Amit Giveon, David Kutasov, Oleg Lunin
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.
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We show in two dimensional space-time (d = 2) the relation between a N = 2 nonlinear supersymmetric (NLSUSY) model and a N = 2 linear (L) SUSY Yang-Mills (SYM) theory with matter (N = 2 LSUSY QCD theory). We give a new interpretation of four Nambu-Goldstone fermion (superon) contact terms, which emerge from a N = 2 general SUSY QCD (composite) action, as mass terms for LSUSY supermultiplets and discuss the possible SUSY breaking mechanism in NL/L SUSY relation for SUSY gauge theories in d = 2.
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 me…
Motivated by a recent conjecture [1] that quantum corrections and the UV/IR connection modify the classical relation between SUSY breaking and the cosmological constant to the phenomenologically acceptable : $M_{SUSY} \sim M_P (Λ/M_P^4)^{1/8}$, we study SUSY breaking by boundary conditions in noncommutative field theories. In commutative field theory the violations of SUSY are finite and vanish as the inverse fourth power of the radius of the SUSY violating circle. We show that in the noncommutative theory, as a consequence of its UV/IR connection, the perturbative corrections to SUSY breaking…
The analysis of spontaneous gauge symmetry breaking of N=1 supersymmetric SU(N_c) Yang-Mills theory with matter is performed. The supersymmetric $R_ξ$-gauge is used and its non-local effects investigated. Superpropagators and vertices are computed, and it is shown that the non-local terms introduced by the $R_ξ$-gauge-fixing are well-behaved in general gauge at one-loop. It is argued that this feature generalizes to multiple loops.
In these notes, we emphasize the rôle of spontaneous broken global discrete symmetries acting on the moduli space of $N=2$ susy Yang-Mills theories and show how they can be used, together with the BPS condition, as a spectrum generating symmetry. In particular, in the strong-coupling region, all BPS states come in multiplets of this broken symmetry. This played a key rôle in the determination of the strong-coupling spectra.
We show explicitly by the heuristic and practical arguments that for $N = 2$ supersymmetry (SUSY) a SUSY invariant relation between component fields of a vector supermultiplet of linear SUSY and Nambu-Goldstone fermions of the Volkov-Akulov model of nonlinear SUSY is written by using only three arbitrary dimensionless parameters, which can be recasted as the vacuum expectation values of auxiliary fields in the vector supermultiplet.
The multidimensional N=4 supersymmetric quantum mechanics (SUSY QM) is constructed and the various possibilities for partial supersymmetry breaking are discussed. It is shown that quantum mechanical models with one quarter, one half and three quarters of unbroken(broken) supersymmetries can exist in the framework of the multidimensional N=4 SUSY QM.
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 consider the problem of supersymmetry breaking in 5 dimensional N=1 supersymmetric models with $S^1/Z_2$ compactification.
We review recent work identifying soft SUSY-breaking terms in local type II string models with branes and magnetic fluxes. We then make a new observation about the configuration space of D-branes in Calabi-Yau backgrounds, and identify vevs for nonperturbative charged hypermultiplets in Calabi-Yau backgrounds with N=2 Fayet-Iliopoulos terms.
We show that the physics of D-brane theories that exhibit dynamical SUSY breaking due to stringy instanton effects is well captured by geometric transitions, which recast the non-perturbative superpotential as a classical flux superpotential. This allows for simple engineering of Fayet, Polonyi, O'Raifeartaigh, and other canonical models of supersymmetry breaking in which an exponentially small scale of breaking can be understood either as coming from stringy instantons or as arising from the classical dynamics of fluxes.
We review the Seiberg-Witten construction of low-energy effective actions and BPS spectra in SUSY gauge theories and its formulation in terms of integrable systems. It is also demonstrated how this formulation naturally appears from the compactified version of the theory with partially broken supersymmetry so that the integrable structures arise from the relation between bare and quantum variables and superpotentials of SUSY gauge theories. The Whitham integrable systems, literally corresponding to the uncompactified theory, are then restored by averaging over fast variables in the decompactif…
The effective potential in the model introduced by Buchbinder-Inagaki-Odintsov (BIO) which represents SUSY NJL model non-minimally coupled with the external gravitational field is found. The topology of the space is considered to be non-trivial. Chiral symmetry breaking under the action of external curvature and non-trivial topology is investigated.
