The Shadows of Pygmalion

For as long as anyone knows, beings called "Puppets" have been an invisible part of our world. They operate in service of a force unknown, quietly manipulating the course of history.

Hajiro Mina is an ordinary high-school girl and the protagonist of this story. One day, she has a chance encounter with one of these Puppets, setting her on a trajectory to meet three girls—and ultimately changing her life forever.

The girls belong to an organization that specializes in the extermination of Puppets. They have been granted extraordinary powers by a doll named Ruka, and their job is to locate and eradicate the inhuman enemies lurking in the crowds.

As Mina finds herself entangled in this supernatural conflict, it becomes clearer with each passing day that there are greater forces at play.

[From MangaGamer]