{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/cubic-interaction-vertices-and-one-loop-self","title":"Cubic Interaction Vertices and One-loop Self-energy in the Stable String Bit Model","arxiv_id":"1701.04806","date":"2017-01-17","proceeding":null,"authors":["Gaoli Chen"],"abstract":"We provide a formalism to calculate the cubic interaction vertices of the stable string bit model, in which string bits have $s$ spin degrees of freedom but no space to move. With the vertices, we obtain a formula for one-loop self-energy, i.e., the $\\mathcal{O}\\left(1/N^{2}\\right)$ correction to the energy spectrum. A rough analysis shows that, when the bit number $M$ is large, the ground state one-loop self-energy $\\Delta E_{G}$ scale as $M^{5-s/4}$ for even $s$ and $M^{4-s/4}$ for odd $s$. Particularly, in $s=24$, we have $\\Delta E_{G}\\sim 1/M$, which resembles the Poincar\\'e invariant relation $P^{-}\\sim 1/P^{+}$ in $(1+1)$ dimensions. We calculate analytically the one-loop correction for the ground energies with $M=3$ and $s=1,\\,2$. We then numerically confirm that the large $M$ behavior holds for $s\\leq4$ cases.","url_abs":"http://arxiv.org/abs/1701.04806v3","url_pdf":"http://arxiv.org/pdf/1701.04806v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"cubic-interaction-vertices-and-one-loop-self","repo_url":"https://github.com/gaolichen/stringbit","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}