Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of N=2 supersymmetric CFT_{4}s: Indefinite Series   Using geometric engineering method of 4D $\mathcal{N}=2$ quiver gauge
theories and results on the classification of Kac-Moody (KM) algebras, we show
on explicit examples that there exist three sectors of $\mathcal{N}=2$ infrared
CFT$_{4}$s. Since the geometric engineering of these CFT$_{4}$s involve type II
strings on K3 fibered CY3 singularities, we conjecture the existence of three
kinds of singular complex surfaces containing, in addition to the two standard
classes, a third indefinite set. To illustrate this hypothesis, we give
explicit examples of K3 surfaces with H$_{3}^{4}$ and E$_{10}$ hyperbolic
singularities. We also derive a hierarchy of indefinite complex algebraic
geometries based on affine $A_{r}$ and T$%_{(p,q,r)}$ algebras going beyond the
hyperbolic subset. Such hierarchical surfaces have a remarkable signature that
is manifested by the presence of poles.

11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th