercomplex and hyperk\"{a}hler
cases in $\mathcal{N} = (4,4)$ theories. They are expressed, as a T-duality
covariant fashion, in the generalized hyperk\"{a}hler structures and form the
split-bi-quaternion algebras. As a concrete example, we show the explicit
T-duality relation between the hyperk\"{a}hler structures of the KK-monopole
(Taub-NUT space) and the bi-hypercomplex structures of the H-monopole (smeared
NS5-brane). Utilizing this result, we comment on a T-duality relation for the
worldsheet instantons in these geometries.

16
The categories of this paper are: stat
9
The categories of this paper are: nlin
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph