Spontaneous Supersymmetry Breaking Research Articles

Spontaneous supersymmetry breaking in matrix models

Spontaneous supersymmetry breaking in matrix models

Spontaneous supersymmetry breaking in large- N matrix models with slowly varying potential

We construct a class of matrix models, where supersymmetry (SUSY) is spontaneously broken at the matrix size N infinite. The models are obtained by dimensional reduction of matrix-valued SUSY quantum mechanics. The potential of the models is slowly varying, and the large- N limit is taken with the slowly varying limit. First, we explain our formalism, introducing an external field to detect spontaneous SUSY breaking, analogously to ordinary (bosonic) symmetry breaking. It is observed that SUSY is possibly broken even in systems in less than one-dimension, for example, discretized quantum mechanics with a finite number of discretized time steps. Then, we consider spontaneous SUSY breaking in the SUSY matrix models with slowly varying potential, where the external field is turned off after the large- N and slowly varying limit, analogously to the thermodynamic limit in statistical systems. On the other hand, without taking the slowly varying limit, in the SUSY matrix model with a double-well potential whose SUSY is broken due to instantons for finite N, a number of supersymmetric behavior is explicitly seen at large N. It convinces us that the instanton effect disappears and the SUSY gets restored in the large- N limit.

Alternative auxiliary fields for chiral multiplets

We study 3-form auxiliary field formulation for chiral multiplets in the Wess-Zumino model. The conventional auxiliary fields $F$ and $G$ are replaced by their Hodge duals ${K}_{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}\ensuremath{\sigma}}$ and ${H}_{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}\ensuremath{\sigma}}$ which are the field strengths of the 3-form potential auxiliary fields ${G}_{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}}$ and ${F}_{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}}$. Even though duality transformations connect these two formulations, there exist certain differences from the conventional formulation. When boundary conditions are taken into account, the field equations in the 3-form formulation are equivalent to the conventional ones, while our Lagrangian is not. We also show that the new field strengths acquire generalized Chern-Simons terms. The O'Raifeartaigh mechanism works for spontaneous supersymmetry breaking also in the 3-form auxiliary field formulation via the boundary conditions on the 3-form auxiliary fields.

R-symmetry and supersymmetry breaking at finite temperature

We analyze the spontaneous $U(1)_R$ symmetry breaking at finite temperature for the simple O'Raifeartaigh-type model introduced in [1] in connection with spontaneous supersymmetry breaking. We calculate the finite temperature effective potential (free energy) to one loop order and study the thermal evolution of the model. We find that the R-symmetry breaking occurs through a second order phase transition. Its associated meta-stable supersymmetry breaking vacuum is thermodynamically favored at high temperatures and the model remains trapped in this state by a potential barrier, as the temperature lowers all the way until T=0.

Linear delta expansion applied to the O’Raifeartaigh model

We reassess the method of the linear delta expansion for the calculation of effective potentials in superspace, by adopting the improved version of the super-Feynman rules in the framework of the O'Raifeartaigh model for spontaneous supersymmetry breaking. The effective potential is calculated using both the fastest apparent convergence and the principle of minimal sensitivity criteria and the consistency and efficacy of the method are checked in deriving the Coleman-Weinberg potential.

Spontaneous SUSY breaking in various dimensions

We generalize the ISS model of spontaneous supersymmetry breaking to lower dimensions. We also comment on the dynamics of the corresponding brane systems in string theory, and on possible applications to gauge/gravity duality.

Scalar potential in supergravity**Supported in part by the Japanese Society for Promotion of Science (JSPS).

We derive a scalar potential in the recently proposed N = 1 supersymmetric generalization of f(R) gravity in four spacetime dimensions. Any such higher-derivative supergravity is classically equivalent to the standard N = 1 supergravity coupled to a chiral (matter) superfield, via a Legendre–Weyl transform in superspace. The Kähler potential, the superpotential and the scalar potential of that theory are all governed by a single holomorphic function. We also find the conditions for the vanishing cosmological constant and spontaneous supersymmetry breaking, without fine tuning, which define a no-scale F(R) supergravity. The F(R) supergravities are suitable for physical applications in the inflationary cosmology based on supergravity and superstrings.

