Supersymmetric bosonic backgrounds governed by first-order BPS equations, can be realised in a much broader setting by relaxing the requirement of closure of the superalgebra beyond the level of quadratic fermion terms. The resulting pseudo-supersymmetric theories can be defined in arbitrary spacetime dimensions. We focus here on the ${\cal N}=1$ pseudo-supersymmetric extensions of the arbitrary-dimensional bosonic string action, which were constructed a few years ago. In this paper, we recast these in the language of generalised geometry. More precisely, we construct the action and the corresponding supersymmetry transformation rules in terms of O($D$)$\times$O($D$) covariant derivatives, and we discuss consistent truncations on manifolds with generalised $G$-structure. As explicit examples, we discuss Minkowski$\times G$ vacuum solutions and their corresponding pseudo-supersymmetry. We also briefly discuss squashed group manifold solutions, including an example with a Lorentzian signature metric on the group manifold $G$.
The correspondence between domain-wall and cosmological solutions of gravity coupled to scalar fields is explained. Any domain wall solution that admits a Killing spinor is shown to correspond to a cosmology that admits a pseudo-Killing spinor: whereas the Killing spinor obeys a Dirac-type equation with hermitian `mass'-matrix, the corresponding pseudo-Killing spinor obeys a Dirac-type equation with a anti-hermitian `mass'-matrix. We comment on some implications of (pseudo)supersymmetry.
We construct a model with long-lived metastable vacua in which all the relevant parameters, including the supersymmetry breaking scale, are generated dynamically by dimensional transmutation. The metastable vacua appear along a pseudo-runaway direction near a point of enhanced symmetry as a result of a balance between non-perturbative and perturbative quantum effects. We show that metastable supersymmetry breaking is a rather generic feature near certain enhanced symmetry points of gauge theory moduli spaces.
For a general mechanical system, it is shown that each solution of the Hamilton-Jacobi equation defines an N=2 pseudo-supersymmetric extension of the system, such that the usual relation of the momenta to Hamilton's principal function is the `BPS' condition for preservation of 1/2 pseudo-supersymmetry. The examples of the relativistic and non-relativistic particle, in a general potential, are worked through in detail, and used to discuss the relation to cosmology and to supersymmetric quantum mechanics.
We discuss how all variant 10d and 11d maximal supergravities, including star supergravities and supergravities in different signatures, can be obtained as different real slices of three complex actions. As an application we study the recently introduced domain-wall/cosmology correspondence in this approach. We give an example in 9d and 10d where the domain-wall and corresponding cosmology can be viewed as different real slices of the same complex solution. We argue how in this case the pseudo-supersymmetry of the cosmological solutions can be understood as the invariance under supersymmetry o…
Previous constructions of supersymmetry for double field theory have relied on the so called strong constraint. In this paper, the strong constraint is relaxed and the theory is shown to possess supersymmetry once the generalised Scherk-Schwarz reduction is imposed. The equivalence between the generalised Scherk-Schwarz reduced theory and the gauged double field theory is then examined in detail for the supersymmetric theory. As a byproduct we write the generalised Killing spinor equations for the supersymmetric double field theory.
Certain supergravity theories admit a remarkable consistent dimensional reduction in which the internal space is a sphere. Examples include type IIB supergravity reduced on S^5, and eleven-dimensional supergravity reduced on S^4 or S^7. Consistency means that any solution of the dimensionally-reduced theory lifts to give a solution in the higher dimension. Although supersymmetry seems to play a role in the consistency of these reductions, it cannot be the whole story since consistent sphere reductions of non-supersymmetric theories are also known, such as the reduction of the effective action …
This is the third paper in a series of four papers which introduce cybersusy, which is a new mechanism for supersymmetry breaking in the supersymmetric standard model (SSM). In this paper we display some solutions to the constraint equations of BRS cohomology in the SSM. In particular we discuss the leptonic dotspinor pseudosupermultiplets that were used in Cybersusy I to calculate leptonic supersymmetry breaking in the supersymmetric standard model. We also introduce examples of hadronic dotspinor pseudosupermultiplets that will induce baryonic supersymmetry breaking in the SSM for the baryon…
Scattering amplitudes have the potential to provide new insights to the study of supergravity theories with gauged R-symmetry and Minkowski vacua. Such gaugings break supersymmetry spontaneously, either partly or completely. In this paper, we develop a framework for double-copy constructions of Abelian and non-Abelian gaugings of N=8 supergravity with these properties. They are generally obtained as the double copy of a spontaneously-broken (possibly supersymmeric) gauge theory and a theory with explicitly-broken supersymmetry. We first identify purely-adjoint deformations of N=4 super-Yang-Mi…
