Related papers: Wall Crossing, Discrete Attractor Flow and Borcher…
We address a number of puzzles relating to the proposed formulae for the degeneracies of dyons in orbifold compactifications of the heterotic string to four dimensions with $N =4$ supersymmetry. The partition function for these dyons is…
The theory of Poisson-Lie groups and Lie bialgebras plays a major role in the study of one dimensional integrable systems; many families of integrable systems can be recovered from a Lax pair which is constructed from a Lie bialgebra…
This paper studies connections between the preprojective representations of a valued quiver, the (+)-admissible sequences of vertices, and the Weyl group by associating to each preprojective representation a canonical (+)-admissible…
We study the BPS spectrum of four-dimensional $\mathcal{N}=2$ superconformal field theory of Argyres-Douglas type, obtained via twisted compactification of six-dimensional $A_{N-1}$ $(2,0)$ theory on a sphere with an irregular puncture, by…
We study the topological dynamics of the action of the diagonal subgroup on quotients Gamma\PSL(2,R)*PSL(2,R), where Gamma is an irreducible lattice. Closed orbits are described and a set of points of dense orbit is explicitly given. Such…
In this work, we derive a set of boost-weighted $w$ functionals of the metric, with $w\in\{2,1,0,-1,-2\}$, which transform semi-covariantly under the action of the near-horizon symmetry group. In particular, we demonstrate that the…
Global aspects of Scherk-Schwarz dimensional reduction are discussed and it is shown that it can usually be viewed as arising from a compactification on the compact space obtained by identifying a (possibly non-compact) group manifold G…
In this article we investigate the gauge invariance and duality properties of DFT based on a metric algebroid formulation given previously in [1]. The derivation of the general action given in this paper does not employ the section…
The present article is the first in a series whose ultimate goal is to prove the Kotschick-Morgan conjecture concerning the wall-crossing formula for the Donaldson invariants of a four-manifold with b^+ = 1. The conjecture asserts that the…
We introduce the notion of Wall-Crossing Structure and discuss it in several examples including complex integrable systems, Donaldson-Thomas invariants and Mirror Symmetry. For a big class of non-compact Calabi-Yau 3-folds we construct…
The degeneracies of supersymmetric quarter BPS dyons in four dimensions and of spinning black holes in five dimensions in a CHL compactification are computed exactly using Borcherds lift. The Hodge anomaly in the construction has a physical…
We investigate the AdS/CFT correspondence for higher-derivative gravity systems, and develop a formalism in which the generating functional of the boundary field theory is given as a functional that depends only on the boundary values of…
We present the third in the series of papers describing Poisson properties of planar directed networks in the disk or in the annulus. In this paper we concentrate on special networks N_{u,v} in the disk that correspond to the choice of a…
We find the exact spectrum of a class of quarter BPS dyons in a generic N=4 supersymmetric Z_N orbifold of type IIA string theory on K3\times T^2 or T^6. We also find the asymptotic expansion of the statistical entropy to first non-leading…
A recently discovered relation between 4D and 5D black holes is used to derive weighted BPS black hole degeneracies for 4D N=4 string theory from the well-known 5D degeneracies. They are found to be given by the Fourier coefficients of the…
Lie algebra involutions and their fixed-point subalgebras give rise to symmetric spaces and real forms of complex Lie algebras, and are well-studied in the context of symmetrizable Kac-Moody algebras. In this paper we study a…
The periodic system of chemical elements is represented within the framework of the weight diagram of the Lie algebra of the fourth rank of the rotation group of an eight-dimensional pseudo-Euclidean space. The hydrogen realization of the…
By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on…
One of the main properties of modulus on graphs is Fulkerson duality. In this paper, we study Fulkerson duality for spanning tree modulus. We introduce a new notion of Beurling partition, and we identify two important ones, which correspond…
This dissertation answers some of the questions raised in Borcherds' papers on Moonshine and Lorentzian reflection groups. We prove (assuming an open conjecture of Burger, Li and Sarnak) that a Lorentzian reflection group with Weyl vector…