Spontaneous Supersymmetry Breaking Research Articles

Duality and confinement in 3d [formula omitted] “chiral” SU(N) gauge theories

We study low-energy dynamics of three-dimensional N=2SU(N) “chiral” gauge theories with F fundamental and F¯ anti-fundamental matters without a Chern–Simons term. Compared to a naive semi-classical analysis of the Coulomb branch, its quantum structure is highly richer than expected due to so-called “dressed” Coulomb branch (monopole) operators. We propose dualities and confinement phases for the “chiral” SU(N) theories. The theories with N>F>F¯ exhibit spontaneous supersymmetry breaking. The very many Coulomb branch operators generally remain exactly massless and are non-trivially mapped under the dualities. Some dualities lead to a novel duality between SU(N) and USp(2N˜) theories. For the 3d N=2SU(2) gauge theory with 2F doublets, there are generally F+2 “chiral” and “non-chiral” dual descriptions.

Gauge principle and spontaneous symmetry breaking

Spatially modulated states of order-parameter fields as gauge (compensating) fields are considered. It is shown that an inhomogeneous vacuum occurs in infinite physical systems only as a result of introducing higher-order derivatives (for scalar fields) into Lagrangians. Possible phase transitions in systems with higher-order derivatives are also investigated. The discrete variants of spontaneous supersymmetry breaking in classical field theories with higher-order derivatives are discussed.

Phases Of Adjoint QCD$_3$ And Dualities

We study 2+1 dimensional gauge theories with a Chern-Simons term and a fermion in the adjoint representation. We apply general considerations of symmetries, anomalies, and renormalization group flows to determine the possible phases of the theory as a function of the gauge group, the Chern-Simons level kk, and the fermion mass. We propose an inherently quantum mechanical phase of adjoint QCD with small enough kk, where the infrared is described by a certain Topological Quantum Field Theory (TQFT). For a special choice of the mass, the theory has {\cal N}=1 supersymmetry. There this TQFT is accompanied by a massless Majorana fermion – a Goldstino signaling spontaneous supersymmetry breaking. Our analysis leads us to conjecture a number of new infrared fermion-fermion dualities involving SUSU, SOSO, and SpSp gauge theories. It also leads us to suggest a phase diagram of SO/SpSO/Sp gauge theories with a fermion in the traceless symmetric/antisymmetric tensor representation of the gauge group.

Quantum no-scale regimes and moduli dynamics

We analyze quantum no-scale regimes (QNSR) in perturbative heterotic string compactified on tori, with total spontaneous breaking of supersymmetry. We show that for marginal deformations initially at any point in moduli space, the dynamics of a flat, homogeneous and isotropic universe can always be attracted to a QNSR. This happens independently of the characteristics of the 1-loop effective potential V1-loop, which can be initially positive, negative or vanishing, and maximal, minimal or at a saddle point. In all cases, the classical no-scale structure is restored at the quantum level, during the cosmological evolution. This is shown analytically by considering moduli evolutions entirely in the vicinity of their initial values. Global attractor mechanisms are analyzed numerically and depend drastically on the sign of V1-loop. We find that all initially expanding cosmological evolutions along which V1-loop is positive are attracted to the QNSR describing a flat, ever-expanding universe. On the contrary, when V1-loop can reach negative values, the expansion comes to a halt and the universe eventually collapses into a Big Crunch, unless the initial conditions are tuned in a tiny region of the phase space. This suggests that flat, ever-expanding universes with positive potentials are way more natural than their counterparts with negative potentials.

Gauged Supergravities and Spontaneous Supersymmetry Breaking from the Double Copy Construction.

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 (spontaneously broken gauge theory)⊗ (gauge theory with broken supersymmetry). We present a simple realization in which the resulting supergravity has U(1)_{R} gauge symmetry, spontaneously broken N=2 supersymmetry, and massive gravitini. This is the first instance of a double copy construction of a gauged supergravity and of a theory with spontaneously broken supersymmetry. The construction extends in a straightforward manner to a large family of gauged Yang-Mills-Einstein supergravity theories with or without spontaneous gauge-symmetry breaking.

