Misaligned Supersymmetry Research Articles

Tachyons and Misaligned Supersymmetry in orientifold vacua

We extend the analysis of Misaligned Supersymmetry to orientifold vacua. The lack of modular invariance in the Klein bottle, annulus and Möbius strip amplitudes implies that the IR properties of the physical spectrum are related to the UV behaviour of closed strings freely propagating between D-branes and O-planes, and vice versa. We thus build sector averaged sums 〈d(n)〉 associated to both representations of each Riemann surface. We find that the 〈d(n)〉’s associated to the loop channel control the coupling of closed-string tachyons to D-branes and/or O-planes, and therefore their vanishing is a necessary, but not sufficient, condition for stability in the closed sector. Similarly, the sector averaged sums associated to the tree-level amplitudes encode the presence of tachyons in the physical spectrum, and their vanishing is a sufficient, but not necessary, condition for classical stability. Using this technology, it is difficult, if not impossible, to formulate necessary and sufficient criteria for the absence of tachyons since, in orientifold vacua, they can be removed from the spectrum by the orientifold projection. Although in these cases one would naively expect a cancellation between 〈d(n)〉’s associated to different amplitudes, this does not occur in practice. We provide several examples in ten and lower dimensions supporting our results.

Tachyons and misaligned supersymmetry in closed string vacua

In a remarkable paper, Dienes discovered that the absence of physical tachyons in closed string theory is intimately related to oscillations in the net number of bosonic minus fermionic degrees of freedom, a pattern predicted by an underlying misaligned supersymmetry. The average of these oscillations was linked to an exponential growth controlled by an effective central charge Ceff smaller than the expected inverse Hagedorn temperature. Dienes also conjectured that Ceff should vanish when tachyons are absent.In this paper, we revisit this problem and show that boson-fermion oscillations are realised even when tachyons are present in the physical spectrum. In fact, we prove that the average growth rate Ceff is set by the mass of the “lightest” state, be it massless or tachyonic, and coincides with the effective inverse Hagedorn temperature of the associated thermal theory. We also provide a general proof that the necessary and sufficient condition for classical stability is the vanishing of the sector averaged sum which implies Ceff = 0, in agreement with Dienes’ conjecture.

Gaugino Masses from Misaligned Supersymmetry Breaking and R-Symmetry Breaking Spurions

In gauge mediation models with multiple spurion fields breaking SUSY and the R-symmetry separately, we show that it is possible to generate gaugino masses in one loop if the R-charge arrangement satisfies a certain condition. The resulting gaugino masses are calculated and suppressed by a power of the messenger’s mass scale. We present two simple examples to demonstrate this possibility and discuss possible phenomenology implications.

Modular invariance, misalignment and finiteness in non-supersymmetric strings

In this article we show that finite perturbative corrections in non-supersymmetric strings can be understood via an interplay between modular invariance and misaligned supersymmetry. While modular invariance is known to be crucial in closed-string models, its presence and role for open strings is more subtle. Nevertheless, we argue that it leads to cancellations in physical quantities such as the one-loop cosmological constant and prevents them from diverging. In particular, we show that if the sector-averaged number of states does not grow exponentially, as predicted by misaligned supersymmetry, all exponential divergences in the one-loop cosmological constant cancel out as well. To account for the absence of power-law divergences, instead, we need to resort to the modular structure of the partition function. We finally comment on the presence of misaligned supersymmetry in the known 10-dimensional tachyon-free non-supersymmetric string theories.

Type 0 ℤ2 × ℤ2 heterotic string orbifolds and misaligned supersymmetry

The [Formula: see text] heterotic string orbifold yielded a large space of phenomenological three generation models and serves as a testing ground to explore how the Standard Model of particle physics may be incorporated in a theory of quantum gravity. In this paper, we explore the existence of type 0 models in this class of string compactifications. We demonstrate the existence of type 0 [Formula: see text] heterotic string orbifolds, and show that there exist a large degree of redundancy in the space of GGSO projection coefficients when the type 0 restrictions are implemented. We explore the existence of such configurations in several constructions. The first correspond to essentially a unique configuration out of a priori [Formula: see text] discrete GGSO choices. We demonstrate this uniqueness analytically, as well as by the corresponding analysis of the partition function. A wider classification is performed in [Formula: see text]-models and [Formula: see text]-models, where the first class correspond to compactifications of a tachyonic ten-dimensional heterotic string vacuum, whereas the second correspond to compactifications of the ten-dimensional nontachyonic [Formula: see text]. We show that the type 0 models in both cases contain physical tachyons at the free fermionic point in the moduli space. These vacua are therefore necessarily unstable, but may be instrumental in exploring the string dynamics in cosmological scenarios. We analyze the properties of the string one-loop amplitude. Naturally, these are divergent due to the existence of tachyonic states. We show that once the tachyonic states are removed by hand the amplitudes are finite and exhibit a form of misaligned supersymmetry.

