Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Geometry of the SU(2)$\times$ G$_2$-model   We study elliptic fibrations that geometrically engineer an SU(2)$\times$
G$_2$ gauge theory realized by Weierstrass model for the collision
III+$\text{I}_0^{*\text{ns}}$. We construct the four possible crepant
resolutions of such a Weierstrass model and show that they form a chain of four
minimal models connected by flops. We compute the generating function for the
Euler characteristic of these crepant resolutions. In the case of a Calabi-Yau
threefold, we consider the compactification of M-theory and F-theory on an
SU(2)$\times$ G$_2$-model to a five and six-dimensional supergravity with eight
supercharges. By matching each crepant resolution with each Coulomb chamber of
the five-dimensional theory, we determine the number of multiplets and compute
the prepotential in each Coulomb chamber. In particular, we discuss counting
number of hypermultiplets in presence of singularities. We discuss in detail
the cancellation of anomalies of the six-dimensional theory.

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The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
18
The categories of this paper are: econ