https://doi.org/10.1140/epjc/s10052-009-1132-x
Regular Article - Theoretical Physics
Taking off the square root of Nambu–Goto action and obtaining Filippov–Lie algebra gauge theory action
1
Department of Physics, Sogang University, Shinsu-dong, Mapo-gu, Seoul, 121-742, Korea
2
University College, Sungkyunkwan University, Suwon, 440-746, Korea
* e-mail: park@sogang.ac.kr
Received:
23
June
2009
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
