Regular Article - Theoretical Physics
Taking off the square root of Nambu–Goto action and obtaining Filippov–Lie algebra gauge theory action
Department of Physics, Sogang University, Shinsu-dong, Mapo-gu, Seoul, 121-742, Korea
2 University College, Sungkyunkwan University, Suwon, 440-746, Korea
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Published online: 12 September 2009
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.
© Springer-Verlag , 2009