Monstrous string-string duality

Abstract

We analyze the general class of supersymmetry preserving orbifolds of strong/weak Type IIA/heterotic dual pairs in six dimensions and below. A unified treatment is given by considering compactification to two spacetime dimensions and constructing orbifolds by subgroups of the Fischer-Greiss monster, utilizing the moonshine results of Conway and Norton. Duality requires nontrivial Ramond-Ramond fluxes on the Type IIA side which are localized at the fixed points. Further orbifolding by (−1) F L gives examples of new four dimensional N=2 Type IIA vacua which are not conformal field theory backgrounds.December 1995

Fricke S-duality in CHL models

“…1 Introduction and summary CHL models are orbifolds of heterotic string theory on T 6 preserving N = 4 supersymmetry, or, equivalently, of type II string theory on K3 × T 2 [1][2][3][4]. These models have been a remarkable arena for testing string dualities and analyzing black hole microstates (see [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] for a sample of references).…”

“…All such symmetries g have been classified in [25]. They correspond to elements of O(Γ 4,20 ) that fix a four-dimensional positive definite subspace of Γ 4,20 ⊗ R. With each such symmetry one can associate an element in the Conway group Co 0 , the group of automorphisms of the Leech lattice, that fix a sublattice of rank (at least) four. The conjugacy class of this element is uniquely determined by the condition that it has the same eigenvalues as g in the 24-dimensional representation.…”

“…All such symmetries were classified in [25] and shown to correspond to elements of the Conway group Co 0 . The group G acts by an automorphism g ∈ O(Γ 4,20 ) of order N on the K3-sigma model and by a shift on the circle S 1 .…”

Spontaneous decompactification

“…Flat directions in moduli space have been a long-standing problem in string theory. Recent developments in compactifications with fluxes and branes [4][5][6][7][8][9][10][11][12][13][14] have provided examples of dynamics that fixes these moduli [15,16]. In particular, [16] showed that by adding an anti-D3 brane to the solutions of [15], one can lift the vacuum energy and find locally stable minima with positive cosmological constant.…”

“…However, in this case, we also expect the reverse process to be possible. Moreover, we expect that, if the system can indeed be thought of as a thermal ensemble and the de Sitter entropies as accurate representations of the number of states, the solution that dominates the ensemble 5 A similar description has been advocated for the crunch singularities appearing in transitions towards AdS minima [22].…”