R-charges, Chiral rings and RG flows in supersymmetric Chern-Simons-Matter theories

We discuss the non-perturbative behavior of the U(1)_R symmetry in N=2 superconformal Chern-Simons theories coupled to matter in the (anti)fundamental and adjoint representations of the gauge group, which we take to be U(N). Inequalities constraining this behavior are obtained as consequences of spontaneous breaking of supersymmetry and Seiberg duality. This information reveals a web of RG flows connecting different interacting superconformal field theories in three dimensions. We observe that a subclass of these theories admits an ADE classification. In addition, we postulate new examples of Seiberg duality in N=2 and N=3 Chern-Simons-matter theories and point out interesting parallels with familiar non-perturbative properties in N=1 (adjoint) SQCD theories in four dimensions where the exact U(1)_R symmetry can be determined using a-maximization.

D-terms on the resolved conifold

We derive a novel deformation of the warped resolved conifold background with supersymmetry breaking ISD (1,2) fluxes by adding D7-branes to this type IIB theory. We find spontaneous supersymmetry breaking without generating a bulk cosmological constant. In the compactified form, our background will no longer be a Calabi-Yau manifold as it allows a non-vanishing first Chern class. In the presence of D7-branes the (1,2) fluxes can give rise to non-trivial D-terms. We study the Ouyang embedding of D7-branes in detail and find that in this case the D-terms are indeed non-zero. In the limit when we approach the singular conifold, the D-terms vanish for Ouyang's embedding, although supersymmetry appears to be broken. We also construct the F-theory lift of our background and demonstrate how these IIB (1,2) fluxes lift to non-primitive (2,2) flux on the fourfold. The seven branes correspond to normalisable harmonic forms. We briefly sketch a possible way to attain an inflaton potential in this background once extra D3-branes are introduced and point out some possibilities of restoring supersymmetry in our background that could in principle be used as the end point of the inflationary set-up. In a companion paper we will analyse in details the inflationary dynamics in this background.

Spontaneous supersymmetry breaking with anomalousU(1)symmetry in metastable vacua and moduli stabilization

We show that in (anomalous) U(1) gauge theories with the Fayet-Iliopoulos (FI) term and with generic interactions there are meta-stable vacua in which supersymmetry (SUSY) is spontaneously broken even without U(1)_R symmetry and various hierarchical structures, for example, Yukawa hierarchy, can be explained by the smallness of the FI parameter. When we introduce generic interactions, i.e., all interactions including higher dimensional interactions which are allowed by the symmetry of the theory with O(1) coefficients, various scales can be determined by the symmetry (U(1) charges of the introduced fields). We examine how to determine the various scales, the vacuum expectation values (VEVs), and the scales of F-term and of D-term. Moreover, we propose a new scenario for the stabilization of the moduli in the SUSY breaking models.

Attraction to a radiation-like era in early superstring cosmologies

Starting from an initial classical four-dimensional flat background of the heterotic or type II superstrings, we are able to determine at the string one-loop level the quantum corrections to the effective potential due to the spontaneous breaking of supersymmetry by “geometrical fluxes”. Furthermore, considering a gas of strings at finite temperature, the full “effective thermal potential” is determined, giving rise to an effective non-trivial pressure. The backreaction of the quantum and thermal corrections to the space–time metric as well as to the moduli fields induces a cosmological evolution that depends on the early time initial conditions and the number of spontaneously broken supersymmetries. We show that for a whole set of initial conditions, the cosmological solutions converge at late times to two qualitatively different trajectories: They are either attracted to (i) a thermal evolution similar to a radiation dominated cosmology, implemented by a coherent motion of some moduli fields, or to (ii) a “Big Crunch” non-thermal cosmological evolution dominated by the non-thermal part of the effective potential or the moduli kinetic energy. During the attraction to the radiation-like era, periods of accelerated cosmology can occur. However, they do not give rise to enough inflation ( e -fold ≃ 0.2 ) for the models we consider, where N ⩾ 2 supersymmetry is spontaneously broken to N = 0 .

String dynamics, spontaneous breaking of supersymmetry, and dual scalar field theory

The dynamics of a vortex string, which describes the Nambu-Goldstone modes of the spontaneous breakdown of the target space $D=4$, $N=1$ supersymmetry and internal $U(1{)}_{R}$ symmetry to the world sheet $\mathrm{ISO}(1,1)$ symmetry, is constructed by using the approach of nonlinear realization. The resulting action describing the low energy oscillations of the string into the covolume (super)space is found to have an invariant synthesis form of the Akulov-Volkov and Nambu-Goto actions. Its dual scalar field action is obtained by means of introducing two vectorial Lagrangian multipliers into the action of the string.

