2025/01/16 by G. Papadopoulos, Papadopoulos, Georgios · 3 citations
Mathematics · Physics and Astronomy · #Geometry and complex manifolds #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2501.09474
We investigate the geometry of the moduli spaces \mathscrM\HE^*(M2n) of Hermitian-Einstein irreducible connections on a vector bundle E over a Kähler with torsion (KT) manifold M2n that admits holomorphic and \h∇-covariantly constant vector fields, where \h∇ is the connection with skew-symmetric torsion H. We demonstrate that such vector fields induce an action on \mathscrM\HE^*(M2n) that leaves both the metric and complex structure invariant. Moreover, if an additional condition is satisfied, the induced vector fields are covariantly constant with respect to the connection with skew-symmetric torsion \h D on \mathscrM\HE^*(M2n). We demonstrate that in the presence of such vector fields, the geometry of \mathscrM\HE^*(M2n) can be modelled on that of holomorphic toric principal bundles with base space KT manifolds and give some examples. We also extend our analysis to the moduli spaces \mathscrM\asd^*(M4) of instanton connections on vector bundles over KT, bi-KT (generalised Kähler) and hyper-Kähler with torsion (HKT) manifolds M4. We find that the geometry of \mathscrM\asd^*(S3× S1) can be modelled on that of principal bundles with fibre S3× S1 over Quaternionic Kähler manifolds with torsion (QKT). In addition motivated by applications to AdS/CFT, we explore the (superconformal) symmetry algebras of two-dimensional sigma models with target spaces such moduli spaces.