Related papers: Borcherds-Kac-Moody Symmetry of N=4 Dyons

We study N=4 supersymmetric Yang-Mills theory on a Kaehler manifold with $b_2^+ \geq 3$. Adding suitable perturbations we show that the partition function of the N=4 theory is the sum of contributions from two branches: (i) instantons, (ii)…

We construct a Borcherds Kac-Moody (BKM) superalgebra on which the Conway group Co$_0$ acts faithfully. We show that the BKM algebra is generated by the BRST-closed states in a chiral superstring theory. We use this construction to produce…

We derive a family of matrix models which encode solutions to the Seiberg-Witten theory in 4 and 5 dimensions. Partition functions of these matrix models are equal to the corresponding Nekrasov partition functions, and their spectral curves…

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…

We investigate special compactifications of the heterotic string for which the space of half-BPS states is, in a natural way, a representation of various subgroups of the Conway group. These compactifications provide a useful framework for…

We discuss an orbifold of the toroidally compactified heterotic string which gives a global reduction of the dimension of the moduli space while preserving the supersymmetry. This construction yields the moduli space of the first of a…

We classify all groups G and all pairs (V,W) of absolutely simple Yetter-Drinfeld modules over G such that the support of the direct sum of V and W generates G, the square of the braiding between V and W is not the identity, and the Nichols…

We present a variant of the Theory of Lorentzian (i. e. with a hyperbolic generalized Cartan matrix) Kac-Moody algebras recently developed by V. A. Gritsenko and the author. It is closely related with and strongly uses results of R.…

We study new compactifications of the SO(32) heterotic string theory on compact complex non-Kahler manifolds. These manifolds have many interesting features like fewer moduli, torsional constraints, vanishing Euler character and vanishing…

Following the suggestion of hep-th/0506249 and hep-th/0612011, we represent quarter BPS dyons in N=4 supersymmetric string theories as string network configuration and explore the role of genus two surfaces in determining the spectrum of…

We analyse the classical moduli spaces of supersymmetric vacua of 3d N=2 Chern-Simons quiver gauge theories. We show quite generally that the moduli space of the 3d theory always contains a baryonic branch of a parent 4d N=1 quiver gauge…

We classify orbifold geometries which can be interpreted as moduli spaces of four-dimensional $\mathcal{N}\geq 3$ superconformal field theories up to rank 2 (complex dimension 6). The large majority of the geometries we find correspond to…

We define a new class of completions of locally symmetric varieties of type IV which interpolates between the Baily-Borel compactification and Mumford's toric compactifications. An arithmetic arrangement in a locally symmetric variety of…

We compute the genus-two chiral partition function of the left-moving heterotic string for a $\mathbb{Z}_2$ CHL orbifold. The required twisted determinants can be evaluated explicitly in terms of the untwisted determinants and theta…

The explicit solvability of quantum superintegrable systems is due to symmetry, but the symmetry is often "hidden". The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under commutation to define quadratic…

Infinite-dimensional Lie superalgebras, particularly Borcherds-Kac-Moody (BKM) superalgebras, play a fundamental role in mathematical physics, number theory, and representation theory. In this paper, we study the root multiplicities of BKM…

We use freely acting asymmetric orbifolds of type IIB string theory to construct a class of theories in five dimensions with eight supercharges whose moduli spaces for vector multiplets and hypermultiplets can be determined exactly. We…

In this thesis, we explore two approaches to string phenomenology. In the first half of the work, we investigate M-theory compactifications on spaces with co-dimension four, orbifold singularities. We construct M-theory on C^2/Z_N by…

We study the Weyl groups of hyperbolic Kac-Moody algebras of `over-extended' type and ranks 3, 4, 6 and 10, which are intimately linked with the four normed division algebras K=R,C,H,O, respectively. A crucial role is played by integral…

We study the Borcherds superalgebra obtained by adding an odd (fermionic) null root to the set of simple roots of a simple finite-dimensional Lie algebra. We compare it to the Kac-Moody algebra obtained by replacing the odd null root by an…