Taking off the square root of Nambu-Goto action and obtaining Filippov-Lie algebra gauge theory action

초록

We propose a novel prescription to take off the square root of the Nambu-Goto action for a p-brane, which generalizes the Brink-Di Vecchia-Howe-Tucker, also known as the Polyakov method. With an arbitrary decomposition, d+n=p+1, our resulting action is a modified d-dimensional Polyakov action, which is gauged and possesses a Nambu n-bracket squared potential. We first spell out how the (p+1)-dimensional diffeomorphism is realized in the lower dimensional action. Then we discuss a possible gauge fixing of it to a direct product of d-dimensional diffeomorphism and n-dimensional volume preserving diffeomorphism. We show that the latter naturally leads to a novel Filippov-Lie n-algebra based gauge theory action in d dimensions.

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