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arXiv · 1808.03483

Theta-problem and the String Swampland

Sergio Cecotti·Cumrun Vafa
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Abstract

In the context of $\mathcal{N}=2$ supergravity without vector multiplets coupled to hypermultiplets, the coupling constant of graviphoton $\tau$ is apriori a free parameter. Stringy realization of this and using a mathematical conjecture leads to the statement that $j(\tau)\in \mathbb{R}$ so that the $\theta$-angle is $0$ or $\pi$. We conjecture that for any consistent realization of $\mathcal{N}=2$ supergravity theories coupled only to hypermultiplets this is the case and the rest belong to the swampland. This leads to the speculation that the $\theta$-angle for QCD or QED may also be fixed to $0$ for quantum gravitational consistency.

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Sergio Cecotti, Cumrun Vafa. 2018-08-10. Theta-problem and the String Swampland. https://arxiv.org/abs/1808.03483

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