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Recently a BPS Alice string has been found in a $U(1)\times SU(2)$ gaugetheory coupled with a charged complex adjoint scalar field arXiv:1703.08971. Itis a half BPS state preserving a half of supercharges when embedded into asupersymmetric gauge theory. In this paper, we study zero modes of a BPS Alicestring. After presenting $U(1)$ and translational zero modes, we construct theeffective action of these modes. In contrast to previous analysis of theconventional Alice string for which only large distance behaviors are known, wecan perform calculation exactly in the full space thanks to BPS properties.

The effective action of a BPS Alice string