Supersymmetry (SUSY) breaking without messenger fields is proposed. We assume that our world is on a wall and SUSY is broken only by the coexistence of another wall with some distance from our wall. The Nambu-Goldstone (NG) fermion is localized on the distant wall. Its overlap with the wave functions of physical fields on our wall gives the mass splitting of physical fields on our wall thanks to a low-energy theorem. We propose that this overlap provides a practical method to evaluate mass splitting in models with SUSY breaking due to the coexistence of walls.
A new simple mechanism for SUSY breaking is proposed due to the coexistence of BPS domain walls. It is assumed that our world is on a BPS domain wall and that the other BPS wall breaks the SUSY preserved by our wall. This mechanism requires no messenger fields nor complicated SUSY breaking sector on any of the walls. We obtain an ${\cal N}=1$ model in four dimensions which has an exact solution of a stable non-BPS configuration of two walls. We propose that the overlap of the wave functions of the N-G fermion and those of physical fields provides a practical method to evaluate SUSY breaking ma…
We propose a new mechanism of spontaneous supersymmetry breaking. The existence of extra dimensions with nontrivial topology plays an important role. We investigate new features resulted from the mechanism in two simple supersymmetric Z_2 and U(1) models. One of remarkable features is that there exists a phase in which the translational invariance for the compactified directions is broken spontaneously, accompanying the breakdown of the supersymmetry. The mass spectrum of the models appeared in reduced dimensions is a full of variety, reflecting the highly nontrivial vacuum structure of the mo…
We present simple string models which dynamically break supersymmetry without non-Abelian gauge dynamics. The Fayet model, the Polonyi model, and the O'Raifeartaigh model each arise from D-branes at a specific type of singularity. D-brane instanton effects generate the requisite exponentially small scale of supersymmetry breaking.
I present a heuristic calculation of the critical exponent relating the gravitino mass to the cosmological constant in a de Sitter universe. The ingredients for the calculation are the area law for entropy, an R symmetry of the low energy effective Lagrangian, and a crude picture of the degenerate levels of the cosmological horizon.
A generic lesson of string theory is that the coupling constants of an effective low energy theory are determined by the vacuum values of a set of fields - the so-called moduli - some of which are stabilized at relatively low masses by non-perturbative effects. We argue that the physics of these moduli cannot be separated from the issues of dynamical and gauge mediated supersymmetry breaking. To illustrate this point we present a modified version of the type IIB KKLT model where the criteria for gauge mediated SUSY breaking may be realized.
It is well known that D-brane instantons can generate contributions to the effective superpotential of gauge theories living on D-branes which are perturbatively forbidden by global U(1) symmetries. We extend this idea to theories with supersymmetry breaking, studying the effect of D-brane instantons stretched between the SUSY-breaking and visible sectors. Analogously to what happens in the SUSY case, this mechanism can give rise to perturbatively forbidden soft terms (among other effects). We introduce and discuss general properties of instanton mediation. We illustrate our ideas in simple Ty…
A simple mechanism for SUSY breaking is proposed due to the coexistence of BPS domain walls. It requires no messenger fields nor complicated SUSY breaking sector on any of the walls. We assumed that our world is on a BPS domain wall and that the other BPS wall breaks the SUSY preserved by our wall. We obtain an ${\cal N}=1$ model in four dimensions which admits an exact solution of a stable non-BPS configuration of two walls. The stability is assured by a topological quantum number associated with the winding on the field space of the topology of $S^1$. We propose that the overlap of the wave …
In this letter we would like to apply the superconformal index technique to give one more evidence for the theory proposed by Intriligator, Seiberg and Shenker (ISS) as being described by interacting conformal field theory in its IR fixed point.