Quantum Vacuum, Dark Matter, Dark Energy, and Spontaneous Supersymmetry Breaking

We study the behavior of the vacuum condensates characterizing many physical phenomena. We show that condensates due to thermal states, to fields in curved space, and to neutrino mixing, may represent new components of the dark matter, whereas the condensate due to axion-photon mixing can contribute to the dark energy. Moreover, by considering a supersymmetric framework, we show that the nonzero energy of vacuum condensates may induce a spontaneous supersymmetry breaking.

Fayet-Iliopoulos terms in supergravity without gauged R-symmetry

We construct a supergravity-Maxwell theory with a novel embedding of the Fayet-Iliopoulos D-term, leading to spontaneous supersymmetry breaking. The gauging of the R-symmetry is not required and a gravitino mass is allowed for a generic vacuum. When matter couplings are introduced, an uplift through a positive definite contribution to the scalar potential is obtained. We observe a notable similarity to the overline{D}3 uplift constructions and we give a natural description in terms of constrained multiplets.

Spontaneous SUSY breaking without R symmetry in supergravity

We discuss spontaneous supersymmetry (SUSY) breaking in a model with an anomalous $U(1)_A$ symmetry. In this model, the size of the each term in the superpotential is controlled by the $U(1)_A$ charge assignment and SUSY is spontaneously broken via the Fayet-Iliopoulos of $U(1)_A$ at the meta-stable vacuum. In the global SUSY analysis, the gaugino masses become much smaller than the sfermion masses, because an approximate R-symmetry appears at the SUSY breaking vacuum. In this paper, we show that gaugino masses can be as large as gravitino mass, taking the supergravity effect into consideration. This is because the R-symmetry is not imposed so that the constant term in the superpotential, which is irrelevant to the global SUSY analysis, largely contributes to the soft SUSY breaking terms in the supergravity. As the mediation mechanism, we introduce the contributions of the field not charged under $U(1)_A$ and the moduli field to cancel the anomaly of $U(1)_A$. We comment on the application of our SUSY breaking scenario to the GUT models.

Quantum no-scale regimes in string theory

We show that in generic no-scale models in string theory, the flat, expanding cosmological evolutions found at the quantum level can be attracted to a “quantum no-scale regime”, where the no-scale structure is restored asymptotically. In this regime, the quantum effective potential is dominated by the classical kinetic energies of the no-scale modulus and dilaton. We find that this natural preservation of the classical no-scale structure at the quantum level occurs when the initial conditions of the evolutions sit in a subcritical region of their space. On the contrary, supercritical initial conditions yield solutions that have no analogue at the classical level. The associated intrinsically quantum universes are sentenced to collapse and their histories last finite cosmic times. Our analysis is done at 1-loop, in perturbative heterotic string compactified on tori, with spontaneous supersymmetry breaking implemented by a stringy version of the Scherk–Schwarz mechanism.

Tensor network formulation for two-dimensional lattice mathcal{N} = 1 Wess-Zumino model

Supersymmetric models with spontaneous supersymmetry breaking suffer from the notorious sign problem in stochastic approaches. By contrast, the tensor network approaches do not have such a problem since they are based on deterministic procedures. In this work, we present a tensor network formulation of the two-dimensional lattice mathcal{N} = 1 Wess-Zumino model while showing that numerical results agree with the exact solutions for the free case.

Removing instability of inflation in Polonyi–Starobinsky supergravity by adding FI term

Polonyi–Starobinsky (PS) supergravity is the [Formula: see text] supergravity model of Starobinsky inflation with spontaneous supersymmetry breaking (after inflation) due to Polonyi superfield, and inflaton belonging to a massive vector supermultiplet. The PS model is used for an explicit realization of the (super-heavy) gravitino dark matter scenario in cosmology. We find a potential instability in this model, and offer a mechanism for its removal by adding a Fayet–Iliopoulos (FI) term.

