Related papers: Horizontality with infinite complexity in the twis…

Using a ``Superstrings with Torsion'' type description, we study a class of IIB orientifolds in which spacefilling O5 planes and D5 branes wrap the T^2 fiber in a warped modification of the product of 4D Minkowski space and a T^2 fibration.…

We review the Reidemeister torsion, Ray-Singer's analytic torsion and the Cheeger-M"uller theorem. We describe the analytic torsion of the de Rham complex twisted by a flux form introduced by the current authors and recall its properties.…

The calculation of entanglement entropy S of quantum fields in spacetimes with horizon shows that, quite generically, S (a) is proportional to the area A of the horizon and (b) is divergent. I argue that this divergence, which arises even…

A hypercomplex structure on a differentiable manifold consists of three integrable almost complex structures that satisfy quaternionic relations. If, in addition, there exists a metric on the manifold which is Hermitian with respect to the…

We define twistorial topological strings by considering tt* geometry of the 4d N=2 supersymmetric theories on the Nekrasov-Shatashvili half-Omega background, which leads to quantization of the associated hyperKahler geometries. We show that…

Let $X=\overline{X}-D$ be a smooth quasi-projective curve. In arXiv:2110.12300 we constructed a Deligne-Hitchin modui space with Hecke gauge groupoid for connections of rank $2$. We extend this construction to the case of any rank $r$,…

We investigate deformations of the Kerr-(A)dS near horizon geometry and derive partial infinitesimal rigidity results for it. The proof comprises two parts. First, we follow the analysis of Jezierski and Kami\'nski [Gen Rel Grav 45 (2013)…

We study growth of holomorphic vector bundles E over smooth affine manifolds. We define Finsler metrics of finite order on E by estimates on the holomorphic bisectional curvature. These estimates are very similar to the ones used by…

Twistors in four dimensions d=4 have provided a convenient description of massless particles with any spin, and this led to remarkable computational techniques in Yang-Mills field theory. Recently it was shown that the same d=4 twistor…

We use ku-cohomology to determine lower bounds for the topological complexity of 2-torsion lens spaces. In the process, we give an almost-complete description of the tensor product of two copies of the ku-homology of infinite mod 2^e lens…

We use twistor theory to identify the harmonic hull of an arbitrary connected open subset U of R^{2m} for m at least 2. It is the natural domain of analytic continuation in C^{2m} for harmonic functions on U.

A hyperkaehler manifold with a circle action fixing just one complex structure admits a natural a hyperholomorphic line bundle. This forms the basis for the construction of a corresponding quaternionic Kaehler manifold in the work of…

For a field theory with a gravitational dual, following Susskind's proposal we define holographic complexity for a subsystem. The holographic complexity is proportional to the volume of a co-dimension one time slice in the bulk geometry…

An orthogonal bundle over a curve has an isotropic Segre invariant determined by the maximal degree of a Lagrangian subbundle. This invariant, and the induced stratifications on moduli spaces of orthogonal bundles, were studied for bundles…

We consider the holographic duality between type-A higher-spin gravity in AdS_4 and the free U(N) vector model. In the bulk, linearized solutions can be translated into twistor functions via the Penrose transform. We propose a holographic…

We define two model structures on the category of bicomplexes concentrated in the right half plane. The first model structure has weak equivalences detected by the totalisation functor. The second model structure's weak equivalences are…

Let (M,g) be a Riemannian 4-manifold. The twistor space Z->M is a CP1-bundle whose total space Z admits a natural metric h. The aim of this article is to study properties of complex structures on (Z,h) which are compatible with the…

On a smooth complex projective variety $X$ of dimension $n$, consider an ample vector bundle $\mathcal{E}$ of rank $r \leq n-2$ and an ample line bundle $H$. A numerical character $m_2=m_2(X,\mathcal{E},H)$ of the triplet…

Bryant and Salamon gave a construction of metrics of G2 holonomy on the total space of the bundle of anti-self-dual (ASD) 2-forms over a 4-dimensional self-dual Einstein manifold. We generalise it by considering the total space of an SO(3)…

We introduce a framework to prove integral rigidity results for the Seiberg-Witten invariants of a closed $4$-manifold $X$ containing a non-separating hypersurface $Y$ satisfying suitable (chain-level) Floer theoretic conditions. As a…