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Integrality, duality and finiteness in combinatoric topological strings

de Mello Koch, R., He, Y-H. ORCID: 0000-0002-0787-8380, Kemp, G. & Ramgoolam, S. (2022). Integrality, duality and finiteness in combinatoric topological strings. Journal of High Energy Physics, 71. doi: 10.1007/JHEP01(2022)071

Abstract

A remarkable result at the intersection of number theory and group theory states that the order of a finite group G (denoted |G|) is divisible by the dimension dR of any irreducible complex representation of G. We show that the integer ratios |G|2/dR2 are combinatorially constructible using finite algorithms which take as input the amplitudes of combinatoric topological strings (G-CTST) of finite groups based on 2D Dijkgraaf-Witten topological field theories (G-TQFT2). The ratios are also shown to be eigenvalues of handle creation operators in G-TQFT2/G-CTST. These strings have recently been discussed as toy models of wormholes and baby universes by Marolf and Maxfield, and Gardiner and Megas. Boundary amplitudes of the G-TQFT2/G-CTST provide algorithms for combinatoric constructions of normalized characters. Stringy S-duality for closed G-CTST gives a dual expansion generated by disconnected entangled surfaces. There are universal relations between G-TQFT2 amplitudes due to the finiteness of the number K of conjugacy classes. These relations can be labelled by Young diagrams and are captured by null states in an inner product constructed by coupling the G-TQFT2 to a universal TQFT2 based on symmetric group algebras. We discuss the scenario of a 3D holographic dual for this coupled theory and the implications of the scenario for the factorization puzzle of 2D/3D holography raised by wormholes in 3D.

Publication Type: Article
Additional Information: This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Publisher Keywords: M(atrix) Theories, Topological Field Theories, Topological Strings
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
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