Genuine and effective actions, the Master Equation and Suppressed SUSY

Genuine theories are defined to be those governed by a Master Equation. All other theories are defined to be Effective Theories. It is straightforward to integrate heavy particles out of a Genuine Theory to get an Effective Theory, but putting together a Genuine Theory takes years. The Minimal Supersymmetric Standard Model is an Effective Theory, which arises because of the hypothesis of an invisible sector where spontaneous breaking of Supersymmetry (SUSY) occurs. Suppressed SUSY allows us to construct a Genuine Theory for SUSY, without the need for spontaneous breaking of SUSY.

Supersymmetry breaking in spatially modulated vacua

We study spontaneous supersymmetry breaking in spatially modulated stable or meta-stable vacua in supersymmetric field theories. Such spatial modulation can be realized in a higher derivative chiral model for which vacuum energies are either positive, negative or zero, depending on the model parameters. There appears a Nambu-Goldstone boson associated with the spontaneously breaking of the translational and $U(1)$ symmetries without the quadratic kinetic term and with a quartic derivative term in the modulated direction, and a gapless Higgs mode. We show that there appears a Goldstino associated with the supersymmetry breaking at a meta-stable vacuum, where energy is positive, while it becomes a fermionic ghost in the negative energy vacuum, and zero norm state and disappears from the physical sector in the zero energy vacuum.

Realization of a spontaneous gauge and supersymmetry breaking vacuum

It is one of the major issues to realize a vacuum which breaks supersymmetry (SUSY) and R-symmetry, in a supersymmetric model. We study the model, where the same sector breaks the gauge symmetry and SUSY. In general, the SUSY breaking model without gauge symmetry has a flat direction at the minimum of F-term scalar potential. When we introduce U(1) gauge symmetry to such a SUSY breaking model, there can appear a runaway direction. Such a runway direction can be lifted by loop effects, and the gauge symmetry breaking and SUSY breaking are realized. The R-symmetry, that is assigned to break SUSY, is also spontaneously broken at the vacuum. This scenario can be extended to non-Abelian gauge theories. We also discuss application to the Pati-Salam model and the SU(5) grand unified theory. We see that non-vanishing gaugino masses are radiatively generated by the R-symmetry breaking and the gauge messenger contribution.

Sgoldstino-less inflation and low energy SUSY breaking

We assess the range of validity of sgoldstino-less inflation in a scenario of low energy supersymmetry breaking. We first analyze the consistency conditions that an effective theory of the inflaton and goldstino superfields should satisfy in order to be faithfully described by a sgoldstino-less model. Enlarging the scope of previous studies, we investigate the case where the effective field theory cut-off, and hence also the sgoldstino mass, are inflaton-dependent. We then introduce a UV complete model where one can realize successfully sgoldstino-less inflation and gauge mediation of supersymmetry breaking, combining the α-attractor mechanism and a weakly coupled model of spontaneous breaking of supersymmetry. In this class of models we find that, given current limits on superpartner masses, the gravitino mass has a lower bound of the order of the MeV, i.e. we cannot reach very low supersymmetry breaking scales. On the plus side, we recognize that in this framework, one can derive the complete superpartner spectrum as well as compute inflation observables, the reheating temperature, and address the gravitino overabundance problem. We then show that further constraints come from collider results and inflation observables. Their non trivial interplay seems a staple feature of phenomenological studies of supersymmetric inflationary models.

On non-relativistic supersymmetry and its spontaneous breaking

We study non-relativistic supersymmetric field theories in diverse dimensions. The theories consist of scalars and fermions and possess two, four or eight real supercharges. We analyze their spontaneous supersymmetry breaking structure and calculate the gapless spectrum. We calculate the perturbative quantum corrections at the supersymmetric vacua and show that while supersymmetry is preserved, scale invariance is broken and the theories are IR free.

