Abstract
The charges of WZW D-branes form a finite abelian group called the charge group. One approach to finding these groups is to use the conformal field theory description of D-branes, i.e. the charge equation. Using this approach, we work out the charge groups for the non-simply connected group \(C_{3}/\mathbb{Z}_{2}\), which requires knowing the NIM-rep of the underlying conformal field theory.
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Notes
- 1.
We usually normalize this to q 0 = 1.
- 2.
These matrices control the modularity of the RCFT characters and yield a representation of the modular group SL\(_{2}(\mathbb{Z})\) via the assignment
$$\displaystyle{ \left (\begin{array}{lr} 0 & - 1\\ 1 & 0 \end{array} \right )\mapsto S\quad \; \quad \left (\begin{array}{lr} 1 & 1\\ 0 & 1 \end{array} \right )\mapsto T. }$$
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Acknowledgements
The author wishes to thank the organizers of the workshop for their kind hospitality and stimulating work environment during the workshop.
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Beltaos, E. (2014). The D-Brane Charges of C 3/\(\mathbb{Z}_{2}\) . In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. Springer Proceedings in Mathematics & Statistics, vol 111. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55285-7_14
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DOI: https://doi.org/10.1007/978-4-431-55285-7_14
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