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arXiv · hep-th/0310128

Loop Variables with Chan-Paton Factors

B. Sathiapalan
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Abstract

The Loop Variable method that has been developed for the U(1) bosonic open string is generalized to include non-Abelian gauge invariance by incorporating "Chan-Paton" gauge group indices. The scale transformation symmetry $k(s) \to k(s) λ(s)$ that was responsible for gauge invariance in the U(1) case continues to be a symmetry. In addition there is a "rotation" symmetry. Both symmetries crucially involve the massive modes. However it is plausible that only a linear combination, which is the usual Yang-Mills transformation on massless fields, has a smooth (world sheet) continuum limit. We also illustrate how an infinite number of terms in the equation of motion in the cutoff theory add up to give a term that has a smooth continuum limit, and thus contributes to the low energy Yang-Mills equation of motion.

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B. Sathiapalan. 2003-10-27. Loop Variables with Chan-Paton Factors. https://doi.org/10.1142/s0217732304012381

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