Exceptional field theory

In physics, exceptional field theory is a reformulation or an extension of eleven-dimensional supergravity in which exceptional Lie group symmetries are manifest. Exceptional group symmetries such as E_n(n) are manifestations of U-duality in the context of M-theory.

Background

In 1979, Eugène Cremmer and Bernard Julia found that E₇₍₇₎ symmetries are present upon toroidal compactification of 11-dimensional supergravity to 4 dimensions.^[1] In 1985, Bernard de Wit and Hermann Nicolai reformulated eleven-dimensional supergravity in a way that has manifest gauge invariance under SU(8), a subgroup of E₇₍₇₎.^[2] The theory was extended in 2013 by Henning Samtleben and Olaf Hohm to have E₆₍₆₎, E₇₍₇₎, and E₈₍₈₎ symmetries, calling such theories under the term, exceptional field theory.^[3][4][5][6] Early attempts to make duality symmetries manifest in supergravity involved the development of generalized geometry by Coimbra, Strickland-Constable, and Waldram.^[7][8]

Exceptional field theory has been applied to construct consistent Kaluza-Klein truncations of supergravity using generalized Scherk-Schwarz ansätze, an important step for ensuring that solutions of the lower-dimensional theory are solutions of the higher-dimensional theory. In particular, it was utilized to derive explicit non-linear reduction formulas showing that type IIB supergravity on AdS₅×S⁵ admits a consistent truncation to five-dimensional maximal SO(6) gauged supergravity, confirming a previously conjectured result.^[9]

Exceptional field theory has also been used to study the Kaluza-Klein mass spectrum of fluctuations around compactification backgrounds in supergravity. These techniques can be applied for computations of the mass spectrum and interactions of Kaluza-Klein modes for both maximally supersymmetric and less symmetric, or non-supersymmetric backgrounds.^[10]

See also

• T-duality
• Double field theory