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Is nonsymmetric gravity related to string theory?

In this work we raise the question whether nonsymmetric gravity and string theory are related. We start making the observation, that the gravitational field $ g_{μν}$ and the nonsymmetric gauge field $ A_{μν}$ arising in the low energy limit in the string theory are exactly the same two basic fields used in four dimensions in nonsymmetric gravity. We argue, that this connection between nonsymmetric gravity and string theory at the level of the gauge fields $ g_{μν}$ and $ A_{μν}$ is not, however, reflected at the level of the corresponding associated actions. In an effort to find a connection between such an actions we discover a new gravitational action, which suggests an alternative version of the bosonic string in which the target and the world-volume metrics are unified.