Misaligned supersymmetry and open strings

The study of non-supersymmetric string theories is shedding light on an important corner of the string landscape and might ultimately explain why, so far, we did not observe supersymmetry in our universe. We review how misaligned supersymmetry in closed-string theories leads to a cancellation between bosons and fermions even in non-supersymmetric string theories. We then show that the same cancellation takes place for open strings by studying an anti-Dp-brane placed on top of an Op-plane in type II string theory. Misaligned supersymmetry consists in cancellations between bosons and fermions at different energy levels, in such a way that the averaged number of states grows at a rate dominated by a factor {mathrm{e}}^{C_{mathrm{e}mathrm{ff}}sqrt{n}} , with Ceff< Ctot, where Ctot is the inverse Hagedorn temperature. We prove the previously conjectured complete cancellation, i.e. we prove that Ceff = 0, for a vast class of models.

The Pauli sum rules imply BSM physics

Some 68 years ago (1951) Wolfgang Pauli mooted the three sum rules:∑n(−1)2Sngn=0;∑n(−1)2Sngnmn2=0;∑n(−1)2Sngnmn4=0. These three sum rules are intimately related to both the Lorentz invariance and the finiteness of the zero-point stress–energy tensor. Further afield, these three constraints are also intimately related to the existence of finite QFTs ultimately based on Fermi–Bose cancellations. (Supersymmetry is neither necessary nor sufficient for the existence of these finite QFTs; though softly but explicitly broken supersymmetry or mis-aligned supersymmetry can be used as a book-keeping device to keep the calculations manageable.) In the current article I shall instead take these three Pauli sum rules as given, assume their exact non-perturbative validity, contrast them with the observed standard model particle physics spectrum, and use them to extract as much model-independent information as possible regarding beyond standard model (BSM) physics.

Bose-Fermi degeneracies in large N adjoint QCD

We analyze the large $N$ limit of adjoint QCD, an $SU(N)$ gauge theory with $N_f$ flavors of massless adjoint Majorana fermions, compactified on $S^3 \times S^1$. We focus on the weakly-coupled confining small-$S^3$ regime. If the fermions are given periodic boundary conditions on $S^1$, we show that there are large cancellations between bosonic and fermionic contributions to the twisted partition function. These cancellations follow a pattern previously seen in the context of misaligned supersymmetry, and lead to the absence of Hagedorn instabilities for any $S^1$ size $L$, even though the bosonic and fermionic densities of states both have Hagedorn growth. Adjoint QCD stays in the confining phase for any $L \sim N^0$, explaining how it is able to enjoy large $N$ volume independence for any $L$. The large $N$ boson-fermion cancellations take place in a setting where adjoint QCD is manifestly non-supersymmetric at any finite $N$, and are consistent with the recent conjecture that adjoint QCD has emergent fermionic symmetries in the large $N$ limit.

SUGGESTION OF EXPLICIT FIELD TRANSFORMATIONS UNDERLYING MISALIGNED SUPERSYMMETRY

In order that nonsupersymmetric quiver gauge theories can satisfy naturalness requirements to all orders of perturbation theory, one expects a global symmetry similar to, but different from, supersymmetry. Consistent with the generalized no-go theorem published by Haag et al. in 1975, we suggest a generalization of supersymmetry to a misaligned supersymmetry where fermionic generators do not commute with gauge transformations. An explicit form for the corresponding field transformations is suggested.

Solving the hierarchy problem without supersymmetry or extra dimensions: an alternative approach

In this paper, we propose a possible new approach towards solving the gauge hierarchy problem without supersymmetry and without extra spacetime dimensions. This approach relies on the finiteness of string theory and the conjectured stability of certain non-supersymmetric string vacua. One crucial ingredient in this approach is the idea of “misaligned supersymmetry”, which explains how string theories may be finite even without exhibiting spacetime supersymmetry. This approach towards solving the gauge hierarchy problem is therefore complementary to recent proposals involving both large and small extra spacetime dimensions. This approach may also give a new perspective towards simultaneously solving the cosmological constant problem.

String theory, misaligned supersymmetry, and the supertrace constraints.

We demonstrate that string consistency in four spacetime dimensions leads to a spectrum of string states which satisfies the supertrace constraints $\mathrm{Str}1\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ and $\mathrm{Str}{M}^{2}\ensuremath{\propto}\ensuremath{\Lambda}$ at tree level, where $\ensuremath{\Lambda}$ is the one-loop string cosmological constant. This result holds for a large class of string theories, including critical heterotic strings. For strings lacking spacetime supersymmetry, these supertrace constraints will be satisfied as a consequence of a hidden ``misaligned supersymmetry'' in the string spectrum. These results suggest a new intrinsically stringy mechanism whereby such supertrace constraints may be satisfied without phenomenologically unacceptable consequences.

Modular invariance, finiteness, and misaligned supersymmetry: New constraints on the numbers of physical string states

We investigate the genetic distribution of bosonic and fermionic states at all mass levels in non-supersymmetric string theories, and find that a hidden “misaligned supersymmetry” must always appear in the string spectrum. We show that this misaligned supersymmetry is ultimately responsible for the finiteness of string amplitudes in the absence of full spacetime supersymmetry, and therefore the existence of misaligned supersymmetry provides a natural constraint on the degree to which spacetime supersymmetry can be broken in string theory without destroying the finiteness of string amplitudes. Misaligned supersymmetry also explains how the requirements of modular invariance and absence of physical tachyons generically affect the distribution of states throughout the string spectrum, and implicitly furnishes a two-variable generalization of some well-known results in the theory of modular functions.