#### Alladi Ramakrishnan Hall

#### Obstructions in non-Abelian vortices and BPS Alice strings

#### Chandrasekhar Chatterjee

##### Keio University, Japan

*In this lecture we discuss Alice strings. When a charged particle encircles around an Alice string, it changes the sign of the electric charge, the generator of unbroken group. In this lecture we discuss a BPS-saturated Alice string in U(1) × SO(3) gauge theory with charged complex scalar fields belonging to the vector representation. After performing BPS completion we discuss the possible numerical solutions of BPS equations. Then we discuss zero modes of a BPS Alice string. After presenting U(1) zero modes we construct the effective action of this mode. In contrast to previous analysis of the conventional Alice string for which only large distance behaviors are known, we can perform calculation exactly in the full space thanks to BPS properties.*

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