Bose-Fermi Degeneracy Research Articles

Super no-scale models with Pati-Salam gauge group

We construct and classify heterotic models where N=1 supersymmetry is spontaneously broken à la Scherk-Schwarz. The theories contain chiral matter transforming under an observable Pati-Salam gauge symmetry and are classified according to a minimal set of phenomenological requirements, including the shape of their one-loop effective potential. The latter is essentially controlled by two parameters that are easily computable in terms of the defining string data. By imposing Bose-Fermi degeneracy at the massless level, known as the super no-scale condition, it is possible to suppress the value of the effective potential to exponentially small values, provided the compactification scale is sufficiently lower than the string scale. Furthermore, we compare the space of ∼1010 Pati-Salam models with their parent theories based on SO(10) gauge symmetry and confirm the universality structure of their effective one-loop potentials.

Global anomalies on the Hilbert space

We show that certain global anomalies can be detected in an elementary fashion by analyzing the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory. Distinct anomalous behaviours imprinted in the Hilbert space are identified with the distinct cohomology “layers” that appear in the classification of anomalies in terms of cobordism groups. We illustrate the manifestation of the layers in the Hilbert for a variety of anomalous symmetries and spacetime dimensions, including time-reversal symmetry, and both in systems of fermions and in anomalous topological quantum field theories (TQFTs) in 2 + 1d. We argue that anomalies can imply an exact bose-fermi degeneracy in the Hilbert space, thus revealing a supersymmetric spectrum of states; we provide a sharp characterization of when this phenomenon occurs and give nontrivial examples in various dimensions, including in strongly coupled QFTs. Unraveling the anomalies of TQFTs leads us to develop the construction of the Hilbert spaces, the action of operators and the modular data in spin TQFTs, material that can be read on its own.

On the stability of open-string orbifold models with broken supersymmetry

We consider an open-string realisation of N=2→N=0 spontaneous breaking of supersymmetry in four-dimensional Minkowski spacetime. It is based on type IIB orientifold theory compactified on T2×T4/Z2, with Scherk–Schwarz supersymmetry breaking implemented along T2. We show that in the regions of moduli space where the supersymmetry breaking scale is lower than the other scales, there exist configurations with minima that have massless Bose-Fermi degeneracy and hence vanishing one-loop effective potential, up to exponentially suppressed corrections. These backgrounds describe non-Abelian gauge theories, with all open-string moduli and blowing up modes of T4/Z2 stabilized, while all untwisted closed-string moduli remain flat directions. Other backgrounds with strictly positive effective potentials exist, where the only instabilities arising at one loop are associated with the supersymmetry breaking scale, which runs away. All of these backgrounds are consistent non-perturbatively.

Exponential suppression of the cosmological constant in nonsupersymmetric string vacua at two loops and beyond

Two independent criteria are presented that together guarantee exponential suppression of the two-loop cosmological constant in non-supersymmetric heterotic strings. They are derived by performing calculations in both the full string theory and in its underlying effective field theory, and come respectively from contributions that involve only physical untwisted states, and contributions that include orbifold twisted states. The criteria depend purely on the spectrum and charges, so a model that satisfies them will do so with no fine-tuning. An additional consistency condition (emerging from the so-called separating degeneration limit of the two-loop diagram) is that the one-loop cosmological constant must also be suppressed, by Bose-Fermi degeneracy in the massless spectrum. We remark that theories of this kind, that have continued exponential suppression to higher orders, can form the basis for a string implementation of the "naturalness without supersymmetry" idea.

A dynamical mechanism for large volumes with consistent couplings

A mechanism for addressing the 'decompactification problem' is proposed, which consists of balancing the vacuum energy in Scherk-Schwarzed theories against contributions coming from non- perturbative physics. Universality of threshold corrections ensures that, in such situations, the stable minimum will have consistent gauge couplings for any gauge group that shares the same N = 2 beta function for the bulk excitations as the gauge group that takes part in the minimisation. Scherk- Schwarz compactification from 6D to 4D in heterotic strings is discussed explicitly, together with two alternative possibilities for the non-perturbative physics, namely metastable SQCD vacua and a single gaugino condensate. In the former case, it is shown that modular symmetries gives various consistency checks, and allow one to follow soft-terms, playing a similar role to R-symmetry in global SQCD. The latter case is particularly attractive when there is nett Bose-Fermi degeneracy in the massless sector. In such cases, because the original Casimir energy is generated entirely by excited and/or non-physical string modes, it is completely immune to the non-perturbative IR physics. The large separation between UV and IR contributions to the potential greatly simplifies the analysis of stabilisation, and is a general possibility that has not been considered before.

Quasirealistic heterotic-string models with vanishing one-loop cosmological constant and perturbatively broken supersymmetry?