Tree level spontaneous R-symmetry breaking in O'Raifeartaigh models

We show that in O'Raifeartaigh models of spontaneous supersymmetry breaking, R-symmetries can be broken by non-zero values of fields at tree level, rather than by vacuum expectation values of pseudomoduli at loop level. As a complement of the recent result by Shih, we show that there must be a field in the theory with R-charge different from zero and two in order for R-symmetry breaking to occur, no matter whether the breaking happens at tree or loop level. We review the example by CDFM, and construct two types of tree level R-symmetry breaking models with a wide range of parameters and free of runaway problem. And the R-symmetry is broken everywhere on the pseudomoduli space in these models. This provides a rich set of candidates for SUSY model building and phenomenology.

R-Axion: A New LHC Physics Signature Involving Muon Pairs

In a class of models with gauge mediated supersymmetry breaking, the existence of a light pseudo scalar particle, R-axion, with a mass in hundreds MeV range is predicted. The striking feature of such a light R-axion is that it mainly decays into a pair of muons and leaves a displaced vertex inside detectors once it is produced. In this talk, we show how we can search for the R-axion at the coming LHC experiments. The one main goal of the LHC experiments is discovering supersymmetry which has been anticipated for a long time to solve the hierarchy problem. Once the supersymmetric standard model (SSM) is confirmed experimentally, the next question is how the supersymmetry is broken and how the effects of symmetry breaking are mediated to the SSM sector. In most cases, such investigations on 'beyond the SSM physics' rely on arguments based on extrapolations of the observed supersymmetry mass parameters to higher energies. However, there is one class of models of supersymmetry breaking where we can get a direct glimpse of the structure of the hidden sector with the help of the R-symmetry. The R-symmetry plays an important role in rather generic models of spontaneous supersymmetry breaking. At themore » same time, however, it must be broken in some way in order for the gauginos in the SSM sector to have non-vanishing masses. One possibility of the gaugino mass generation is to consider models where the gaugino masses are generated as a result of the explicit breaking of the R-symmetries. Unfortunately, in those models, the R-symmetry leaves little trace for the collider experiments, since the mass of the R-axion is typically heavy and beyond the reach of the LHC experiments. In this talk, instead, we consider a class of models with gauge mediation where the R-symmetry in the hidden/messenger sectors is exact in the limit of the infinite reduced Planck scale, i.e. M{sub PL} {yields} {infinity}. In this case, the gaugino masses are generated only after the R-symmetry is broken spontaneously. We also assume that the R-symmetry is respected by the SSM sector as well as the origin of the higgsino mass {mu} and the Higgs mass mixing B{mu} at the classical level. We call this scenario, the minimal R-symmetry breaking scenario.« less

Large-Nsolution of the heteroticN=(0,2)two-dimensionalCP(N−1)model

We continue explorations of non-Abelian strings, focusing on the solution of a heterotic deformation of the $CP(N\ensuremath{-}1)$ model with an extra right-handed fermion field and $\mathcal{N}=(0,2)$ supersymmetry. This model emerges as a low-energy theory on the world sheet of the Bogomol'nyi-Prasad-Sommerfield-saturated flux tubes (strings) in $\mathcal{N}=2$ supersymmetric QCD deformed by a superpotential of a special type breaking $\mathcal{N}=2$ supersymmetry down to $\mathcal{N}=1$. Using large-$N$ expansion we solve this model to the leading order in $1/N$. Our solution exhibits spontaneous supersymmetry breaking for all values of the deformation parameter. We identify the Goldstino field. The discrete ${Z}_{2N}$ symmetry is shown to be spontaneously broken down to ${Z}_{2}$; therefore the world sheet model has $N$ strictly degenerate vacua (with nonvanishing vacuum energy). Thus, the heterotic $CP(N\ensuremath{-}1)$ model is in the deconfinement phase. We can compare this dynamical pattern, on the one hand, with the $\mathcal{N}=(2,2)$ $CP(N\ensuremath{-}1)$ model which has $N$ degenerate vacua with unbroken supersymmetry, and, on the other hand, with the nonsupersymmetric $CP(N\ensuremath{-}1)$ model with split quasivacua and the Coulomb/confining phase. We determine the mass spectrum of the heterotic $CP(N\ensuremath{-}1)$ model in the large-$N$ limit.