An analytic construction of compact Calabi-Yau manifolds with del Pezzo singularities is found. We present complete intersection CY manifolds for all del Pezzo singularities and study the complex deformations of these singularities. An example of the quintic CY manifold with del Pezzo 6 singularity and some number of conifold singularities is studied in details. The possibilities for the 'geometric' and ISS mechanisms of dynamical SUSY breaking are discussed. As an example, we construct the ISS vacuum for the del Pezzo 6 singularity.
We claim that 3d monopole quivers, theories with product gauge groups interacting through Affleck-Harvey-Witten superpotentials, are a natural setup for the study of spontaneous breaking 3d $\mathcal{N}=2$ supersymmetry. We give evidence of this statement by studying various examples of increasing complexity, considering quivers that are mirror dual to Wess-Zumino models. These Wess-Zumino models, in opportune regimes of parameters, break supersymmetry in perturbatively controllable (meta)stable vacua.
We propose a new mechanism of spontaneous supersymmetry breaking. The existence of extra dimensions with nontrivial topology plays an important role. We investigate new features resulting from this mechanism. One noteworthy feature is that there exists a phase in which the translational invariance for the compactified directions is broken spontaneously. The mechanism we propose also yields quite different vacuum structures for models with different global symmetries.
This is the written version of a talk given at the Santa Barbara Workshop on Supersymmetry in December of 1995. It summarizes a collection of results on superstring cosmology obtained by the author and various collaborators, and contains some speculations about the resolution of the cosmological constant and vacuum selection problems in string theory.
We introduce an explicit supersymmetric unification model where grand unified gauge symmetry breaking and supersymmetry (SUSY) breaking are caused by the same field. Besides, the SM-charged particles are also predicted by the symmetry breaking sector, and their loop corrections induce the soft SUSY breaking terms. Especially, nonzero A-term and B-term are generated at one-loop level according to the mediation via the vector superfields, so that the electro-weak symmetry breaking and 125 GeV Higgs mass could be achieved even if the stop mass is around 1 TeV.
We study supersymmetry breaking metastable vacua arising from beta deformed quiver gauge theories. The relation between the bounds on metastability and the deformation are discussed. Metastable supersymmetry breaking vacua are found in the IR of beta deformed cascading quivers with vector-like field content. Furthermore the limiting case of massive Nf=Nc SQCD appears in the IR of gauge theories with chiral-like field content. We comment on the field theory origin of the deformation and on possible applications in AdS/CFT.
Spontaneous supersymmetry (SUSY) breaking is revealed in all phenomena in which vacuum condensates are physically relevant. The dynamical breakdown of SUSY is generated by the condensates themselves, which lift the zero point energy. Evidence is presented in the case of the Wess-Zuimino model, and the flavor mixing case is treated in detail.
We show the existence of a supersymmetry-breaking mechanism in string theory, where N=4 supersymmetry is broken spontaneously to N=2 and N=1 with moduli-dependent gravitino masses. The BPS spectrum of the theory with lower supersymmetry is in one-to-one correspondence with the spectrum of the heterotic N=4 string. The mass splitting of the N=4 spectrum depends on the moduli as well as the three R-symmetry charges. In the case of N=4 \to N=2, the perturbative N=2 prepotential is determined by the perturbative N=4 BPS states. This observation led us to suggest a method that determines the exact …
In this paper we investigate the localisation of SUSY-breaking branes which, in the smeared approximation, support specific non-BPS vacua. We show, for a wide class of boundary conditions, that there is no flux vacuum when the branes are described by a genuine delta-function. Even more, we find that the smeared solution is the unique solution with a regular brane profile. Our setup consists of a non-BPS AdS_7 solution in massive IIA supergravity with smeared anti-D6-branes and fluxes T-dual to ISD fluxes in IIB supergravity.
We settle a result on generic exactness of SUSY in 3-D, and provide a mechanism of F-term spontaneous breaking of 3-D SUSY, with a different set of tools from those used by O'Raifeartaigh in his seminal work on 4-D SUSY. In our study, we use techniques of projective algebraic geometry so as to deal successfully with cubic hypersurfaces.
