ABSTRACT
I review some recent work on consistent reductions of gravity and supergravity theories. An important distinction is made between reductions on a group manifold('De-Witt reductions') for which reduction is unproblematic, and reductions on a coset space ('Pauli reductions'), which are in general inconsistent. It is emphasised that only special conspiracies between the gravity and matter sectors allow consistent Pauli reductions.In some cases, one may obtain a Pauli reduction by taking a Kaluza style https://www.w3.org/1998/Math/MathML"> U ( 1 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq526.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> quotient of a De-Witt reduction. Of special interest are models derived from string theory. That based on the bosonic string allows consistent reduction on https://www.w3.org/1998/Math/MathML"> S 3 ≡ SO ( 4 ) / SO ( 3 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq527.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> in all dimensions. A truly remarkable example of a consistent reduction is the six-dimensional supergravity model of Salam and Sezgin. This allows a supersymmetric monopole reduction on https://www.w3.org/1998/Math/MathML"> S 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq528.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> to give a supersymmetric coupling of gravity, https://www.w3.org/1998/Math/MathML"> SU ( 2 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq529.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Yang-Mills and an axion and a dilaton in four dimensions with a flat supersymmetric Minkowski vacuum. Subject to the assumption of maximal spacetime symmetry, the ground state is unique. The model may be obtained by a consistent reduction from ten-dimensional supergravity on the non-compact riemannian hyperboloid https://www.w3.org/1998/Math/MathML"> H 2 , 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq530.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> followed by a Kaluza reduction and chiral truncation.
