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تسجيل مستخدم جديدDoubled Aspects of Vaisman Algebroid and Gauge Symmetry in Double Field Theory
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The metric algebroid proposed by Vaisman (the Vaisman algebroid) governs the gauge symmetry algebra generated by the C-bracket in double field theory (DFT). We show that the Vaisman algebroid is obtained by an analogue of the Drinfeld double of Lie algebroids. Based on a geometric realization of doubled space-time as a para-Hermitian manifold, we examine exterior algebras and a para-Dolbeault cohomology on DFT and discuss the structure of the Drinfeld double behind the DFT gauge symmetry. Similar to the Courant algebroid in the generalized geometry, Lagrangian subbundles $(L,tilde{L})$ in a para-Hermitian manifold play Dirac-like structures in the Vaisman algebroid. We find that an algebraic origin of the strong constraint in DFT is traced back to the compatibility condition needed for $(L,tilde{L})$ be a Lie bialgebroid. The analysis provides a foundation toward the coquecigrue problem for the gauge symmetry in DFT.
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