I discuss effective field theories of brane-world models where different sectors break different halves of the extended bulk supersymmetry. It is shown how to consistently couple N=2 supersymmetric matter to N=1 superfields that lack N=2 partners but transform in a non-linear representation of the N=2 algebra. In particular, I explain how to couple an N=2 vector to N=1 chiral fields such that the second supersymmetry is non-linearly realized. This method is then used to study systems where different sectors break different halves of supersymmetry, which appear naturally in models of intersecti…
We construct the ${\cal N}=1$ supersymmetric extension of Double Field Theory for Riemannian and the non-Riemannian in a unified approach. The inclusion of fermions in the double geometry force us to use the generalized frame formalism to construct the generalized flux components for these geometries. We focus on the most general prescription required to get the $D=10$ minimal supergravity model. We study how to consistently avoid the gauge fixing procedure of the double Lorentz symmetry when $n=\bar n$ and $0\le n \le 5$, which gives rise to a bigravity structure (pair of vielbeins producing …
We construct a supersymmetric quantum Hall liquid with a deformed supersymmetry. One parameter is introduced in the supersymmetric Laughlin wavefunction to realize the original Laughlin wavefunction and the Moore-Read wavefunction in two extremal limits of the parameter. The introduced parameter corresponds to the coherence factor in the BCS theory. It is pointed out that the parameter-dependent supersymmetric Laughlin wavefunction enjoys a deformed supersymmetry. Based on the deformed supersymmetry, we construct a pseudo-potential Hamiltonian whose groundstate is exactly the parameter-depende…
We show that the metric operator for a pseudo-supersymmetric Hamiltonian that has at least one negative real eigenvalue is necessarily indefinite. We introduce pseudo-Hermitian fermion (phermion) and abnormal phermion algebras and provide a pair of basic realizations of the algebra of N=2 pseudo-supersymmetric quantum mechanics in which pseudo-supersymmetry is identified with either a boson-phermion or a boson-abnormal-phermion exchange symmetry. We further establish the physical equivalence (non-equivalence) of phermions (abnormal phermions) with ordinary fermions, describe the underlying Lie…
We analyze the transmission of supersymmetry breaking in brane-world models of pseudo-supersymmetry. In these models two branes preserve different halves of the bulk supersymmetry. Thus supersymmetry is broken although each sector of the model is supersymmetric when considered separately. The world-volume theory on one brane feels the breakdown of supersymmetry only through two-loop interactions involving a coupling to fields from the other brane. In a 5D toy model with bulk vectors, we compute the diagrams that contribute to scalar masses on one brane and find that the masses are proportional…
Supergravities with gauged R-symmetry and Minkowski vacua allow for spontaneous supersymmetry breaking and, as such, provide a framework for building supergravity models of phenomenological relevance. In this letter we initiate the study of double-copy constructions for these supergravities. We argue that, on general grounds, we expect their scattering amplitudes to be described by a double copy of the type: (Higgsed gauge theory) x (gauge theory with broken SUSY). We present a simple realization in which the resulting supergravity has U(1)_R gauge symmetry, spontaneously-broken N=2 supersymme…
We elaborate on a new N=2, d=3 supermultiplet (double-vector multiplet) with a non-trivial off-shell realization of the central charge. Its bosonic sector comprises two abelian gauge vector fields forming an SO(2) vector. We present a superfield formulation of this multiplet in the central-charge extended N=2, d=3 superspace and then employ it, in the framework of the nonlinear realizations approach, as the Goldstone one for the partial breaking N=4 -> N=2 in three dimensions. The covariant equations of motion for the self-interacting Goldstone superfield arise as a natural generalization of t…
We analyze theories in which a supersymmetric sector is coupled to a supersymmetry-breaking sector described by a non-linear realization. We show how to consistently couple N=1 supersymmetric matter to non-supersymmetric matter in such a way that all interactions are invariant under non-linear supersymmetry transformations. We extend this formalism to couple N=2 supersymmetric matter to N=1 superfields that lack N=2 partners but transform in a non-linear representation of the N=2 algebra. In particular, we show how to couple an N=2 vector to N=1 chiral fields in a consistent way. This has impo…
We discuss the conditions for additional supersymmetry and twisted supersymmetry in N = (2, 2) supersymmetric non-linear sigma models described by one left and one right semi-chiral superfield and carrying a pair of non-commuting complex structures. Focus is on linear non-manifest transformations of these fields that have an algebra that closes off-shell. We find that additional linear supersymmetry has no interesting solution, whereas additional linear twisted supersymmetry has solutions with interesting geometrical properties. We solve the conditions for invariance of the action and show tha…
