Related papers: Holomorphic anomaly equations for $\mathbb{C}^5/\m…
We study the full spectrum of spherically symmetric solutions in the five dimensional non-projectable Horava-Lifshitz type gravity theories. For appropriate ranges of the coupling parameters, we have found several classes of solutions which…
We discuss various issues related to the understanding of the conformal anomaly matching in CFT from the dual holographic viewpoint. First, we act with a PBH diffeomorphism on a generic 5D RG flow geometry and show that the corresponding…
We review the holomorphic block factorisation of partition functions of supersymmetric theories on compact manifolds in various dimensions. We then show how to interpret 3d and 5d partition functions as correlation functions with underlying…
Complex supermanifold structures being deformations of the exterior algebra of a holomorphic vector bundle, have been parametrized by orbits of a group on non-abelian cohomology by P. Green. For the case of odd dimension $4$ and $5$ an…
This paper examines the classification of hyperbolic equations. We study a class of equations of the form $$\frac{\partial^2 u}{\partial x\partial y}=F\left(\frac{\partial u}{\partial x},\frac{\partial u}{\partial y},u\right),$$ where…
Spherically symmetric solutions of the SU(5) Einstein-Yang-Mills-Higgs system are constructed using the harmonic map ansatz \cite{IS}. This way the problem reduces to solving a set of ordinary differential equations for the appropriate…
We prove existence of all possible bi-axisymmetric near-horizon geometries of 5-dimensional minimal supergravity. These solutions possess the cross-sectional horizon topology $S^3$, $S^1\times S^2$, or $L(p,q)$ and come with prescribed…
By studying modular invariance properties of some characteristic forms, we prove some new anomaly cancellation formulas which generalize the Han-Zhang and Han-Liu-Zhang anomaly cancellation formulas
We investigate holographic spectral functions for general Sasaki-Einstein 5-manifolds dual to four-dimensional superconformal field theories, including supersymmetric indices, supersymmetric zeta functions, and supersymmetric determinants.…
We prove some isomorphisms between exceptional W-algebras associated with exceptional simple Lie algebras.
Using the representation of the isometries as 2x2 invertible matrices over the division algebra $\H$ of quaternions, we give an algebraic characterization of the dynamical types of the orientation-preserving isometries of the hyperbolic…
In this paper, we classify all the orientable hyperbolic 5-manifolds that arise as a hyperbolic space form $H^5/\Gamma$ where $\Gamma$ is a torsion-free subgroup of minimal index of the congruence two subgroup $\Gamma^5_2$ of the group…
We present a geometrical framework which incorporates higher derivative corrections to the action of N = 2 vector multiplets in terms of an enlarged scalar manifold which includes a complex deformation parameter. This enlarged space carries…
Counterexamples to the Modular Isomorphism Problem were discovered recently. These are non-isomorphic finite $2$-groups $G$ and $H$ that have isomorphic group algebras over the field $\mathbb{Z}/2\mathbb{Z}$ and non-isomorphic group…
We give a formula computing the irregular Hodge numbers for a confluent hypergeometric differential equation.
A new supersymmetric, asymptotically anti-de Sitter, black hole solution of five-dimensional U(1)^3 gauged supergravity is presented. All known examples of such black holes arise as special cases of this solution, which is characterized by…
The Holographic Wess--Zumino (HWZ) consistency conditions are shown through a step by step mapping of renormalization group flows to Hamiltonian systems, to lead to the Holographic anomaly. These conditions codify how the energy scale, when…
In this paper, we establish strong holomorphic Morse inequalities on non-compact manifolds under the condition of optimal fundamental estimates. We show that optimal fundamental estimates are satisfied and then strong holomorphic Morse…
We prove matrix and scalar differential Harnack inequalities for linear parabolic equations on Riemannian and K\"ahler manifolds.
We establish the uniqueness of solutions of the Camassa-Holm equation on a finite interval with non-homogeneous boundary conditions in the case of bounded momentum. A similar result for the higher-order Camassa-Holm system is also given.…