2024/04/04 by Chao-Hsiang Sheu, Mikhail Shifman, Sheu, Chao-Hsiang +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2404.03630
openalex publication_date 2024/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We discuss various questions which emerge in connection with the Lie-algebraic deformation of \mathbbCP1 sigma model in two dimensions. First we supersymmetrize the original model endowing it with the minimal \cal N=(0,2) and extended \cal N=(2,2) supersymmetries. Then we derive the general hypercurrent anomaly in the both cases. In the latter case this anomaly is one-loop but is somewhat different from the standard expressions one can find in the literature because the target manifold is non-symmetric. We also show how to introduce the twisted masses and the θ term, and study the BPS equation for instantons, in particular the value of the topological charge. Then we demonstrate that the second loop in the β function of the non-supersymmetric Lie-algebraic sigma model is due to an infrared effect. To this end we use a supersymmetric regularization. We also conjecture that the above statement is valid for higher loops too, similar to the parallel phenomenon in four-dimensional \cal N=1 super-Yang-Mills. In the second part of the paper we develop a special dimensional reduction -- namely, starting from the two-dimensional Lie-algebraic model we arrive at a quasi-exactly solvable quantum-mechanical problem of the Lamé type.