Euclidean lattice simulation for dynamical supersymmetry breaking

The global supersymmetry is spontaneously broken if and only if the ground-state energy is strictly positive. We propose to use this fact to observe the spontaneous supersymmetry breaking in Euclidean lattice simulations. For lattice formulations that possess a manifest fermionic symmetry, there exists a natural choice of a Hamiltonian operator that is consistent with a topological property of the Witten index. We confirm validity of our idea in models of the supersymmetric quantum mechanics. We then examine a possibility of a dynamical supersymmetry breaking in the two-dimensional $\mathcal{N}=(2,2)$ super Yang-Mills theory with the gauge group $\mathrm{SU}(2)$, for which the Witten index is unknown. Differently from a recent conjectural claim, our numerical result tempts us to conclude that supersymmetry is not spontaneously broken in this system.

Observing Dynamical Supersymmetry Breaking with Euclidean Lattice Simulations

A strict positivity of the ground-state energy is a necessary and sufficient condition for spontaneous supersymmetry breaking. This ground-state energy may be directly determined from the expectation value of the Hamiltonian in the functional integral, defined with an antiperiodic temporal boundary condition for all fermionic variables. We propose to use this fact to observe the dynamical spontaneous supersymmetry breaking in Euclidean lattice simulations. If a lattice formulation possesses a manifestly preserved fermionic symmetry, there exists a natural choice of a Hamiltonian operator that is consistent with a topological nature of the Witten index. We numerically confirm the validity of our idea in models of supersymmetric quantum mechanics. We further examine the possibility of dynamical supersymmetry breaking in the two-dimensional = (2, 2) super Yang-Mills theory with the gauge group SU (2), for which the Witten index is unknown. Although statistical errors are still large, we do not observe positive ground-state energy, at least within one standard deviation. This prompts us to draw a different conclusion from a recent conjectural claim that supersymmetry is dynamically broken in this system.

Supersymmetric models with higher dimensional operators

Using a superfield language it is shown that a 4D N=1 supersymmetric theory with higher derivative operators in either the Kahler or the superpotential part of the Lagrangian and with an otherwise arbitrary superpotential, is equivalent to a 4D N=1 theory of second order (i.e. without higher derivatives) with additional superfields and renormalised interactions. If the theory has no other higher dimensional operators, under additional assumptions for the analytical continuation Minkowski-Euclidean space, the theory can be renormalisable. We provide examples where a free theory with trivial supersymmetry breaking provided by a linear superpotential becomes, in the presence of higher derivatives terms and in the second order version, a non-trivial interactive one with spontaneous supersymmetry breaking. The couplings of the equivalent theory acquire a threshold correction through their dependence on the scale of the higher dimensional operator(s). The scalar potential in the second order theory is not necessarily positive definite, and one can in principle have a vanishing potential with broken supersymmetry. We provide an application to MSSM and argue that at tree-level and for a mass scale associated to a higher derivative term in the TeV range, the Higgs mass can be lifted above the current experimental limits.

Spontaneous R-symmetry breaking in O'Raifeartaigh models

We study the question of whether spontaneous U(1)_R breaking can occur in O'Raifeartaigh-type models of spontaneous supersymmetry breaking. We show that in order for it to occur, there must be a field in the theory with R-charge different from 0 or 2. We construct the simplest O'Raifeartaigh model with this property, and we find that for a wide range of parameters, it has a meta-stable vacuum where U(1)_R is spontaneously broken. This suggests that spontaneous U(1)_R breaking actually occurs in generic O'Raifeartaigh models.

Spontaneous supersymmetry breaking by large- N matrices

Motivated by supersymmetry breaking in matrix model formulations of superstrings, we present some concrete models, in which the supersymmetry is preserved for any finite N, but gets broken at infinite N, where N is the rank of matrix variables. The models are defined as supersymmetric field theories coupled to some matrix models, and in the induced action obtained after integrating out the matrices, supersymmetry is spontaneously broken only when N is infinity. In our models, the large value of N gives a natural explanation for the origin of small parameters appearing in the field theories which trigger the supersymmetry breaking. In particular, in the case of the O'Raifeartaigh model coupled to a certain supersymmetric matrix model, a nonsupersymmetric metastable vacuum appears near the origin of the field space, which is far from the position of the supersymmetric vacuum. We estimate its lifetime as a function of N.