# Higher dimensional supergravity d.o.f

From where do the antisymmetric tensor d.o.f. arises from superpoincare group in 10 and 11 dimensional ${\cal N}=1$ SUGRAs? I mean, beyond the d.o.f. matching. Why it need's to be antisymmetric?

• Do you have an alternative model to CJS with perfect d.o.f. matching and in a rep of the Poincare? – Cosmas Zachos May 7 '18 at 22:03
• Can you recast your question in the language of this? Are you asking how it was discovered, or why nothing else has been, since? – Cosmas Zachos May 7 '18 at 22:10
• I am asking how can be constructed the gravity supermultiplet, a little related in how it was discovered. Why 'nothing else', is outside my interest. – Iliado Odiseo May 8 '18 at 14:36
• Try learning how other, simpler supermultiplets are constructed. You start with the highest spin state and descend by successive applications if busy generators. That's why (Pascal's triangle) the multiplicities matter. Given the multiplicities, it is child's play to accommodate them into Lorentz tensors and spinors. You then confirm your busy transformations (with blood, sweat and tears, to be sure) and you are done, unless you fail, which is why the "nothing else" matters. Most good reviews and books on sugra do this, and a question here is asking for an impossible summary tutorial. – Cosmas Zachos May 8 '18 at 14:51
• I am not familiar with the plethora of books and reviews that have populated the market in the intervening 40 years... But some of them surely illustrate the hit-or-miss sudoku-like procedure: review first how the N=8, D=4 theory was put together, and the rest should come easily. – Cosmas Zachos May 8 '18 at 16:11