Defines a macroscopic Kähler metric linking geometric thermodynamics to the Fisher matrix and computes exact partition functions on CV manifolds with an extended Souriau framework using Casimir functions.
Tits-Satake projections of homogeneous special geometries
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abstract
We organize the homogeneous special geometries, describing as well the couplings of D=6, 5, 4 and 3 supergravities with 8 supercharges, in a small number of universality classes. This relates manifolds on which similar types of dynamical solutions can exist. The mathematical ingredient is the Tits-Satake projection of real simple Lie algebras, which we extend to all solvable Lie algebras occurring in these homogeneous special geometries. Apart from some exotic cases all the other, 'very special', homogeneous manifolds can be grouped in seven universality classes. The organization of these classes, which capture the essential features of their basic dynamics, commutes with the r- and c-map. Different members are distinguished by different choices of the paint group, a notion discovered in the context of cosmic billiard dynamics of non maximally supersymmetric supergravities. We comment on the usefulness of this organization in universality classes both in relation with cosmic billiard dynamics and with configurations of branes and orbifolds defining special geometry backgrounds.
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hep-th 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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The macroscopic Kaehler metric of Geometric Thermodynamics versus the microscopic one on the Event Manifold: Exact Partition Functions on CV manifolds. Extended Souriau temperatures and spontaneous magnetizations
Defines a macroscopic Kähler metric linking geometric thermodynamics to the Fisher matrix and computes exact partition functions on CV manifolds with an extended Souriau framework using Casimir functions.