2017/10/31 by Pietro Fré, Fré, Pietro, Pietro Antonio Grassi +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.1710.11498
openalex publication_date 2017/10/31 · openalex created_date 2017/11/10 · openalex updated_date 2026/07/28
We consider super Yang-Mills theory on supermanifolds M(D|m) using integral forms. The latter are used to define a geometric theory of integration and are essential for a consistent action principle. The construction relies on Picture Changing Operators \mathbbY(0|m), analogous to those introduced in String Theory, that admit the geometric interpretation of Poincaré duals of closed submanifolds of superspace S(D|0) ⊂ M(D|m) having maximal bosonic dimension D. We discuss the case of Super-Yang-Mills theory in D=10 with N=1 supersymmetry and we show how to retrieve its pure-spinor formulation from the rheonomic lagrangian Lrheo of D'Auria, Fré and Da Silva, choosing a suitable \mathbbY(0|m)ps. From the same lagrangian Lrheo, with another choice \mathbbY(0|m)comp of the PCO, one retrieves the component form of the SYM action. Equivalence of the formulations is ensured when the corresponding PCO.s are cohomologous, which is true, in this case, of \mathbbY(0|m)ps and \mathbbY(0|m)comp.