Related papers: Mathieu moonshine in four dimensional $\mathcal{N}…
There is a `Mathieu moonshine' relating the elliptic genus of K3 to the sporadic group M_{24}. Here, we give evidence that this moonshine extends to part of the web of dualities connecting heterotic strings compactified on K3 \times T^2 to…
We construct super vertex operator algebras which lead to modules for moonshine relations connecting the four smaller sporadic simple Mathieu groups with distinguished mock modular forms. Starting with an orbifold of a free fermion theory,…
Generalised moonshine is reviewed from the point of view of holomorphic orbifolds, putting special emphasis on the role of the third cohomology group H^3(G, U(1)) in characterising consistent constructions. These ideas are then applied to…
We revisit our earlier work which lead to a periodic table of Borcherds-Kac-Moody algebras that appeared in the context of the refined generating function of quarter-BPS (dyons) in $\mathcal{N}=4$ supersymmetric four-dimensional string…
The simplest string theory compactifications to 3D with 16 supercharges -- the heterotic string on $T^7$, and type II strings on $K3 \times T^3$ -- are related by U-duality, and share a moduli space of vacua parametrized by $O(8,24;…
We study the relation between the instanton expansion of the Seiberg-Witten prepotential for $D=4$, ${\cal N}=2$ $SU(2)$ SUSY gauge theory for $N_f=0$ and $1$ and the monstrous moonshine. By utilizing a newly developed simple method to…
We show using string dualities that Mathieu moonshine controls Gromov-Witten invariants and periods of the holomorphic 3-form $\Omega$ for certain $CY_3$ manifolds. We also discuss how the period vectors appear in flux compactifications on…
We study aspects of Calabi-Yau four-folds as compactification manifolds of F-theory, using mirror symmetry of toric hypersurfaces. Correlation functions of the topological field theory are determined directly in terms of a natural ring…
We continue the study of a relationship between the instanton expansion of the Seiberg-Witten (SW) prepotential of $D = 4$, ${\cal N }= 2$ $SU(2)$ SUSY gauge theory and the monstrous moonshine. Extending the previous results, we show for…
We consider the ${\cal N}=4$ Liouville theory by varying the linear dilaton coupling constant $\cal{Q}$. It is known that at two different values of coupling constant ${\cal Q}=\sqrt{{2\over N}},-(N-1)\sqrt{{2\over N}}$ system exhibits two…
M-theory on ${\mathbf{S}}^1\vee{\mathbf{S}}^1$ has recently been proposed to yield, via quotients, ten-dimensional non-supersymmetric string theories. We revisit the construction that leads to the heterotic theories, finding a consistent…
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…
The classical theory of monstrous moonshine describes the unexpected connection between the representation theory of the monster group $M$, the largest of the simple sporadic groups, and certain modular functions, called Hauptmodln. In…
An arithmetic framework to string compactification is described. The approach is exemplified by formulating a strategy that allows to construct geometric compactifications from exactly solvable theories at $c=3$. It is shown that the…
We consider compactifications of the matrix model of M-theory on $S^1/Z_2\times T^d$ for $d>0$, and interpret them as orbifolds of the supersymmetric U(N) Yang-Mills theory on $R\times T^{d+1}$. The orbifold group acts both on the gauge…
Extending recent work of Kachru and Silverstein, we consider ``orbifolds'' of 4-dimensional $\mathcal{N}=4$ SU(n) super-Yang-Mills theories with respect to discrete subgroups of the SU(4) $R$-symmetry which act nontrivially on the gauge…
In this talk I summarize several recent results concerning the four-dimensional effective supergravity obtained using a Calabi-Yau compactification of the $E_8\times E_8$ heterotic string from M-theory. A simple macroscopic study is…
The Mathieu twisted twining genera, i.e. the analogues of Norton's generalised Moonshine functions, are constructed for the elliptic genus of K3. It is shown that they satisfy the expected consistency conditions, and that their behaviour…
We construct heterotic string theories on spacetimes of the form R^{d-1,1} times N=2 linear dilaton, where d=6,4,2,0. There are two lines of supersymmetric theories descending from the two supersymmetric ten-dimensional heterotic theories.…
We propose a moonshine for the sporadic Mathieu group M_12 that relates its conjugacy classes to various modular forms and Borcherds Kac-Moody Lie superalgebras.