The Dirac Hamiltonian in the (2+1) dimensional curved space-time has been studied with a metric for an expanding de Sitter space-time which is a two sphere. The spectrum and the exact solutions of the time dependent non-Hermitian and angle dependent Hamiltonians are obtained in terms of the Jacobi and Romanovski polynomials. Hermitian equivalent of the Hamiltonian obtained from the Dirac equation is discussed in the frame of pseudo-Hermiticity. Furthermore, pseudo-supersymmetric quantum mechanical techniques are expanded to a curved Dirac Hamiltonian and a partner curved Dirac Hamiltonian is g…
We show that small soft terms can create a supersymmetry breaking minimum along a pseudo-flat direction of a hidden sector which would otherwise be incapable of spontaneous supersymmetry breaking. As this minimum lies along a pseudo-flat direction, with non-zero F- or D-terms, the resultant supersymmetry breaking in the hidden sector can be orders of magnitude greater than the soft terms which created the minimum. This opens new avenues for building models of gauge mediation, may have consequences for the cosmology of hidden sectors, and strengthens the case for multiple supersymmetry breaking…
It was recently shown how to break supersymmetry in certain $AdS_3$ spaces, without destabilizing the background, by using a ``double trace'' deformation which localizes on the boundary of space-time. By viewing spatial sections of $AdS_3$ as a compactification space, one can convert this into a SUSY breaking mechanism which exists uniformly throughout a large 3+1 dimensional space-time, without generating any dangerous tadpoles. This is a generalization of a Visser type infinite extra dimensions compactification. Although the model is not Lorentz invariant, the dispersion relation is relativi…
A counterpart of the modular double for quantum superalgebra $\cU_q(\osp(1|2))$ is constructed by means of supersymmetric quantum mechanics. We also construct the $R$-matrix operator acting in the corresponding representations, which is expressed via quantum dilogarithm.
We apply the background field technique, recently developed for a general class of nonlinear symmetries, at tree level, to the Volkov-Akulov theory with spontaneously broken N=1 supersymmetry. We find that the background field expansion in terms of the free fields to the lowest order reproduces the nonlinear supersymmetry transformation rules. The double soft limit of the background field is, in agreement with the new general identities, defined by the algebra of the nonlinear symmetries.
A re-formulated, non-Hermitian version of the Witten's supersymmetric quantum mechanics is presented. Its use of pseudo-Hermitian (so called PT symmetric) Hamiltonians is reviewed and illustrated via several forms of an innovated supersymmetric partnership between strongly singular ("spiked") harmonic oscillators.
Chongqing University（重庆大学）；Universidad de Guanajuato（瓜纳华托大学）；Secretaría de Ciencia, de Humanidades, Tecnología e Innovación（科学、人文、技术与创新秘书处）；Dual CP Institute of High Energy Physics（双CP高能物理研究所）
We propose the Supersymmetric Standard Models (SSMs) with a pseudo-Dirac gluino from hybrid $F-$ and $D-$term supersymmetry (SUSY) breakings. Similar to the SSMs before the LHC, all the supersymmetric particles in the Minimal SSM (MSSM) obtain the SUSY breaking soft terms from the traditional gravity mediation and have masses within about 1 TeV except gluino. To evade the LHC SUSY search constraints, the gluino also has a heavy Dirac mass above 3 TeV from $D-$term SUSY breaking. Interestingly, such a heavy Dirac gluino mass will not induce the electroweak fine-tuning problem. We realize such S…
The `Wave Geometry' equation of the pre-WWII Hiroshima program is also the key equation of the current `fake supergravity' program. I review the status of (fake) supersymmetric domain walls and (fake) pseudo-supersymmetric cosmologies. An extension of the domain-wall/cosmology correspondence to a triple correspondence with instantons shows that `pseudo-supersymmetry' has another interpretation as Euclidean supersymmetry.
We discuss generalizations of Intriligator-Seiberg-Shih (ISS) vacua to chiral models. We study one example, of an s-confining theory, in detail. In the IR, this example reduces to two ISS-like sectors, and exhibits a supersymmetry-breaking vacuum with all pseudo-moduli stabilized at the origin, and with the R-symmetry unbroken. The IR theory is interesting from the point of view of R-symmetry breaking. This theory is an O'Raifeartaigh model with all charges zero or two, but the presence of a second R-charged pseudo-modulus with superpotential couplings to the messengers in principle allows for…
We consider candidates for dark matter in models of gauge mediated supersymmetry breaking, in which the supersymmetry breaking sector is weakly coupled and calculable. Such models typically contain classically flat directions, that receive one-loop masses of a few TeV. These pseudo-flat directions provide a new mechanism to account for the cold dark matter relic abundance. We discuss also the possibility of heavy gravitino dark matter in such models.
