Exploring the landscape of CHL strings on Td

Abstract

Compactifications of the heterotic string on special Td/ℤ2 orbifolds realize a landscape of string models with 16 supercharges and a gauge group on the left-moving sector of reduced rank d + 8. The momenta of untwisted and twisted states span a lattice known as the Mikhailov lattice II(d), which is not self-dual for d > 1. By using computer algorithms which exploit the properties of lattice embeddings, we perform a systematic exploration of the moduli space for d ≤ 2, and give a list of maximally enhanced points where the U(1)d+8 enhances to a rank d + 8 non-Abelian gauge group. For d = 1, these groups are simply-laced and simply-connected, and in fact can be obtained from the Dynkin diagram of E10. For d = 2 there are also symplectic and doubly-connected groups. For the latter we find the precise form of their fundamental groups from embeddings of lattices into the dual of II(2). Our results easily generalize to d > 2.

Compactness of Brane Moduli and the String Lamppost Principle in $d>6$

“…Table 3: List of possible maximally enhanced rank 9 theories in nine dimensions which is obtained by Swampland considerations. The above table match with the Table 3 in [49] which have string theory realizations.…”

Compactness of brane moduli and the String Lamppost Principle in d > 6

“…List of possible maximally enhanced rank 9 theories in nine dimensions which is obtained by Swampland considerations. The above table matches with table 3 in[50] which have string theory realizations.…”

“…By comparing with (3.11), we can see that the O8 (−1) theory in table 1 is naturally interpreted as a worldvolume theory for D4-brane probing the O8 (−1) plane. Table 3 of [50] lists all the patterns of the maximally enhanced gauge groups in the 9-dimensional CHL string vacuum, which matches the ones in table 3.…”

“…Let us compare the above with string compactifications. In string theory, there are four classes of vacua [9,25,[49][50][51][52]. To make the comparison with (3.11) easier to understand, we write each class as follows.…”

Taming the Landscape of Effective Theories

“…labelling the allowed groups G and Γ, are finite. Showing finiteness statements of this type is the aim of much current research [10][11][12][13][14][15][16][17][18][19][20][21][22].…”