Softness and amplitudes\u2019 positivity for spinning particles

We derive positivity bounds for scattering amplitudes of particles with arbitrary spin using unitarity, analyticity and crossing symmetry. The bounds imply the positivity of certain low-energy coefficients of the effective action that controls the dynamics of the light degrees of freedom. We show that low-energy amplitudes strictly softer than O(p4) do not admit unitary ultraviolet completions unless the theory is free. This enforces a bound on the energy growth of scattering amplitudes in the region of validity of the effective theory. We discuss explicit examples including the Goldstino from spontaneous supersymmetry breaking, and the theory of a spin-1/2 fermion with a shift symmetry.

Fermions on the antibrane: Higher order interactions and spontaneously broken supersymmetry

It has been recently argued that inserting a probe anti-D3-brane in a flux background breaks supersymmetry spontaneously instead of explicitly, as previously thought. In this paper we argue that such spontaneous breaking of supersymmetry persists even when the probe anti-D3-brane is kept in a curved background with an internal space that doesn't have to be a Calabi-Yau manifold. To show this we take a specific curved background generated by fractional three-branes and fluxes on a non-Kahler resolved conifold where supersymmetry breaking appears directly from certain world-volume fermions becoming massive. In fact this turns out to be a generic property even if we change the dimensionality of the anti-brane, or allow higher order fermionic interactions on the anti-brane. We argue for the former by taking a probe anti-D7-brane in a flux background and demonstrate the spontaneous breaking of supersymmetry using world-volume fermions. We argue for the latter by constructing an all order fermionic action for the anti-D3-brane from which the spontaneous nature of supersymmetry breaking can be demonstrated by bringing it to a kappa-symmetric form.

Super no-scale models in string theory

We consider “super no-scale models” in the framework of the heterotic string, where the N=4,2,1→0 spontaneous breaking of supersymmetry is induced by geometrical fluxes realizing a stringy Scherk–Schwarz perturbative mechanism. Classically, these backgrounds are characterized by a boson/fermion degeneracy at the massless level, even if supersymmetry is broken. At the 1-loop level, the vacuum energy is exponentially suppressed, provided the supersymmetry breaking scale is small, m3/2≪Mstring. We show that the “super no-scale string models” under consideration are free of Hagedorn-like tachyonic singularities, even when the supersymmetry breaking scale is large, m3/2≃Mstring. The vacuum energy decreases monotonically and converges exponentially to zero, when m3/2 varies from Mstring to 0. We also show that all Wilson lines associated to asymptotically free gauge symmetries are dynamically stabilized by the 1-loop effective potential, while those corresponding to non-asymptotically free gauge groups lead to instabilities and condense. The Wilson lines of the conformal gauge symmetries remain massless. When stable, the stringy super no-scale models admit low energy effective actions, where decoupling gravity yields theories in flat spacetime, with softly broken supersymmetry.

Supersymmetry protected topological phases of isostatic lattices and kagome antiferromagnets

I generalize the theory of phonon topological band structures of isostatic lattices to frustrated antiferromagnets. I achieve this with a discovery of a many-body supersymmetry (SUSY) in the phonon problem of balls and springs and its connection to local constraints satisfied by ground states. The Witten index of the SUSY model demands the Maxwell-Calladine index of mechanical structures. "Spontaneous supersymmetry breaking" is identified as the need to gap all modes in the bulk to create the topological isostatic lattice state. Since ground states of magnetic systems also satisfy local constraint conditions (such as the vanishing of the total spin on a triangle) I identify a similar SUSY structure for many common models of antiferromagnets including the square, triangluar, kagome, pyrochlore nearest neighbor antiferromagnets, and the $J_2 = J_1/2$ square lattice antiferromagnet. Remarkably, the kagome family of antiferromagnets is the analog of topological isostatic lattices among this collections of models. Thus, a solid state realization of the theory of phonon topological band structure may be found in frustrated magnetic materials.