Exactly solvable string compactifications on manifolds of SU(N) holonomy

A variety of heterotic string compactifications on the K3 surface, manifolds of SU(3) holomony, and higher holomony manifolds, are solved exactly. An example of the quintic hypersurface in CP₄ is worked out in detail. It is conjectured, and demonstrated in part, that any supersymmetric compactification of the heterotic string with an N=2 superconformal theory is equivalent to a compactification on a manifold of SU(N) holonomy, and in particular an arbitrary gluing of the discrete models with c=9 gives a solvable heterotic string compactification on some Calabi-Yau manifold. Calabi-Yau compactifications are seen to be exact vacua of string theory, retaining their topological and geometrical characteristics. Previously unknown enhanced gauge symmetries are found to arise for certain backgrounds.     

How chiral are type-II superstrings?

We study the type-II superstrings in four dimensions by studying vacua where massless chiral multiplets transform as complex representations of the non-abelian gauge group. We show that the gauge group can only be SU(3) and that such fields transform as 3 of SU(3). However, attempts to obtain the theory with N=1 supergravity fail. It turns out that the “different” constructions via asymmetric orbifolds give the same massless spectrum with necessarily N=2 supergravity.     

The criterion for vacuum stability in Kaluza-Klein supergravity

We prove that in the spectrum of the d = 4 theory obtained by Freund-Rubin compactification of d = 11 superconductivity, only fields of spin 0⁺ can give rise to classical instabilities. The criterion for stability in the 0⁺ sector can be expressed as a certain lower bound on the Lichnerowicz operator Δ_L on the d = 7 compact space. Thus not only are supersymmetric vacua always stable but so are the corresponding non-supersymmetric vacua obtained by reversing the orientation of the compact space, since the 0⁺ spectrum is insensitive to the orientation. Examples are the orientation-reversed spaces with N = 0 obtained from the squashed seven-sphere with N = 1 and from SU(3) ×SU(2) ×U(1) spaces with N = 2 supersymmetry. Product spaces, on the other hand, are always unstable. Finally, we examine the massless sectors of the squashed seven-sphere vacua, and find an additional 135 massless scalars.     

D-brane SM-like and scalar dark matter in type IIA superstring theory

In light of the present LHC Run II at √s = 13 TeV, a SM-like string model is studied. Specifically, a singlet S scalar-extended SM given in terms of four stacks of intersecting D6-branes in a type IIA superstring compactification producing a large gauge symmetry is examined. The scales involved are dealt with. According to the dark matter relic density, the mass of the scalar dark matter beyond the SM m _S ? 10³ GeV and the corresponding Higgs portal couplings λ _SH ? 10^–8 have been obtained.     

Compactification of d = 11 supergravity on S4 (or 11 = 7 + 4, too)

Eleven-dimensional supergravity can compactify spontaneously on either S⁷ or S⁴. We study the latter case, with attention to its connection with a possible gauged N = 4 supergravity in d = 7. We derive the linearized field equations and supersymmetry transformation rules for the effective d = 7 supergravity multiplet. There are five third rank antisymmetric tensors in this multiplet which are in the 5 representation of the gauge group USp(4) and they are propagated with a self-duality condition in 7 dimensions. There is also a 14 of scalar fields and they are found to propagate with a non-conformal wave operator.     

Heterotic strings on homogeneous spaces

We construct heterotic string backgrounds corresponding to families of homogeneous spaces as exact conformal field theories. They contain left cosets of compact groups by their maximal tori supported by NS‐NS 2‐forms and gauge field fluxes. We give the general formalism and modular‐invariant partition functions, then we consider some examples such as SU (2)/U (1) ~ S² (already described in a previous paper) and the SU (3)/U(1)² flag space. As an application we construct new supersymmetric string vacua with magnetic fluxes and a linear dilaton.     

