/pdf/handbook-of-magma-functions-5anhrdxxj3.pdf

Handbook of magma functions

The low-energy effective theories describing string compactifications in the presence of fluxes are the so-called gauged supergravities: deformations of the standard Abelian supergravity theories. The deformation parameters can be identified with the various possible (geometric and non-geometric) flux components. In these lecture notes we review the construction of gauged supergravities in a manifestly duality covariant way and illustrate the construction in several examples.

Lectures on gauged supergravity and flux compactifications

Deformations of maximal supergravity theories induced by gauging non-abelian subgroups of the duality group reveal the presence of charged M-theory degrees of freedom that are not necessarily contained in supergravity. The relation with M-theory degrees of freedom is confirmed by the representation assignments under the duality group of the gauge charges and the ensuing vector and tensor gauge fields. The underlying hierarchy of these gauge fields is required for consistency of general gaugings. As an example gauged maximal supergravity in three space-time dimensions is presented in a version where all possible tensor fields appear.

/pdf/gauged-supergravities-tensor-hierarchies-and-m-theory-1x08dsblgv.pdf

Gauged Supergravities, Tensor Hierarchies, and M-Theory

All maximal supergravities in four space-time dimensions are presented. The ungauged Lagrangians can be encoded in an E_7(7)\Sp(56,R)/GL(28) matrix associated with the freedom of performing electric/magnetic duality transformations. The gauging is defined in terms of an embedding tensor which encodes the subgroup of E_7(7) that is realized as a local invariance. This embedding tensor may imply the presence of magnetic charges which require corresponding dual gauge fields. The latter can be incorporated by using a recently proposed formulation that involves tensor gauge fields in the adjoint representation of E_7(7). In this formulation the results take a universal form irrespective of the electric/magnetic duality basis. We present the general class of supersymmetric and gauge invariant Lagrangians and discuss a number of applications.

The maximal D = 4 supergravities

We classify the four-dimensional purely fermionic gauge theories that give a UV completion of composite Higgs models. Our analysis is at the group theoretical level, addressing the necessary (but not sufficient) conditions forthe viability of these models, such as the existence of top partners and custodial symmetry. The minimal cosets arising are those of type SU(5)/SO(5) and SU(4)/Sp(4). We list all the possible "hyper-color" groups allowed and point out the simplest and most promising ones.

/pdf/fermionic-uv-completions-of-composite-higgs-models-z0hdcyqv09.pdf

Fermionic UV completions of Composite Higgs models

Lie : a package for Lie group computations

In this paper, we prove t h a t the Lie group of type E 8 hw a unique conjugacy class of subgroups isomorphic to the finite simple group L(2 61) of linear fractional transformations over t h e field of 6 1 elements. This result settles the last open case of a conjecture made by B. Kostant in 1983 [Iiost] concerning the occurrence of the finite simple group in a complex simple Lie group with Coxeter number h. It also settles a case left open in the classifications of finite simple subgroups of obtained by the first two authors in 1987.

/pdf/the-group-l-2-61-embeds-in-the-lie-group-of-type-e-8-xjiz5i3d1b.pdf

The group L(2,61) embeds in the Lie group of type $E_8$

/pdf/lie-manual-draft-describing-lie-version-2-0-4zqgzo4na4.pdf

LiE manual draft:describing LiE version 2.0

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Lie : a package for Lie group computations

The group L(2,61) embeds in the Lie group of type $E_8$

LiE manual draft:describing LiE version 2.0