“…The resulting group is an extension of the superPoincare group with infinitely many generators which carry internal and space-time indices. It is a closed algebra since all Jacobi identities are satisfied and it has therefore explicit matrix representations. …”
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“…The isomorphism between current algebra representations gives rise to a number of chiral character identities, reminiscent of the recently-discovered MSDS symmetry.…”
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“…The classification pattern is based on the algebra homomorphisms relating the Bianchi group and the duality group SO(3). …”
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“…We consider four supergravities with 16+16, 32+32, 64+64, 128+128 degrees of freedom displaying some curious properties: (1) They exhibit minimal supersymmetry (N=1, 2, 2, 1) but maximal rank (r=7, 6, 4, 0) of the scalar coset in D=4, 5, 7, 11. (2) They couple naturally to supermembranes and admit these membranes as solutions. (3) Although the D=4, 5, 7 supergravities follow from truncating the maximally supersymmetric ones, there nevertheless exist M-theory compactifications with G2, SU(3), SU(2) holonomy having these supergravities as their massless sectors. (4) They reduce to N=1, 2, 4, 8 theories all with maximum rank 7 in D=4 which (5) correspond to 0, 1, 3, 7 lines of the Fano plane and hence admit a division algebra (R,C,H,O) interpretation consistent with the black-hole/qubit correspondence, (6) are generalized self-mirror and hence (7) have vanishing on-shell trace anomaly.…”
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“…Moreover, those models defined by the Supergravity algebra so(3,1)^2 also contain Minkowski/de Sitter minima that are totally stable. …”
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“…Special geometry allows us to recast these equations in algebraic form, and we find an infinite class of new N=0 and N=1 AdS_4 solutions, displaying a rich pattern of non-trivial charges associated with NSNS and RR fluxes. …”
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“…Within this method we are able to derive algebraic expressions for the generalised GSO projections for all sectors that appear in the models. …”
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“…Thus this construction provides exact solutions of the modified Bianchi identity. By solving algebraically these CFTs we compute the exact tree-level heterotic string spectrum and describe worldsheet non-perturbative effects. …”
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“…The field vector sum control is considered for multiple cavities driven by one klystron. An algebraic, complex domain model is proposed for the system analysis. …”
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“…To this end we exploit the mathematical framework of integral Jordan algebras and Freudenthal triple systems. The charge vector of the dyonic black string in D=6 is SO(5,5;Z) related to a two-charge reduced canonical form uniquely specified by a set of two arithmetic U-duality invariants. …”
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