Quasirealistic string models in the free fermionic formulation typically contain an anomalous $U(1)$, which gives rise to a Fayet-Iliopoulos $D$-term that breaks supersymmetry at the one-loop level in string perturbation theory. Supersymmetry is traditionally restored by imposing $F$ and $D$ flatness on the vacuum. By employing the standard analysis of flat directions, we present a quasirealistic three-generation string model in which stringent $F$- and $D$-flat solutions do not appear to exist to all orders in the superpotential. We speculate that this result is indicative of the nonexistence of supersymmetric flat $F$ and $D$ solutions in this model. We provide some arguments in support of this scenario and discuss its potential implications. Bose-Fermi degeneracy of the string spectrum implies that the one-loop partition function, and hence the one-loop cosmological constant, vanishes in the model. If our assertion is correct, this model may represent the first known example with vanishing cosmological constant and perturbatively broken supersymmetry. We discuss the distinctive properties of the internal free fermion boundary conditions that may correspond to a large set of models that share these properties. The geometrical moduli in this class of models are fixed due to asymmetric boundary conditions, whereas absence of supersymmetric flat directions would imply that the supersymmetric moduli are fixed as well and the dilaton may be fixed by hidden sector nonperturbative effects.

Brane-Inspired Orientifold Field Theories

In this paper we consider the gauge theory living on the world-volume of a stack of N D3-branes of type 0B/Ω'I6(−1)FL and of its orbifolds C2/2 and C3/(2 × 2). The gauge theories obtained in the three cases are a brane realization of ``orientifold field theories'' having the bosonic sector common with = 4,2,1 super Yang-Mills respectively. In these non-supersymmetric theories, we investigate the possibility of keeping the gauge/gravity correspondence that has revealed itself so successful in the case of supersymmetric theories. In the open string framework we compute the coefficient of the gauge kinetic term showing that the perturbative behaviour of the orientifold field theory can be obtained from the closed string channel in the large N limit, where the theory exhibits Bose-Fermi degeneracy.

Gauge fields and fermions in tachyon effective field theories

In this paper we incorporate gauge fields into the tachyon field theory models for unstable D-branes in bosonic and in Type II string theories. The chosen couplings yield massless gauge fields and an infinite set of equally spaced massive gauge fields on codimension one branes. A lack of a continuum spectrum is taken as evidence that the stable tachyon vacuum does not support conventional gauge excitations. For the bosonic string model we find two possible solvable couplings, one closely related to Born-Infeld forms and the other allowing a detailed comparison to the open string modes on bosonic D-branes. We also show how to include fermions in the type II model. They localize correctly on stable codimension one branes resulting in bose-fermi degeneracy at the massless level. Finally, we establish the solvability of a large class of models that include kinetic terms with more than two derivatives.

Non-BPS branes on a Calabi-Yau threefold and Bose-Fermi degeneracy

We consider the spectrum of open strings for non-BPS D-brane configuration in type II string theory on a Calabi-Yau threefold. In general, there is no degeneracy between bosonic and fermionic states. However we find special values for the moduli space of Calabi-Yau threefolds there are non-BPS brane configurations which have an exact degeneracy between bosonic and fermionic states. For these values there is no force between pairs of non-BPS D-branes. This gives rise to a possibility of building diverse non-supersymmetric gauge field theories on the brane world-volume. We use the approach recently elaborated by Gaberdiel and Sen.

Bose-Fermi degeneracy and duality in non-supersymmetric strings

Following Kachru, Kumar and Silverstein, we construct a set of non-supersymmetric Type II string models which have equal numbers of bosons and fermions at each mass level. The models are asymmetric Z 2⊗ Z 2′ orbifolds. We demonstrate that this Bose-Fermi degeneracy feature implies that both the one-loop and the two-loop contributions to the cosmological constant vanish. We conjecture that the cosmological constant actually vanishes to all loops. We construct a strongweak dual pair of models, both of which have Bose-Fermi degeneracy. This implies that at least some of the non-perturbative corrections to the cosmological constant are absent.

Semi-local cosmic strings and the cosmological constant problem

We study the cosmological constant problem in a three-dimensional N = 2 supergravity theory with gauge group SU(2) global × U(1) local. The model we consider is known to admit string-like configurations, the so-called semi-local cosmic strings. We show that the stability of these solitonic solutions is provided by supersymmetry through the existence of a lower bound for the energy, even though the manifold of the Higgs vacuum does not contain non-contractible loops. Charged Killing spinors do exist over configurations that saturate the Bogomol'nyi bound, as a consequence of an Aharonov-Bohmlike effect. Nevertheless, there are no physical fermionic zero modes on these backgrounds. The exact vanishing of the cosmological constant does not imply, then, Bose-Fermi degeneracy. This provides a non-trivial example of the recent claim made by Witten on the vanishing of the cosmological constant in three dimensions without unphysical degeneracies.

Three-dimensional supergravity and the cosmological constant.

Witten has argued that in $2+1$ dimensions local supersymmetry can ensure the vanishing of the cosmological constant without requiring the equality of bose and fermi masses. We find that this mechanism is implemented in a novel fashion in the (2+1)-dimensional supersymmetric abelian Higgs model coupled to supergravity. The vortex solitons are annihilated by half of the supersymmetry transformations. The covariantly constant spinors required to define these supersymmetries exist by virtue of a surprising cancellation between the Aharonov-Bohm phase and the phase associated with the holonomy of the spin connection. However the other half of the supersymmetry transformations, whose actions ordinarily generate the soliton supermultiplet, are not well-defined and bose-fermi degeneracy is consequently absent in the soliton spectrum.