Preprint

PUBDB-2025-01931

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Three-point functions from integrability in $\mathcal{N}=2$ orbifold theories

le Plat, D. ; Skrzypek, T. (Corresponding author)DESY*

2025

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Please use a persistent id in citations: doi:10.3204/PUBDB-2025-01931

Report No.: DESY-25-088; arXiv:2506.21323

Abstract: Besides solving the spectral problem of $\mathcal{N}=4$ Super-Yang-Mills (SYM) theory, integrability also provides us with tools to compute the structure constants of the theory, most prominently through the hexagon formalism. We show that, with minor modifications, this formalism can also be applied to orbifolds of $\mathcal{N}=4$ SYM theory, which are integrable theories in their own right.To substantiate this claim, we test our results against a direct gauge theory calculation at tree-level. We focus here on a family of $\mathcal{N}=2$ supersymmetric $\mathbb{Z}_M$-orbifold theories. BPS-correlators in these theories have recently been investigated with independent localisation techniques and a tentative matching with wrapping-corrections in the hexagon formalism was observed. Together with our weak-coupling evidence, this suggests that a full determination of the structure constants of orbifold theories at finite coupling may be within reach.

Note: 36 pages, 5 figures, 122 structure constants; v2: References added

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Contributing Institute(s):

1. Theorie-Gruppe (T)

Research Program(s):

1. 611 - Fundamental Particles and Forces (POF4-611) (POF4-611)
2. DFG project G:(GEPRIS)506632645 - SFB 1624: Höhere Strukturen, Modulräume und Integrabilität (506632645) (506632645)
3. DFG project G:(GEPRIS)390833306 - EXC 2121: Quantum Universe (390833306) (390833306)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2025

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