A minimal gauge inflation model

In this paper, we present a gauge inflation model based on the orbifold M_4×S~1/Z_2 with non-Abelian SU(2) gauge symmetry, which is probably the simplest model in this category. As the inflaton potential is fully radiatively generated exclusively by gauge self-interactions, the model is predictive; thus, it is protected by gauge symmetry itself, without the introduction of any additional matter fields or arbitrary interactions. We show that the model fully agrees with the recent cosmological observations within the controlled perturbative regime of gauge interactions, g4≤1/(2πRMP), with the compactification radius(10 ≤ RMP ≤ 100): the expected magnitude of the curvature perturbation power spectrum and the value of the corresponding spectral index are in perfect agreement with the recent observations. The model also predicts a large fraction of the gravitational waves, negligible nonGaussianity, and a sufficiently high reheating temperature.     

On the fermion spectrum of spontaneously generated fuzzy extra dimensions with fluxes

We consider certain vacua of four‐dimensional SU(N) gauge theory with the same field content as the 𝒩 = 4 supersymmetric Yang‐Mills theory, resulting from potentials which break the 𝒩 = 4 supersymmetry as well as its global SO(6) symmetry down to SO(3) × SO(3). We show that the theory behaves at intermediate scales as Yang‐Mills theory on M⁴ × S_L² × S_R², where the extra dimensions are fuzzy spheres with magnetic fluxes. We determine in particular the structure of the zero modes due to the fluxes, which leads to low‐energy mirror models.     

Quantum phase transitions in cascading gauge theory

We study N=1 supersymmetric SU(K+P)×SU(K) cascading gauge theory of Klebanov et al. (2000) [1] and [2] on R×S³ at zero temperature, and at the origin of the baryonic branch. A radius of S³ sets a compactification scale μ. An interplay between μ and the strong coupling scale Λ of the theory leads to an interesting pattern of quantum phases of the system. For μ?μχSB=1.240467(8)Λ the vacuum state of the theory is chirally symmetric. At μ=μχSB the theory undergoes the first-order transition to a phase with spontaneous breaking of the chiral symmetry. We further demonstrate that the chirally symmetric state of cascading gauge theory becomes perturbatively unstable at scales below μc=0.950634(5)μχSB. Finally, we point out that for μ<1.486402(5)Λ the stress-energy tensor of cascading gauge theory can source inflation of a closed Universe.     

Phenomenology ofSO(10) unified superstring models with intermediate scaleSU R(2) breaking

Electroweak breaking and the supersymmetric particle spectrum are discussed in superstring theories where the gauge group after compactification isSO(10)×E _s ^′ , and where the gauge symmetry after flux breaking isSU(3)×SU(2)×SU(2)×U(1).     

The parallelizing S7 torsion in gauged N=8 supergravity

Using the parallelizing S⁷ torsion as an ansatz we investigate two solutions of gauged N=8 supergravity with SO(7) invariance. Supersymmetry is uniformly broken. We calculate the masses for these solutions which are both unstable. Certain apparent discrepancies with the results obtained by spontaneous compactification of d=11 supergravity are discussed. We establish that the compactification on the parallelized S⁷ has an SO(7) invariance and clarify the issue of supersymmetry breaking. The lack of stability in d=4 indicates that this d=11 solution is unstable.     

Gauge coupling renormalisation with several U(1) factors

We examine the renormalisation of gauge coupling constants in theories with a G × U(1)^N gauge group (which appears to be the gauge symmetry of many possible superstring vacua). In general, the abelian gauge bosons mix among themselves, so a correct renormalisation requires including this mixing in the evolution of the gauge couplings. We present general results and note that the mixing is scale independent to all orders if the renormalization group trajectory passes through a unification point. We discuss the cases of one loop and two loops explicitly. An example, based on a possible superstring-inspired model, is given.     

A six-dimensional gauge-Higgs unification model based on E6 gauge symmetry

We construct a six-dimensional gauge-Higgs unification model with the enlarged gauge group of E₆ on S²/Z₂$S^2/Z_2$ orbifold compactification. The standard model particle contents and gauge symmetry are obtained by utilizing a monopole background field and imposing appropriate parity conditions on the orbifold. In particular, a realistic Higgs potential suitable for breaking the electroweak gauge symmetry is obtained without introducing extra matter or assuming an additional symmetry relation between the SU(2) isometry transformation on the S²$S^2$ and the gauge symmetry. The Higgs boson is a KK mode associated with the extra-dimensional components of gauge field. We also compute the KK masses of all fields at tree level.     

