| 1. |
- Gaberdiel, Matthias R., et al.
(författare)
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Borcherds algebras and N=4 topological amplitudes
- 2011
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Ingår i: Journal of High Energy Physics. - 1029-8479 .- 1126-6708. ; 2011:6, s. 125-
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Tidskriftsartikel (refereegranskat)abstract
- The perturbative spectrum of BPS-states in the E(8)xE(8) heterotic string theory compactified on T(2) is analysed. We show that the space of BPS-states forms a representation of a certain Borcherds algebra G which we construct explicitly using an auxiliary conformal field theory. The denominator formula of an extension G(ext) superset of G of this algebra is then found to appear in a certain heterotic one-loop N = 4 topological string amplitude. Our construction thus gives an N = 4 realisation of the idea envisioned by Harvey and Moore, namely that the 'algebra of BPS-states' controls the threshold corrections in the heterotic string.
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| 2. |
- Gaberdiel, Matthias R., et al.
(författare)
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Generalized Mathieu Moonshine
- 2013
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Ingår i: Communications in Number Theory and Physics. - 1931-4531 .- 1931-4523. ; 7:1, s. 145-223
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Tidskriftsartikel (refereegranskat)abstract
- The Mathieu twisted twining genera, i.e., the analogues of Norton's generalized Moonshine functions, are constructed for the elliptic genus of K3. It is shown that they satisfy the expected consistency conditions, and that their behaviour under modular transformations is controlled by a 3-cocycle in H-3(M-24, U(1)), just as for the case of holomorphic orbifolds. This suggests that a holomorphic VOA may be underlying Mathieu Moonshine.
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| 3. |
- Persson, Daniel, 1978, et al.
(författare)
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Generalised Moonshine and Holomorphic Orbifolds
- 2015
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Ingår i: Proceedings of Symposia in Pure Mathematics - Conference on String-Math 2012. - Providence, Rhode Island : American Mathematical Society. - 2324-707X. - 9780821894958 ; 90, s. 73-86
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Konferensbidrag (refereegranskat)abstract
- 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 the case of Mathieu moonshine, i.e. the recently discovered connection between the largest Mathieu group M_24 and the elliptic genus of K3. In particular, we find a complete list of twisted twining genera whose modular properties are controlled by a class in H^3(M_24, U(1)), as expected from general orbifold considerations.
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