Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $CP$ violation in modular invariant flavor models   We study the spontaneous $CP$ violation through the stabilization of the
modulus $\tau$ in modular invariant flavor models. The $CP$-invaraiant
potentential has the minimum only at ${\rm Re}[\tau] = 0$ or 1/2. From this
prediction, we study $CP$ violation in modular invariant flavor models. The
physical $CP$ phase is vanishing. The important point for the $CP$ conservation
is the $T$ transformation in the modular symmetry. One needs the violation of
$T$ symmetry to realize the spontaneous $CP$ violation.

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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: nucl-th