Супергравитация существует

Существует множество интересных модификаций теории Калуцы — Клейна в многомерных пространствах, в которые произвольно добавлены фермионные поля. Однако такой произвол нарушает первозданную простоту основной идеи Калуцы. Хотелось бы иметь теорию, в которой число фермионных полей, равно как и число дополнительных измерений пространства-времени, следовало бы из самой структуры теории.

Примером подобной теории является супергравитаиия. Самое главное в ней — обобщение ОТО на основе единообразного рассмотрения бозонов и фермионов. Так, гравитон имеет в этой теории партнера — ферми- он, называемый гравитино. В эйнштейновском варианте ОТО можно добавлять или убирать фермионные поля произвольно, но в супергравнта- ции каждому бозону соответствует свой фермионный партнер. Таким образом, в супергравитацин с самого начала присутствует определенное число фермионов, необходимых для описания наблюдаемого строения вещества.

На число измерений пространства- времени супергравитация также накладывает определенные ограничения. Как мы отметили выше, по- видимому, теории супергравитацин не приемлемы, если число измерений превышает 11. В пространствах более высокой размерности нельзя удовлетворить математическим требованиям, обеспечивающим партнерство бозонных и фермионных полей. Более того, Эдвард Виттен из Принстонского университета показал, что к обычным четырем измерениям пространства-времени необходимо добавить по крайней мере семь скрытых измерений для того, чтобы включить в теорию Калуцы — Клейна сильные, слабые и электромагнитные взаимодействия. У теории Калуцы — Клейна в 11-мерном пространстве-времени есть еше одна характерная особенность, которая носит случайный характер, но сильно привлекает теоретиков. Все многомерные теории супергравитации в пространствах с меньшим числом измерений имеют несколько вариантов, различающихся математически. В ! 1-мерном пространстве-времени теория супергра- витации единственна.

Минимальный набор ингредиентов теории Калуцы — Клейна содержит гравитационное и фермионное поля, которые приводят в конечном итоге к бозонам и фермионам, наблюдаемым в нашем мире. Кроме того, нужно по крайней мере еще одно бозонное поле, приводящее к компактификации, т.е. сворачиванию, дополнительных скрытых измерений. Замечательно, что 11-мерная супергравитация содержит в точности все три ингредиента.

Еще более удивительно для теоретиков то, что дополнительное бозонное поле вызывает только два вида компактификации. В одном случае сворачивается семь измерений из одиннадцати; этот вид компактифи- кации объясняет 4-мерность наблюдаемого пространства-времени. В альтернативном случае сворачиваются лишь четыре измерения. Такой сценарий привел бы к 7-мерному наблюдаемому миру. Быть может, физики последующих поколений смогут объяснить, почему 4-мерный мир оказался в привилегированном положении.

Для развития теории Калуцы —

Клейна, основанной на супергравитации в 11 -ти измерениях, физики должны сначала решить уравнения супергравитации. Множество решений приводит к такой конструкции, когда полное пространство-время порождается обычным четырехмерным пространством-временем и небольшой замкнутой 7-мерной поверхностью. Затем надо изучить группу симметрии каждой поверхности, соответствующей какому-то решению полевых уравнений, и группу симметрии той неабелевой калибровочной теории, которую надо объединить с гравитацией. Различные замкнутые поверхности имеют разные группы симметрии, и каждая из них приводит к различным объединенным теориям не- гравитационных сил.

Окончательным шагом в развитии теории Калуцы — Клейна должен быть анализ сложных стационарных волновых образований, допускаемых данной замкнутой поверхностью. Эти образования определяют массы и другие свойства частиц, предсказываемых теорией для обычного 4-мерного пространства-времени. Каждая из

7-мерных поверхностей, возникающих в результате решения уравнений супергравитацин, должна быть подвергнута подобному анализу.

 

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