TY - JOUR
T1 - Geometry and symmetries of Hermitian-Einstein and instanton connection moduli spaces
AU - Papadopoulos, Georgios
N1 - Publisher Copyright:
© 2025 The Author(s)
PY - 2025/7
Y1 - 2025/7
N2 - We investigate the geometry of the moduli spaces MHE⁎(M2n) of Hermitian-Einstein irreducible connections on a vector bundle E over a Kähler with torsion (KT) manifold M2n that admits holomorphic ∇ˆ-covariantly constant vector fields, where ∇ˆ is the connection with skew-symmetric torsion H. We demonstrate that such vector fields induce an action on MHE⁎(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 Dˆ on MHE⁎(M2n). We demonstrate that in the presence of such vector fields, the geometry of MHE⁎(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 Masd⁎(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 Masd⁎(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.
AB - We investigate the geometry of the moduli spaces MHE⁎(M2n) of Hermitian-Einstein irreducible connections on a vector bundle E over a Kähler with torsion (KT) manifold M2n that admits holomorphic ∇ˆ-covariantly constant vector fields, where ∇ˆ is the connection with skew-symmetric torsion H. We demonstrate that such vector fields induce an action on MHE⁎(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 Dˆ on MHE⁎(M2n). We demonstrate that in the presence of such vector fields, the geometry of MHE⁎(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 Masd⁎(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 Masd⁎(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.
KW - AdS/CFT
KW - Conformal field theory
KW - Hermitian-Einstein and instanton connections
KW - Moduli spaces
KW - Sigma models
KW - Symmetries
UR - http://www.scopus.com/inward/record.url?scp=105002146318&partnerID=8YFLogxK
U2 - 10.1016/j.geomphys.2025.105474
DO - 10.1016/j.geomphys.2025.105474
M3 - Article
AN - SCOPUS:105002146318
SN - 0393-0440
VL - 213
JO - JOURNAL OF GEOMETRY AND PHYSICS
JF - JOURNAL OF GEOMETRY AND PHYSICS
M1 - 105474
ER -