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Register a new userGeneralised Scherk-Schwarz reductions from gauged supergravity
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Authors
Gianluca Inverso
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A procedure is described to construct generalised Scherk-Schwarz uplifts of gauged supergravities. The internal manifold, fluxes, and consistent truncation Ansatz are all derived from the embedding tensor of the lower-dimensional theory. We first describe the procedure to construct generalised Leibniz parallelisable spaces where the vector components of the frame are embedded in the adjoint representation of the gauge group, as specified by the embedding tensor. This allows us to recover the generalised Scherk-Schwarz reductions known in the literature and to prove a no-go result for the uplift of $omega$-deformed SO(p,q) gauged maximal supergravities. We then extend the construction to arbitrary generalised Leibniz parallelisable spaces, which turn out to be torus fibrations over manifolds in the class above.
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We demonstrate the relation between the Scherk-Schwarz mechanism and flipped gauged brane-bulk supergravities in five dimensions. We discuss the form of supersymmetry violating Scherk-Schwarz terms in pure supergravity and in supergravity coupled to matter. We point out that brane-induced supersymmetry breakdown in 5d Horava-Witten model is not of the Scherk-Schwarz type. We discuss in detail flipped super-bigravity, which is the locally supersymmetric extension of the (++) bigravity.
We demonstrate the relation between the Scherk-Schwarz mechanism and flipped gauged brane-bulk supergravities in five dimensions. We discuss the form of supersymmetry violating Scherk-Schwarz terms in pure supergravity and in supergravity coupled to matter. Although the Lagrangian mass terms that arise as the result of the Scherk-Schwarz redefinition of fields are naturally of the order of the inverse radius of the orbifold, the effective 4d physical mass terms are rather set by the scale sqrt{|bar{Lambda}|}, where bar{Lambda} is the 4d cosmlogical constant.
We study the effect of Scherk-Schwarz deformations on intersecting branes. Non-chiral fermions in any representation of the Chan-Paton gauge group generically acquire a tree-level mass dependent on the compactification radius and the brane wrapping numbers. This offers an elegant solution to one of the long-standing problems in intersecting-brane-world models where the ubiquitous presence of massless non-chiral fermions is a clear embarrassment for any attempt to describe the Standard Model of Particle Physics.
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We obtain Yang-Mills $SU(2)times G$ gauged supergravity in three dimensions from $SU(2)$ group manifold reduction of (1,0) six dimensional supergravity coupled to an anti-symmetric tensor multiplet and gauge vector multiplets in the adjoint of $G$. The reduced theory is consistently truncated to $N=4$ 3D supergravity coupled to $4(1+textrm{dim}, G)$ bosonic and $4(1+textrm{dim}, G)$ fermionic propagating degrees of freedom. This is in contrast to the reduction in which there are also massive vector fields. The scalar manifold is $mathbf{R}times frac{SO(3,, textrm{dim}, G)}{SO(3)times SO(textrm{dim}, G)}$, and there is a $SU(2)times G$ gauge group. We then construct $N=4$ Chern-Simons $(SO(3)ltimes mathbf{R}^3)times (Gltimes mathbf{R}^{textrm{dim}G})$ three dimensional gauged supergravity with scalar manifold $frac{SO(4,,1+textrm{dim}G)}{SO(4)times SO(1+textrm{dim}G)}$ and explicitly show that this theory is on-shell equivalent to the Yang-Mills $SO(3)times G$ gauged supergravity theory obtained from the $SU(2)$ reduction, after integrating out the scalars and gauge fields corresponding to the translational symmetries $mathbf{R}^3times mathbf{R}^{textrm{dim}, G}$.
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