11-мерная супергравитация

В теориях Калуцы — Клейна, не основанных на супергравитации, этой трудности можно избежать. К уравнениям можно добавить постоянный член, называемый космологической константой, который действует в противоположном направлении, уменьшая кривизну пространства- времени, даже когда остальные семь измерений сильно компактифицированы. 11-мерная супергравитация лишена такой свободы в подгонке исходных уравнений.

Третья проблема в II-мерной супергравитации называется квантовой. Есть надежда, что ее решение может одновременно исключить обе предыдущие проблемы. Исходные теории фундаментальных взаимодействий в программе Калуцы — Клейна основаны на квантовомеханических уравнениях и приводят к появлению бесконечных величин, не имеющих ясной физической интерпретации. Возникновение в теории бесконечно больших величин — общая трудность для всех имеющихся квантовых теорий гравитации. Чтобы обойти эту трудность, при выполнении расчетов приходится прибегать к различного рода упрощениям, пренебрегая теми или иными квантовыми эффектами. При этом предполагают, что со временем можно будет доказать, что возникающие бесконечности связаны не с самой теорией, а с используемыми приближенными методами вычислений, или же надеются на появление когда-нибудь хорошей теории, в которой бесконечные величины

будут вовсе отсутствовать.

В последние несколько месяцев среди теоретиков наблюдается оживление, вызванное перспективой решения проблемы с бесконечными величинами и, возможно, прочих проблем, о которых мы упомянули, с помощью так называемой теории суперструны (см. "Dual-Resonance Models of Elementary Particles", by John H. Schwarz; Scientific American, February, 1975). Теории суперструны обладают рядом преимуществ супергравитацнн. Для математической самосогласованно- сти они должны быть сформулированы в 10-мерном пространстве-време- ни. В 10 измерениях можно построить очень небольшое число теорий. Известно, что в теории суперструны бесконечные величины не появляются, по крайней мере при учете квантовых эффектов в первом приближении. Некоторые физики сейчас полагают, что бесконечнобольшие величины не возникнут и при учете поправок более высоких порядков.

 

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