We carry out a model-independent EFT method study on the vacuum statistics of general F-term SUSY breaking models. Assuming a smooth distribution of Lagrangian parameters, SUSY breaking vacua are rare in global SUSY models with a canonical Kähler potential, and have a peaked distribution near the cut-off of the SUSY breaking scale in both global SUSY and SUGRA models with a general Kähler potential. After including different mass scales in the Lagrangian, we compare the total number of SUSY and non-SUSY vacua and estimate quantitatively the rareness of SUSY breaking. The EFT method provides a …
We suggest simple models of spontaneous parity violation in supersymmetric strong gauge theory. We focus on left-right symmetric model and investigate vacuum with spontaneous parity violation. Non-perturbative effects are calculable in supersymmetric gauge theory, and we suggest two new models. The first model shows confinement, and the second model has a dual description of the theory. The left-right symmetry breaking and electroweak symmetry breaking are simultaneously occurred with the suitable energy scale hierarchy. The second model also induces spontaneous supersymmetry breaking.
We point out consequences of the assumption that supersymmetry breaking is of cosmological origin.
We study soft SUSY breaking terms in heterotic M-theory. We show that both weakly and strongly coupled heterotic string models lead to the same relations of soft SUSY breaking terms, $A=-M$ and $m^2 = M^2/3$, up to $O((αT/S)^2)$.
We investigate supersymmetry (SUSY) breaking scenarios where both SUSY and Lorentz symmetry are broken spontaneously. For concreteness, we propose models in which scalar fluid or vector condensation breaks Lorentz symmetry and accordingly SUSY. Then, we examine whether such scenarios are viable for realistic model buildings. We find, however, that the scalar fluid model suffers from several issues. Then, we extend it to a vector condensation model, which avoids the issues in the scalar fluid case. We show that accelerated expansion and soft SUSY breaking in matter sector can be achieved. In ou…
We compute the SUSY-breaking soft terms in a magnetized D7-brane model with MSSM-like spectrum, under the general assumption of non-vanishing auxiliary fields of the dilaton and Kahler moduli. As a particular scenario we discuss SUSY breaking triggered by ISD or IASD 3-form fluxes.
We study Yukawa unification in string models with moduli-dominant SUSY breaking. This type of SUSY breaking in general leads to non-universal soft masses, i.e., soft scalar masses and gaugino masses. Such non-universality is important for phenomenological aspects of Yukawa unification, i.e., successful electroweak breaking, SUSY corrections to the bottom mass and the branching ratio of $b \to s γ$. We show three regions in the whole parameter space which lead to successful electroweak breaking and allow small SUSY corrections to the bottom mass. For these three regions we investigate the $b \t…
We study aspects of Wess-Zumino models related to SUSY and R-symmetry breaking at tree-level. We present a recipe for constructing a wide class of tree-level SUSY and R-breaking models. We also deduce a general property shared by all tree-level SUSY breaking models that has broad application to model building. In particular, it explains why many models of direct gauge mediation have anomalously light gauginos (even if the R-symmetry is broken spontaneously by an order one amount). This suggests new approaches to dynamical SUSY breaking which can generate large enough gaugino masses.
Scalar decay into gravitinos is studied in the presence of D-term supersymmetry (SUSY) breaking. The gravitinos produced by the decay of coherent oscillations of scalar fields, such as moduli and inflatons, cause cosmological problems. We show the general formula for the partial decay rate of the scalar into two gravitinos. Applying it to a concrete model of D-term SUSY breaking, we find that D-term SUSY breaking can suppress gravitino production.
It is well known that there are different global (i.e. $M_{P}\rightarrow\infty$) limits of N=1 supergravity. We distinguish between these limits and their relevance to low energy phenomenology. We discuss a) fermion mass matrices and recently proved theorems in global SUSY b) stability issues and SUSY breaking d) R-symmetry and a recently derived bound on the superpotential and e) FI terms in global and local SUSY.
