Can the energy bound E ≥ 0 imply supersymmetry?
We utilize the integrality conjecture to show that the torus partition function of a fermionic rational conformal theory in the Ramond-Ramond sector becomes a constant when the bound <i>h<sup>R</sup></i> ≥ <i><sup>c</sup></i>⁄<sub>24<...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
American Physical Society
2023
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| Summary: | We utilize the integrality conjecture to show that the torus partition function of a fermionic rational conformal theory in the Ramond-Ramond sector becomes a constant when the bound <i>h<sup>R</sup></i> ≥ <i><sup>c</sup></i>⁄<sub>24</sub> is satisfied, where <i>h<sup>R</sup></i> denotes the conformal weights of Ramond states and <i>c</i> is the central charge. The constant-valued Ramond-Ramond partition function strongly suggests the presence of supersymmetry unless a given theory has free fermions. The lower bound <i>h<sup>R</sup></i> ≥ <i><sup>c</sup></i>⁄<sub>24</sub> can then be identified with the unitarity bound of <i>N</i> = 1 supersymmetry. We thus propose that, for rational CFTs without free fermions, (<i>h<sup>R</sup></i> − <i>c</i>/24) ≥ 0 can imply supersymmetry. |
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