Lie-algebraic Kähler sigma models with the U(1) isotropy
arxiv(2024)
摘要
We discuss various questions which emerge in connection with the
Lie-algebraic deformation of ℂℙ^1 sigma model in two dimensions.
First we supersymmetrize the original model endowing it with the minimal N=(0,2) and extended 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 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.
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