# Borcherds-Kac-Moody Symmetry of N=4 Dyons

@article{Cheng2008BorcherdsKacMoodySO, title={Borcherds-Kac-Moody Symmetry of N=4 Dyons}, author={Miranda C N Cheng and Atish Dabholkar}, journal={Communications in Number Theory and Physics}, year={2008}, volume={3}, pages={59-110} }

We consider compactifications of heterotic string theory to four dimensions on CHL (Chaudhuri-Hockney-Lykken) orbifolds of the type T /ZN with N = 4 supersymmetry. The exact partition functions of the quarter-BPS (Bogomol’nyi-Prasad-Sommerfeld) dyons in these models are given in terms of genus-two Siegel modular forms. Only the N = 1, 2, 3 models satisfy a certain finiteness condition, and in these cases one can identify a Borcherds–Kac–Moody superalgebra underlying the symmetry structure of…

## 56 Citations

### BKM superalgebras from counting dyons in N=4 supersymmetric type II compactifications

- Mathematics
- 2012

### BKM Lie superalgebras from counting twisted CHL dyons

- MathematicsNuclear Physics B
- 2019

Following Sen, we study the counting of (‘twisted’) BPS states that contribute to twisted helicity trace indices in four-dimensional CHL models with $ \mathcal{N} = 4 $ supersymmetry. The generating…

### No more walls! A tale of modularity, symmetry, and wall crossing for 1/4 BPS dyons

- Mathematics
- 2017

A bstractWe determine the generating functions of 1/4 BPS dyons in a class of 4d N$$ \mathcal{N} $$ = 4 string vacua arising as CHL orbifolds of K3 × T2, a classification of which has been recently…

### N ov 2 01 0 HRI / ST / 1012 BKM Lie superalgebra for the Z 5-orbifolded CHL string

- Mathematics
- 2010

We study the Z5-orbifolding of the CHL string theory by explicitly constructing the modular form Φ̃2 generating the degeneracies of the 1 4 BPS states in the theory. Since the additive seed for the…

### K3 Surfaces, N=4 Dyons, and the Mathieu Group M24

- Mathematics
- 2010

A close relationship between K3 surfaces and the Mathieu groups has been established in the last century. Furthermore, it has been observed recently that the elliptic genus of K3 has a natural…

### $\widehat{sl(2)}$ decomposition of denominator formulae of some BKM Lie superalgebras -- II

- Mathematics
- 2022

The square-root of Siegel modular forms of CHL Z N orbifolds of type II compactiﬁcations are denominator formulae for some Borcherds-Kac-Moody Lie superalgebras for N = 1 , 2 , 3 , 4. We study the…

### Automorphic products, generalized Kac-Moody algebras and string amplitudes

- Mathematics
- 2012

We review automorphic products and generalized Kac-Moody algebras from a physics point of view. We discuss the appearance of automorphic products in BPS-saturated one-loop quantities in heterotic…

### K3 string theory, lattices and moonshine

- MathematicsResearch in the Mathematical Sciences
- 2018

In this paper, we address the following two closely related questions. First, we complete the classification of finite symmetry groups of type IIA string theory on $$K3 \times {\mathbb {R}}^6$$K3×R6,…

### UvA-DARE (Digital Academic Repository) K3 string theory, lattices and moonshine

- Mathematics
- 2018

In this paper, we address the following two closely related questions. First, we complete the classiﬁcation of ﬁnite symmetry groups of type IIA string theory on K 3 × R 6 , where Niemeier lattices…

## References

SHOWING 1-10 OF 56 REFERENCES

### Wall crossing, discrete attractor flow and Borcherds algebra

- Physics
- 2008

The appearance of a generalized (or Borcherds-) Kac-Moody algebra in the spectrum of BPS dyons in N=4, d=4 string theory is elucidated. From the low-energy supergravity analysis, we identify its root…

### Comments on the spectrum of CHL dyons

- Mathematics
- 2008

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 = 4 supersymmetry. The…

### Moduli space of Chaudhuri-Hockney-Lykken strings.

- MathematicsPhysical review. D, Particles and fields
- 1995

An orbifold of the toroidally compactified heterotic string is discussed which gives a global reduction of the dimension of the moduli space while preserving the supersymmetry, and the set of allowed gauge groups is invariant under electric-magnetic duality, providing further evidence for the {ital D}=4 heteroticString duality.

### Partition functions of torsion >1 dyons in heterotic string theory on T 6

- Mathematics
- 2008

The original proposal of Dijkgraaf, Verlinde and Verlinde for the quarter BPS dyon partition function in heterotic string theory on T 6 is known to correctly produce the degeneracy of dyons of…

### Generalities of quarter BPS dyon partition function and dyons of torsion two

- Mathematics
- 2008

We propose a general set of constraints on the partition function of quarter BPS dyons in any N=4 supersymmetric string theory by drawing insight from known examples, and study the consequences of…

### Spectrum of dyons and black holes in CHL orbifolds using Borcherds lift

- Physics
- 2007

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…

### Counting all dyons in $ \mathcal{N} = 4 $ string theory

- Physics
- 2008

For dyons in heterotic string theory compactified on a six-torus, with electric charge vector Q and magnetic charge vector P, the positive integer I ≡ gcd(Q ∧ P) is an invariant of the U-duality…

### Spacelike Singularities and Hidden Symmetries of Gravity

- MathematicsLiving reviews in relativity
- 2008

It is shown that in this limit the gravitational theory can be reformulated in terms of billiard motion in a region of hyperbolic space, revealing that the dynamics is completely determined by a (possibly infinite) sequence of reflections, which are elements of a Lorentzian Coxeter group.