Supersymmetric lattice Ward-Takahashi identities are investigated perturbatively up to two-loop corrections for super doubler approach of $N=2$ lattice Wess-Zumino models in 1- and 2-dimensions. In this approach notorious chiral fermion doublers are treated as physical particles and momentum conservation is modified in such a way that lattice Leibniz rule is satisfied. The two major difficulties to keep exact lattice supersymmetry are overcome. This formulation defines, however, nonlocal field theory. Nevertheless we confirm that exact supersymmetry on the lattice is realized for all superchar…
We examine the properties and consequences of pseudo-supersymmetry for quantum systems admitting a pseudo-Hermitian Hamiltonian. We explore the Witten index of pseudo-supersymmetry and show that every pair of diagonalizable (not necessarily Hermitian) Hamiltonians with discrete spectra and real or complex-conjugate pairs of eigenvalues are isospectral and have identical degeneracy structure except perhaps for the zero eigenvalue if and only if they are pseudo-supersymmetric partners. This implies that pseudo-supersymmetry is the basic framework for generating non-Hermitian PT-symmetric and non…
In the framework of supersymmetry, when $R$-parity is violated the Higgs doublet superfield $H_d$ can be interpreted as another doublet of leptons, since all of them have the same quantum numbers. Thus Higgs scalars are sleptons and Higgsinos are leptons. We argue that this interpretation can be extended to the second Higgs doublet superfield $H_u$, when right-handed neutrinos are assumed to exist. As a consequence, we advocate that this is the minimal construction where the two Higgs doublets can be interpreted in a natural way as a fourth family of lepton superfields, and that this is more s…
I employ heuristically the strictly isospectral double Darboux method based on the general superpotential of unbroken nonrelativistic supersymmetry suggesting a few small steps of principle for extending its range of applications toward relativistic (gauge) physics. The application of the method to minisuperspace quantum cosmology is also briefly presented
We propose a mechanism for mediating supersymmetry breaking in Type I string constructions. The basic set-up consists of a system of three D-branes: two parallel D-branes, a matter D-brane and a source D-brane, with supersymmetry breaking communicated via a third D-brane, the mediating D-brane, which intersects both of the parallel D-branes. We discuss an example in which the first and second family matter fields correspond to open strings living on the intersection of the matter D-brane and mediating D-brane, while the gauge fields, Higgs doublets and third family matter fields correspond to …
In this paper we show how to obtain the heterotic double field theory from exceptional field theory by breaking half of the supersymmetry. We focus on the $\mathrm{SL}(5)$ exceptional field theory and show that when the extended space contains a generalised $\mathrm{SU}(2)$-structure manifold one can define a reduction to obtain the heterotic $\mathrm{SO}(3,n)$ double field theory. In this picture, the reduction on the $\mathrm{SU}(2)$-structure breaks half of the supersymmetry of the exceptional field theory and the gauge group of the heterotic double field theory is given by the embedding te…
The emergent gauge theories are reconsidered in light of supersymmetry and an appropriate emergence conjecture is formulated. Accordingly, it might be expected that only global symmetries are fundamental symmetries of Nature, whereas local symmetries and associated massless gauge fields could solely emerge due to spontaneous breaking of underlying spacetime symmetries involved, such as relativistic invariance and supersymmetry. We further argue that this breaking, taken in the form of the nonlinear sigma-model type pattern for vector fields or superfields, puts essential restrictions on geomet…
We reconsider cosmological perturbation theory for multi-component scalars, enforcing covariance in field-space, and ensuring that phyical observations are independent of field re-definitions. We use the formalism to clarify some issues in the literature, and use pseudo-supersymmetry to derive exact expressions for terms of interest.
We study supersymmetry breaking from a lattice model of N=2 supersymmetric quantum mechanics using the direct computational method proposed in arXiv:1803.07960. The vanishing Witten index is realized as a numerical result in high precision. The expectation value of Hamiltonian is evaluated for the double-well potential. Compared with the previous Monte-Carlo results, the obtained vacuum energy coincides with the known values within small errors for strong couplings. The instanton effect is also reproduced for weak couplings. The used computational method helps us to evaluate the effect of fini…
The field responsible for the cosmological curvature perturbations generated during a stage of primordial inflation might be the ``curvaton'', a field different from the inflaton field. To keep the effective mass of the curvaton small enough compared to the Hubble rate during inflation one may not invoke supersymmetry since the latter is broken by the vacuum energy density. In this paper we propose the idea that the curvaton is a pseudo Nambu-Goldstone boson (PNGB) so that its potential and mass vanish in the limit of unbroken symmetry. We give a general framework within which PNGB curvaton ca…
