Geometry and symmetries of Hermitian-Einstein and instanton connection moduli spaces
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866909554837553152 |
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| author | Papadopoulos, Georgios |
| author_facet | Papadopoulos, Georgios |
| contents | We investigate the geometry of the moduli spaces $\mathscr{M}_{\HE}^*(M^{2n})$ of Hermitian-Einstein irreducible connections on a vector bundle $E$ over a Kähler with torsion (KT) manifold $M^{2n}$ that admits holomorphic and $\h\nabla$-covariantly constant vector fields, where $\h\nabla$ is the connection with skew-symmetric torsion $H$. We demonstrate that such vector fields induce an action on $\mathscr{M}_{\HE}^*(M^{2n})$ 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 $\h{\mathcal{ D}}$ on $\mathscr{M}_{\HE}^*(M^{2n})$. We demonstrate that in the presence of such vector fields, the geometry of $\mathscr{M}_{\HE}^*(M^{2n})$ 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 $\mathscr{M}_{\asd}^*(M^{4})$ of instanton connections on vector bundles over KT, bi-KT (generalised Kähler) and hyper-Kähler with torsion (HKT) manifolds $M^4$. We find that the geometry of $\mathscr{M}_{\asd}^*(S^3\times S^1)$ can be modelled on that of principal bundles with fibre $S^3\times S^1$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09474 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometry and symmetries of Hermitian-Einstein and instanton connection moduli spaces Papadopoulos, Georgios High Energy Physics - Theory Differential Geometry We investigate the geometry of the moduli spaces $\mathscr{M}_{\HE}^*(M^{2n})$ of Hermitian-Einstein irreducible connections on a vector bundle $E$ over a Kähler with torsion (KT) manifold $M^{2n}$ that admits holomorphic and $\h\nabla$-covariantly constant vector fields, where $\h\nabla$ is the connection with skew-symmetric torsion $H$. We demonstrate that such vector fields induce an action on $\mathscr{M}_{\HE}^*(M^{2n})$ 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 $\h{\mathcal{ D}}$ on $\mathscr{M}_{\HE}^*(M^{2n})$. We demonstrate that in the presence of such vector fields, the geometry of $\mathscr{M}_{\HE}^*(M^{2n})$ 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 $\mathscr{M}_{\asd}^*(M^{4})$ of instanton connections on vector bundles over KT, bi-KT (generalised Kähler) and hyper-Kähler with torsion (HKT) manifolds $M^4$. We find that the geometry of $\mathscr{M}_{\asd}^*(S^3\times S^1)$ can be modelled on that of principal bundles with fibre $S^3\times S^1$ 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. |
| title | Geometry and symmetries of Hermitian-Einstein and instanton connection moduli spaces |
| topic | High Energy Physics - Theory Differential Geometry |
| url | https://arxiv.org/abs/2501.09474 |