Super no-scale models with Pati-Salam gauge group

Three-Generation Super No-Scale Models in Heterotic Superstrings

“…Namely, we wish to investigate the structure of the one-loop potential in more generic setups in which the combined orbifold action shuffles all fixed points in each 2-torus, to precisely remove the extra multiplicities. We will show that the condition n B − n F = 0 considered so far in the string literature [20][21][22][23][25][26][27][28][29][30][31][32][33][34][35], albeit necessary, is not sufficient to guarantee an exponential suppression of the one-loop potential at large radii, but rather needs to be supplemented by additional conditions. Furthermore, we will show that a suitable extension of the construction of [23] to super no-scale models with Pati-Salam gauge symmetry [36] and 3 generations of chiral matter is possible, and we will illustrate the analysis of the extended super no-scale conditions with explicit constructions.…”

“…To this purpose, we investigate a class of heterotic string models with Pati-Salam SU (4) × SU (2) L × SU (2) R gauge symmetry [36,[44][45][46]. Following [21,23] we first employ the FFF to define our models and analyse their spectra (c.f. [47][48][49][50]), and then we map them to orbifold compactifications in order to implement Scherk-Schwarz supersymmetry breaking and study the moduli dependence of the effective potential.…”

“…In the FFF, the class of Pati-Salam models under consideration is defined by a basis set of 13 vectors of boundary conditions for world-sheet fermions 6 , y 1,...,6 , ω 1,...,6 |ȳ 1,...,6 , ω1,...,6 , η1,2,3 , ψ1,...,5 , φ1,...,8 } , [51][52][53][54][55], as vector-like pairs. (vii) The two conditions Σ(H 2 ) = 0, H 2 = 0, 1 as defined in (2.14), that guarantee the exponential suppression of the one-loop contributions to the cosmological constant in the large volume regime, T 2 1, along the lines described in [23].…”

“…On the other hand, there are theories where only the coefficient of the power law term in (1.1) vanishes identically, in which case the one-loop contribution to the effective potential is exponentially suppressed. Such theories where the no-scale properties are effectively extended to the one-loop level were termed "super no-scale" models in recent works [20][21][22][23]. The corresponding condition N = 0 was further interpreted as the requirement n B − n F = 0 of having an equal number of bosonic and fermionic states in the massless spectrum of the theory.…”

“…There, explicit examples were presented where the one-loop contribution is indeed positive, but exponentially suppressed. In recent work [23,24], we extended this program by introducing string constructions that further break the gauge symmetry 1 to the Pati-Salam level, while preserving the super no-scale property n B = n F . In the same work, the universal features of the one-loop potential were investigated and the mismatch in the Bose-Fermi degeneracy of the first massive mode was identified as a parameter controlling the positivity of the one-loop potential.…”