Numerical study of the $\mathcal{N}=2$ Landau–Ginzburg model

DOI10.1093/PTEP/PTY088zbMATH Open1477.81092arXiv1805.10735OpenAlexW2803312331MaRDI QIDQ5156726

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Publication date: 11 October 2021

Published in: Unnamed Author (Search for Journal in Brave)

Abstract: It is believed that the two-dimensional massless $mathcalN=2$ Wess--Zumino model becomes the $mathcalN=2$ superconformal field theory (SCFT) in the infrared (IR) limit. We examine this theoretical conjecture of the Landau--Ginzburg (LG) description of the $mathcalN=2$ SCFT by numerical simulations on the basis of a supersymmetric-invariant momentum-cutoff regularization. We study a single supermultiplet with cubic and quartic superpotentials. From two-point correlation functions in the IR region, we measure the scaling dimension and the central charge, which are consistent with the conjectured LG description of the $A_2$ and $A_3$ minimal models, respectively. Our result supports the theoretical conjecture and, at the same time, indicates a possible computational method of correlation functions in the $mathcalN=2$ SCFT from the LG description.

Full work available at URL: https://arxiv.org/abs/1805.10735

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) String and superstring theories in gravitational theory (83E30) Supersymmetric field theories in quantum mechanics (81T60) Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Computational methods for problems pertaining to quantum theory (81-08)

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