R-charge conservation and more in factorizable and non-factorizable orbifolds

Abstract

We consider the string theory origin of R-charge conservation laws in heterotic orbifold compactifications, deriving the corresponding string coupling selection rule for factorizable and non-factorizable orbifolds, with prime ordered and non-prime ordered point groups. R-charge conservation arises due to symmetries among the worldsheet instantons that can mediate the couplings. Among our results is a previously missed non-trivial contribution to the conserved R-charges from the γ-phases in non-prime orbifolds, which weakens the R-charge selection rule. Symmetries among the worldsheet instantons can also lead to additional selection rules for some couplings. We make a similar analysis for Rule 4 or the "torus lattice selection rule". Moreover, we identify a new string selection rule, that we call Rule 6 or the "coset vector selection rule".

Discrete gauge symmetry and Aharonov-Bohm radiation in string theory

“…In string theories, discrete gauge symmetries have been widely studied from various points of view [22][23][24][25][26][27][28][29][30][31][32][33][34][35]. For example, in [30], BF coupling is derived by dimensionally reducing the Chern-Simons coupling in a flux compactification, and, in [27], by dimensional reduction of the kinetic term of an RR-field in a compactification with discrete torsions.…”

Three-generation asymmetric orbifold models from heterotic string theory

“…In [28], Narain lattices are constructed from 24-dimensional Niemeier lattices [31,32] by the lattice engineering technique 3 [35]. Using this method, 106 types of (22,6)-dimensional Narain lattices with a right-moving non-Abalian factor are constructed. Group breaking patterns due to a Z N shift action are also analyzed by extending the argument of breaking patterns of the E 8 group [36].…”

“…A starting point for the asymmetric orbifold construction is a heterotic string theory compactified on some (22,6)-dimensional Narain lattice. The corresponding world-sheet theory splits into left-moving and right-moving degrees of freedom.…”

“…In our case where we have no twist action for the left-movers, I θ (Γ) is a 22-dimensional left-mover lattice which is spanned by 22 basis vectors α i=1... 22 . We also define the dual lattice of the invariant sublatticeĨ θ (Γ) ≡ 22 i=1 n iαi , where theα i satisfy α i ·α j = δ ij and n i are integers.…”

“…Especially, in the framework of heterotic Z N or Z N × Z M orbifold compactifications [1,2], embedding a supersymmetric standard model or a higher dimensional grand unified theory into heterotic string theory is considered [3][4][5][6][7][8][9][10][11][12][13][14] (also see a review [15]). Since strings on an orbifold can be described by a solvable worldsheet conformal field theory [16,17], it is possible to calculate Yukawa couplings and selection rules [18][19][20][21][22]. Furthermore, the geometrical structure of orbifold fixed points can be an origin of a discrete symmetry [23,24], which may lead to a hierarchical structure of masses/mixings of quarks and leptons.…”