Summary
We prove in an explicit example how the general BRS technique of approaching the renormalization of nonlinear σ-models built on compact homogeneous cosets can be suitably modified to the Kählerian case in the analytic parametrization. The structure of the BRS operator we adopt depends on the existence of the Kahler potentials and therefore identifies this class of models. With this choice, the nonrenormalization property of the fields is a direct consequence of the algebraic constraints introduced by the mass term.
Riassunto
Si discute, in un esempio esplicito, come si modifica la tecnica di rinormalizzazione alla BRS nel caso di modelli σ non lineari costruiti su varietà omogenee di Kähler nella parametrizzazione analitica. L–operatore di BRS dipende esplicitamente dai potenziali di Kahler e quindi identifica questa classe di modelli. Le proprietà di non rinormalizzazione dei campi sono una conseguenza diretta dei vincoli algebrici introdotti dal termine di massa.
Резюме
Мы доказываем на конкретном примере, как общая BRS техника перенормировки нелинейных σ-моделей, построенных на компактных однородных смежных классах, может быть обобщена на случай Kехлера с помощью аналитической параметризации. Структура BRS оператора зависит явно от потенциалов Кехлера и, следовательно, идентифицирует этот класс моделей. При таком подходе свойство неперенормируемост и полей представляет прямое следствие алгебраических ограничений, налагаемых массовым членом.
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Blasi, A., Maggiore, N. BRS renormalization of nonlinear σ-models built on Kählerian homogeneous cosets. Nuov Cim B 104, 35–51 (1989). https://doi.org/10.1007/BF02742824
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DOI: https://doi.org/10.1007/BF02742824