Related papers: Timelike Hopf Duality and Type IIA^* String Soluti…
In this paper we study the scalar geometries occurring in the dimensional reduction of minimal five-dimensional supergravity to three Euclidean dimensions, and find that these depend on whether one first reduces over space or over time. In…
Following a recent suggestion by Randall and Sundrum, we consider string compactification scenarios in which a compact slice of AdS-space arises as a subspace of the compactification manifold. A specific example is provided by the type II…
The heterotic string compactified on an (n-1)-dimensional elliptically fibered Calabi-Yau Z-->B is conjectured to be dual to F-theory compactified on an n-dimensional Calabi-Yau X-->B, fibered over the same base with elliptic K3 fibers. In…
We suggest that compactifications on Anti-de-Sitter (AdS) spaces of type IIA, IIB, heterotic strings and eleven dimensional vacuua of M-theory are related by a combination of $T$ and strong/weak dualities. Maldacena conjecture relates then…
We study in detail the moduli space of solutions discovered in LLM relaxing the constraint that guarantees the absence of singularities. The solutions fall into three classes, non-singular, null-singular and time machines with a time-like…
We study Hopf algebras via tools from geometric invariant theory. We show that all the invariants we get can be constructed using the integrals of the Hopf algebra and its dual together with the multiplication and the comultiplication, and…
In general, universal (co)measuring (co)monoids and universal (co)acting bi/Hopf monoids, which prove to be a useful tool in the classification of quantum symmetries, do not always exist. In order to ensure their existence, the support of a…
We construct a family of supersymmetric solutions in Type IIB supergravity of the form ${\rm WAdS}_3\times {\rm WS}^3\times T^4$, where ${\rm WAdS}_3$ and ${\rm WS^3}$ denote a warped anti-de Sitter spacetime and a warped 3-sphere,…
We introduce a natural generalization of the definition of a symmetric Hopf algebroid, internal to any symmetric monoidal category with coequalizers that commute with the monoidal product. Motivation for this is the study of Heisenberg…
We present a new supersymmetric AdS_6 solution of type IIB supergravity with SU(2) isometry. Through the AdS/CFT correspondence, this has potentially very interesting implications for 5d fixed point theories. This solution is the result of…
We consider non-Abelian T-duality on N=1 supergravity backgrounds possessing well understood field theory duals. For the case of D3-branes at the tip of the conifold, we dualise along an SU(2) isometry. The result is a type-IIA geometry…
We construct infinite new classes of supersymmetric solutions of D=11 supergravity that are warped products of AdS_3 with an eight-dimensional manifold M_8 and have non-vanishing four-form flux. In order to be compact, M_8 is constructed as…
Finite-dimensional Hopf algebras admit a correspondence between so-called pairs in involution, one-dimensional anti-Yetter--Drinfeld modules and algebra isomorphisms between the Drinfeld and anti-Drinfeld double. We extend it to general…
The study of the pentagon (fusion) equation leds to the Structure and the Classification theorem for finite dimenasional Hopf algebras: there exists a one to one correspondence between the set of types of n-dimensional Hopf algebtras and…
We establish a map between AdS$_3 \times$S$^2$ and AdS$_7$ solutions to massive IIA supergravity that allows one to interpret the former as holographic duals to D2-D4 defects inside 6d (1,0) CFTs. This relation singles out in a particular…
We consider linear delay differential equations at the verge of Hopf instability, i.e. a pair of roots of the characteristic equation are on the imaginary axis of the complex plane and all other roots have negative real parts. When…
New local solutions in type II supergravity that are foliations of AdS$_3\times S^3\times S^3$ over an interval and preserve at least large $\mathcal{N}=(4,0)$ supersymmetry are found. Some cases have compact internal space, some not and…
The general method of Reshetikhin and Turaev is followed to develop topological invariants of closed, connected, orientable 3-manifolds from a new class of algebras called pseudo-modular Hopf algebras. Pseudo-modular Hopf algebras are a…
We review recent developments in the study of the AdS/CFT correspondence in lower dimensions. We start summarising the classification of AdS$_3\times$S$^2$ solutions in massive Type IIA supergravity with (0,4) supersymmetries, and the…
We discuss the different discrete duality symmetries in six dimensions that act within and between (i) the 10-dimensional heterotic string compactified on $T^4$, (ii) the 10-dimensional Type IIA string compactified on $K3$ and (iii) the…