Orbifold compactifications with three families of Su(3) ×Su(2) ×U(1)n

We construct several N = 1 supersymmetric three-generation models with SU(3)×SU(2)×U(1)ⁿ gauge symmetry, obtained from orbifold compactification of the heterotic string in the presence of constant gauge-background fields. This Wilson-line mechanism also allows us to eliminate extra colour triplets which could mediate fast proton decay.     

Infinite-parameter symmetries and the Higgs effect in gravity-coupled sigma models in D+4 dimensions

We compute the mass spectra of small fluctuations of four-dimensional fields for Kaluza-Klein models in which the compactification from D+4 to 4 (flat) dimensions is induced by the scalar fields of a nonlinear sigma model defined on an S^N or CP^N manifold. The compactifications are stable for all values of N. The fact that the spectra contain no massless vector fields is traced to the absence of a local gauge invariance for the sigma-model action. We introduce a complete basis for the infinite-parameter symmetries that arise from the harmonic analysis of the higher-dimensional dynamical invariances. The spectrum of spin-one and spin-two fields is consistent with the Higgs effect associated with the breaking of the local symmetries corresponding to these generators. The commutation relations of the infinite parameter algebra for the case of CP¹ are also given. The algebra includes the spectrum-generating algebra SO(1,3) of Salam and Strathdee.     

Anomaly-free supergravity theories remain anomaly-free after dimensional reduction

We show that the anomaly after compactification of a supergravity theory coupled to Yang-Mills matter is usually given by an integral of the original anomaly over the compact space, as long as there are no isometries for the compact space. This means that a supergravity theory, whose anomaly vanishes identically (i.e., without the addition of local counter terms to the action), will remain anomaly-free after compactification to any lower dimension, subject to some restrictions on self-dual antisymmetric tensors. We next consider the case where the original anomaly cancels by the Green-Schwarz mechanism. In this case, again subject to the restrictions on self-dual antisymmetric tensors, the anomaly will still cancel after compactification to any lower dimension D > 2, provided that: (1) There are no U(1) gauge groups after compactification. (2) There exists a three-form field strength H such that dH = (TrR₀² + kTrF₀²), or that the compact space is chosen such that (TrR₀² + kTrF₀²) = 0.     

Non-supersymmetric vacua and the D-flatness condition

Some N = 1 gauge theories, including SQED and N_F = 1 SQCD, have the property that, for arbitrary superpotentials, all stationary points of the potential V = F + D are D-flat. For others, stationary points of V are complex gauge transformations of D-flat configurations. As an implication, the technique to parametrize the moduli space of supersymmetric vacua in terms of a set of basic holomorphic G invariants can be extended to non-supersymmetric vacua. A similar situation is found in non-gauge theories with a compact global symmetry group.     

Yang-Mills theories in space-like axial and planar gauges

The quantization of Yang-Mills theories according to a canonical procedure is studied first in the axial gauge A₃^a ≡ 0. We show that the perturbative S-matrix cannot be expressed in terms of well-defined distributions in a Hilbert space involving only physical states without conflicting with unitarity. We then resort to the space-like planar gauge and show that it is possible to define a perturbative S-matrix at the price of introducing a set of free ghost fields. The S-matrix is unitary in the subspace of the physically acceptable states on which A₃^a vanish.     

Universal extra dimensions on real projective plane

We propose a six-dimensional Universal Extra Dimensions (UED) model compactified on a real projective plane RP²${\mathit{RP}}^2$, a two-sphere with its antipodal points being identified. We utilize the Randjbar-Daemi–Salam–Strathdee spontaneous sphere compactification with a monopole configuration of an extra UX₍₁₎$U{(1)}_X$ gauge field that leads to a spontaneous radius stabilization. Unlike the sphere and the S²/Z₂$S^2/Z_2$ orbifold compactifications, the massless UX₍₁₎$U{(1)}_X$ gauge boson is safely projected out. We show how a compactification on a non-orientable manifold results in a chiral four-dimensional gauge theory by utilizing 6D chiral gauge and Yukawa interactions. The resultant Kaluza–Klein mass spectra are distinct from the ordinary UED models compactified on torus. We briefly comment on the anomaly cancellation and also on a possible dark matter candidate in our model.