We investigate the existence of string vacua with Massive Spectrum Degeneracy Symmetry (MSDS) in Heterotic and Type II orbifold constructions. We present a classification of all possible Z_2^N-orbifolds with MSDS symmetry that can be constructed in the formalism of the 2d free fermionic construction. We explicitly construct several two-dimensional models whose Reduced Massive Spectrum Degeneracy Symmetry (RMSDS) is due to a set of Z_2-orbifold projections induced naturally in the framework of the free fermionic construction. In all proposed models the massive boson and fermion degrees of freedom exhibit Massive Spectrum Degeneracy Symmetry while the number of massless bosons n(b) and massless fermions n(f) are different; n(b) neq n(f). This property distinguishes the MSDS Z_2-twisted theories from ordinary supersymmetric ones. Some comments are stated concerning the large marginal (J x barJ)-deformations of the proposed models connecting them to higher-dimensional gauged-supergravity theories with non-trivial geometrical fluxes.
We construct a large class of conformal interfaces between two-dimensional c=1 conformal field theories describing compact free bosons and their Z_2 orbifolds. The interfaces are obtained by constructing boundary states in the corresponding c=2 product theories and applying the unfolding procedure. We compute the fusion products for all of these defects, and identify the invertible topological interfaces associated to global symmetries, the interfaces corresponding to marginal deformations, and the interfaces which map the untwisted sector of an orbifold to the invariant states of the parent t…
The elliptic genus of K3 is an index for the 1/4-BPS states of its sigma model. At the torus orbifold point there is an accidental degeneracy of such states. We blow up the orbifold fixed points using conformal perturbation theory, and find that this fully lifts the accidental degeneracy of the 1/4-BPS states with h=1. At a generic point near the Kummer surface the elliptic genus thus measures not just their index, but counts the actual number of these BPS states. We comment on the implication of this for symmetry surfing and Mathieu moonshine.
We present a general class of natural theories in which the Higgs is a pseudo-goldstone boson in an orbifolded gauge theory. The symmetry protecting the Higgs at low energies is an accidental global symmetry of the quadratic action, rather than a full continuous symmetry. The lightest degrees of freedom protecting the weak scale carry no Standard Model (SM) quantum numbers and interact with visible matter principally through the Higgs portal. We find that the twin Higgs is the simplest example of an orbifold Higgs. This opens the door to the systematic study of "neutral naturalness": natural t…
In this paper we study the properties of two-dimensional CFTs defined by cyclic and symmetric orbifolds of free Dirac fermions, especially by focusing on the partition function and entanglement entropy. Via the bosonization, we construct the twist operators which glue two complex planes to calculate the partition function of Z_2 orbifold CFT on a torus. We also find an expression of Z_N cyclic orbifold in terms of Hecke operators, which provides an explicit relation between the partition functions of cyclic orbifolds and those of symmetric ones. We compute the entanglement entropy and Renyi en…
We consider six-dimensional supergravity compactified on orbifolds with Wilson lines and bulk flux. Torus Wilson lines are decomposed into Wilson lines around the orbifold fixed points, and twisted boundary conditions of matter fields are related to fractional localized flux. Both, orbifold singularities and flux lead to chiral fermions in four dimensions. We show that in addition to the standard bulk and fixed point anomalies the Green-Schwarz term also cancels the four-dimensional anomaly induced by the flux background. The two axions contained in the antisymmetric tensor field both contribu…
The problem of families, "Why are there three families of fermions?", is a long awaited question to be answered within a reasonable framework. We propose anti-SU($N$) groups for the unification of families in grand unification (GUT) groups, where the separation of color and weak gauge groups in the GUT is achieved by antisymmetric tensor Brout-Englert-Higgs boson instead of an adjoint representation. Theories of anti-SU($N$)'s are proposed for the unification of families. The minimal model is found as \antiSD \, GUT with the fermion representation [3]+2[2]+8[\bar-1]. We present an example in a…
The presence of Nambu-Goldstone bosons introduce a natural degeneracy inside the vacuum solutions of the non-linear formulations of massive gravity in the same spirit of the $σ$-models. When the gravitational effects are taken into account, and the observers are located at any distance with respect to the source, this degeneracy corresponds to a multiplicity (flow) of the fundamental scales of the theory. The different values of the fundamental scales are connected each other through the broken generators of the theory.
We construct novel fermion-fermion dualities in $2+1$-dimensions using 3d bosonization dualities. This is achieved by relating two-node quiver theories using both the flavor-bounded and flavor-violated 3d bosonization dualities. Such quivers can be viewed as a generalization of the fermionic particle-vortex duality. A special case of these quivers exhibits a $\mathbb{Z}_2$ symmetry under interchange of the two nodes. Using orbifold techniques, we show that such dualities provide a novel way of deriving known 3d bosonization dualities with adjoint matter, thus unifying the non-Abelian bosonizat…
In string compactifications, frequently there appears the anomalous U(1) gauge symmetry which belonged to E8$\times$E8 of the heterotic string. This anomalous U(1) gauge boson obtains mass at the compactification scale, just below $10^{18\,}$GeV, by absorbing one pseudoscalar (corresponding to the model-independent axion) from the second rank anti-symmetric tensor field $B_{MN}$. Below the compactification scale, there results a global symmetry U(1)$_{\rm anom}$ whose charge $Q_{\rm anom}$ is the original gauge U(1) charge. This is the most natural global symmetry, realizing the "invisible" ax…
We study the origin of electroweak symmetry under the assumption that $SU(4)_{\rm C} \times SU(2)_{\rm L} \times SU(2)_{\rm R}$ is realized on a five-dimensional space-time. The Pati-Salam type gauge symmetry is reduced to $SU(3)_{\rm C} \times SU(2)_{\rm L} \times U(1)_{\rm R} \times U(1)_{\rm B-L}$ by orbifold breaking mechanism on the orbifold $S^1/Z_2$. The breakdown of residual gauge symmetries occurs radiatively via the Coleman-Weinberg mechanism, such that the $U(1)_{\rm R} \times U(1)_{\rm B-L}$ symmetry is broken down to $U(1)_{\rm Y}$ by the vacuum expectation value of an $SU(2)_{\rm…
We build rigorously the attractive five-dimensional model where bulk fermions propagate along the $ \mathcal{S}^1 / \mathbb{Z}_2$ orbifold and interact with a Higgs boson localised at a fixed point of the extra dimension. The analytical calculation of the fermion mass spectrum and effective Yukawa couplings is shown to require the introduction of either Essential Boundary Conditions (EBC) imposed by the model definition or certain Bilinear Brane Terms (BBT) in the action, instead of the usual brane-Higgs regularisations. The obtained fermion profiles along the extra dimension turn out to under…
