Abstract
Quantum field theory (QFT), the framework that describes our world above the Planck scale, has been a rich research subject in Physics. Among QFTs, the supersymmetric ones are extensively studied and many nontrivial facts are discovered although the real-world QFT, which is the standard model below the electroweak scale, is non-supersymmetric.
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Notes
- 1.
The symbol \(\mathscr {N}\) denotes the number of supersymmetries by the unit of minimal spinor representation of the considered dimension, as usual. 6d admits symplectic Majorana-Weyl fermions therefore the type of the supersymmetry algebra is specified by a pair of integers each represents the number of supercharges with \(+/-\) chiralities. In 6d, \(\mathscr {N}=(1,0)\) supersymmetry algebra has 8 supercharges which is equal to the number of supercharges in 4d \(\mathscr {N}=2\) algebra. A brief explanation is in Sect. 2.1. For more detail, see, for example, Appendixes of [3].
- 2.
Here the word “existence” means theoretical (or mathematical) existence. We are not going to discuss whether this world is governed by the string/M-theory.
- 3.
Again we would like to remark that non-Lagrangian means there is no known Lagrangian now.
- 4.
In this thesis the field strength F is multiplied by \(\frac{\mathrm {i}}{2\pi }\) compared to the usual notation used in Physics. With this normalization, F is valued in the integer cohomology when the gauge group is abelian.
- 5.
This statement is not precise. The global structure of 4d gauge group changes under the S-dual, meaning that the 6d theory is not completely invariant under the large diffeomorphism. See [7].
- 6.
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Ohmori, K. (2018). Introduction. In: Six-Dimensional Superconformal Field Theories and Their Torus Compactifications. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-13-3092-6_1
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