On Susy Standard-like models from orbifolds of D=6 Gepner orientifolds

TL;DR

This work develops a framework to realize SUSY Standard-like vacua from Type IIB orientifolds built on Gepner-model internal spaces at $c_{int}=6$, extended by a torus $T^2$ and orbifolded by ${\mathbb Z}_N$. It constructs explicit B-type boundary and crosscap states in six dimensions, computes open/closed amplitudes, and derives tadpole cancellation conditions; the construction is then carried to four dimensions via a simultaneous Gepner$\times T^2$ orbifold, producing ${\cal N}=1$ chiral spectra. An explicit 3-generation Left-Right symmetric model is shown to descend toward a MSSM-like theory, and a detailed $Z_4$-orbifold MSSM example illustrates the method's viability, including RR tadpole consistency and Yukawa-coupling constraints by fusion rules. The approach highlights a controlled RCFT pathway to 4D chiral SUSY models with potential phenomenological benefits, such as large extra dimensions that could lower the string scale, while outlining avenues for further exploration of boundary-state ensembles and Yukawa structure.

Abstract

As a further elaboration of the proposal of Ref. [1] we address the construction of Standard-like models from configurations of stacks of orientifold planes and D-branes on an internal space with the structure ${(Gepner model)^{c=6} \times T^2}/Z_N$. As a first step, the construction of D=6 Type II B orientifolds on Gepner points, in the diagonal invariant case and for both, odd and even, affine levels is discussed. We build up the explicit expressions for B-type boundary states and crosscaps and obtain the amplitudes among them. From such amplitudes we read the corresponding spectra and the tadpole cancellation equations. Further compactification on a T^2 torus, by simultaneously orbifolding the Gepner and the torus internal sectors, is performed. The embedding of the orbifold action in the brane sector breaks the original gauge groups and leads to N=1 supersymmetric chiral spectra. Whenever even orbifold action on the torus is considered, new branes, with worldvolume transverse to torus coordinates, must be included. The detailed rules for obtaining the D=4 model spectra and tadpole equations are shown. As an illustration we present a 3 generations Left-Right symmetric model that can be further broken to a MSSM model.

Figures (2)

• Figure 1: LR symmetric model obtained by orbifolding $6^2 2$$D=6$ model. Original ${\bf L_{10}},{\bf L_{6}}$ boundary states do split, under the action of the modding, into ${\bf L^a_{10}},{\bf L^d_{10}}$ and ${\bf L^b_{6}},{\bf L^c_{6}}$ branes, giving rise to LR spectrum at the intersection.
• Figure 2: By separating ${\bf L^{c+c*}_{6}}\rightarrow {\bf L^c_{6}}+{\bf L^{c*}_{6}}$ away from the orientifold point breaking from LR to MSSM with 3 righthanded neutrini is achieved