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So-called `non-factorisable' toroidal orbifolds can be rewritten in a factorised form as a product of three two-tori by imposing an additional shift symmetry. This finding of Blaszczyk et al., arXiv:1111.5852, provides a new avenue to Conformal Field Theory methods, by which the vector-like massless matter spectrum - and thereby the type of gauge group enhancement on orientifold invariant fractional D6-branes - and the one-loop corrections to the gauge couplings in Type IIA orientifold theories can be computed in addition to the well-established chiral matter spectrum derived from topological intersection numbers among three-cycles. We demonstrate this framework for the $\mathbb{Z}_4 \times \Omega\mathcal{R}$ orientifolds on the $A_3 \times A_1 \times B_2$-type torus. As observed before for factorisable backgrounds, also here the one-loop correction can drive the gauge groups to stronger coupling as demonstrated by means of a four-generation Pati-Salam example., Comment: 65 pages, 10 figures; v3: matches published version (ref + explanatory remarks added)

We present a geometric approach to D-brane model building on the non-factorisable torus backgrounds of $T^6/\mathbb{Z}_4$, which are $A_3 \times A_3$ and $A_3 \times A_1 \times B_2$. Based on the counting of `short' supersymmetric three-cycles per complex structure {\it vev}, the number of physically inequivalent lattice orientations with respect to the anti-holomorphic involution ${\cal R}$ of the Type IIA/$\Omega\cal{R}$ orientifold can be reduced to three for the $A_3 \times A_3$ lattice and four for the $A_3 \times A_1 \times B_2$ lattice. While four independent three-cycles on $A_3 \times A_3$ cannot accommodate phenomenologically interesting global models with a chiral spectrum, the eight-dimensional space of three-cycles on $A_3 \times A_1 \times B_2$ is rich enough to provide for particle physics models, with several globally consistent two- and four-generation Pati-Salam models presented here. We further show that for fractional {\it sLag} three-cycles, the compact geometry can be rewritten in a $(T^2)^3$ factorised form, paving the way for a generalisation of known CFT methods to determine the vector-like spectrum and to derive the low-energy effective action for open string states., Comment: 50+Appendix, 10 figures; v2: references added

Branes at a $\mathbb{F}_0$ singularity give rise to two different toric quiver gauge theories, which are related by Seiberg duality. We study where in the K\"ahler moduli space each of them is physically realized., Comment: 2 pages, contribution to the proceedings of "The String Theory Universe" workshop in Leuven, 7-11 Sept 2015

We consider discrete gauge symmetries in D dimensions arising as remnants of broken continuous gauge symmetries carried by general antisymmetric tensor fields, rather than by standard 1-forms. The lagrangian for such a general ${\bf Z}_p$ gauge theory can be described in terms of a $r$-form gauge field made massive by a $(r-1)$-form, or other dual realizations, that we also discuss. The theory contains charged topological defects of different dimensionalities, generalizing the familiar charged particles and strings in D=4. We describe realizations in string theory compactifications with torsion cycles, or with background field strength fluxes. We also provide examples of non-abelian discrete groups, for which the group elements are associated with charged objects of different dimensionality., Comment: 16 pages; v2: references added and typos fixed

The study of discrete gauge symmetries in field theory and string theory is often carried out by embedding them into continuous symmetries. Many symmetries however do not seem to admit such embedding, for instance discrete isometries given by large diffeomorphisms in compactifications. We show that in the context of string theory even those symmetries can be embedded into continuous ones. This requires extending the system to a supercritical string theory configuration with extra dimensions, on which the continuous symmetry acts. The extra dimensions are subsequently removed by closed string tachyon condensation, which breaks the continuous symmetry but preserves a discrete subgroup. The construction is explicit and the tachyon condensation can even be followed quantitatively for lightlike tachyon profiles. The embedding of discrete into continuous symmetries allows a realization of charged topological defects as closed string tachyon solitons, in tantalizing reminiscence of the construction of D-branes as open tachyon solitons., Comment: 32 pages + appendices

We consider 4d string compactifications in the presence of fluxes, and classify particles, strings and domain walls arising from wrapped branes which have charges conserved modulo an integer p, and whose annihilation is catalized by fluxes, through the Freed-Witten anomaly or its dual versions. The Z_p-valued strings and particles are associated to Z_p discrete gauge symmetries, which we show are realized as discrete subgroups of 4d U(1) symmetries broken by their Chern-Simons couplings to the background fluxes. We also describe examples where the discrete gauge symmetry group is actually non-Abelian. The Z_p-valued domain walls separate vacua which have different flux quanta, yet are actually equivalent by an integer shift of axion fields (or further string duality symmetries). We argue that certain examples are related by T-duality to the realization of discrete gauge symmetries and Z_p charges from torsion (co)homology. At a formal level, the groups classifying these discrete charges should correspond to a generalization of K-theory in the presence of general fluxes (and including fundamental strings and NS5-branes)., Comment: 30 pages + appendices, 5 figures; v2: Small comments added in sections 2.1 and 4. Version published in JHEP

We study the realization of non-Abelian discrete gauge symmetries in 4d field theory and string theory compactifications. The underlying structure generalizes the Abelian case, and follows from the interplay between gaugings of non-Abelian isometries of the scalar manifold and field identifications making axion-like fields periodic. We present several classes of string constructions realizing non-Abelian discrete gauge symmetries. In particular, compactifications with torsion homology classes, where non-Abelianity arises microscopically from the Hanany-Witten effect, or compactifications with non-Abelian discrete isometry groups, like twisted tori. We finally focus on the more interesting case of magnetized branes in toroidal compactifications and quotients thereof (and their heterotic and intersecting duals), in which the non-Abelian discrete gauge symmetries imply powerful selection rules for Yukawa couplings of charged matter fields. In particular, in MSSM-like models they correspond to discrete flavour symmetries constraining the quark and lepton mass matrices, as we show in specific examples., Comment: 58 pages; minor typos corrected and references added

In particle physics model building discrete symmetries are often invoked to forbid unwanted or dangerous couplings. A classical example is the R-parity of the MSSM, which guarantees the absence of dimension four baryon- and lepton-number violating operators. Although phenomenologically useful, these discrete symmetries are, in the context of field theory, poorly motivated at a more fundamental level. Moreover, discrete {\em global} symmetries are expected to be violated in consistent couplings to quantum gravity, while their {\em gauged} versions are expected to actually exist. In this paper we study discrete gauge symmetries in brane models in string theory, and argue that they are fairly generic in this framework. In particular we study the appearance of discrete gauge symmetries in (MS)SM brane constructions in string theory, and show that a few discrete ${Z_N}$ gauge symmetries, including R-parity and {\it baryon triality}, appear naturally as remnants of continuous U(1) gauge symmetries with St\"uckelberg $N(B\wedge F)$ couplings. Interestingly, they correspond to the simplest anomaly-free discrete symmetries of the MSSM as classified in the early 90's. We provide a number of examples based on type IIA intersecting brane constructions with a (MS)SM spectrum. We also study the appearance of discrete generalizations of R-parity in unified SU(5) type IIA orientifolds and local F-theory SU(5) GUTs., Comment: 46 pages, v2, minor changes, references added