We study N=1 global and local supersymmetric theories with a continuous global $U(1)_R$ symmetry as models of dynamical supersymmetry (SUSY) breaking. We introduce explicit R-symmetry breaking terms into such models, in particular a generalized O'Raifeartaigh model. Such explicit R-symmetry breaking terms can lead to a SUSY preserving minimum. We classify explicit R-symmetry breaking terms by the structure of newly appeared SUSY stationary points as a consequence of the R-breaking effect, which could make the SUSY breaking vacuum metastable. We show that the R-breaking terms are basically divi…
A SUSY breaking mechanism with no messenger fields is proposed. We assume that our world is on a domain wall and SUSY is broken only by the coexistence of another wall with some distance from our wall. We find an ${\cal N}=1$ model in four dimensions which admits an exact solution of a stable non-BPS configuration of two walls and studied its properties explicitly. We work out how various soft SUSY breaking terms can arise in our framework. Phenomenological implications are briefly discussed. We also find that effective SUSY breaking scale becomes exponentially small as the distance between tw…
We study moduli-dominated SUSY breaking within the framework of string models. This type of SUSY breaking in general leads to non-universal soft masses, i.e. soft scalar masses and gaugino masses. Further gauginos are lighter than sfermions. This non-universality has phenomenologically important implications. We investigate radiative electroweak symmetry breaking in the mass spectrum derived from moduli-dominated SUSY breaking, where the lightest chargino and neutralino are almost gauginos. Moreover, constraints from the branching ratio of $b \to s γ$ and the relic abundance of the LSP are als…
Supersymmetry (SUSY) relating bosons and fermions plays an important role in unifying different fundamental interactions in particle physics. Since no superpartners of elementary particles have been observed, SUSY, if present, must be broken at low-energy. This makes it important to understand how SUSY is realized and broken, and study their consequences. We show that an $\mathcal{N}=(1,0)$ SUSY, arguably the simplest type, can be realized at the edge of the Moore-Read quantum Hall state. Depending on the absence or presence of edge reconstruction, both SUSY-preserving and SUSY broken phases c…
We discuss the problem of metastable SUSY breaking in the landscape. While this is clearly crucial for the various de Sitter proposals, it is also interesting to consider the SUSY breaking challenge in the AdS context. For example, it could be that a stronger form of the non-SUSY AdS conjecture holds: It would forbid even metastable non-SUSY AdS in cases where the SUSY-breaking scale is parametrically above/below the AdS scale. At the technical level, the present paper proposes to break SUSY using the multi-cosine-shaped axion potentials which arise if a long winding trajectory of a `complex-s…
We present the mechanism of the dynamical supersymmetry (SUSY) breaking at the metastable vacuum in the N=1 U(N) SUSY gauge theory with adjoint superfields. The dynamical SUSY breaking is triggered by the non-vanishing D-term coupled to the observable sector, and is realized by the self-consistent Hartree-Fock approximation of the NJL type while it eventually brings us the non-vanishing F-term as well. We numerically check the local stability of our metastable vacuum.
We build explicit supersymmetric unification models where grand unified gauge symmetry breaking and supersymmetry (SUSY) breaking are caused by the same sector. Besides, the SM-charged particles are also predicted by the symmetry breaking sector, and they give the soft SUSY breaking terms through the so-called gauge mediation. We investigate the mass spectrums in an explicit model with SU(5) and additional gauge groups, and discuss its phenomenological aspects. Especially, nonzero A-term and B-term are generated at one-loop level according to the mediation via the vector superfields, so that t…
We construct an N=2 supersymmetric generalization of the N=1 supercurrent formalism of Komargodski and Seiberg (KS) and use it to show that N=2 theories with linear superconformal anomalies cannot break SUSY under certain broad assumptions. This result suggests that there are no metastable SUSY breaking vacua in a large class of theories that includes N=2 Super Yang-Mills (SYM).
The Hubble parameter during the inflationary era must be smaller than the gravitino mass if the moduli are stabilized by the Kachru-Kallosh-Linde-Trivedi mechanism. This condition represents the difficulty to combine the low scale SUSY breaking and the high scale inflation. We propose a simple mechanism which can naturally separate the inflation scale from the SUSY breaking scale today.
We propose the unified models of cosmological inflation, spontaneous SUSY breaking, and the dark energy (de Sitter vacuum) in $N=1$ supergravity with the dilaton-axion chiral superfield $T$ in the presence of an $N=1$ vector multiplet with the alternative Fayet-Iliopoulos term. By using the Kähler potential as $K=-α\log(T+\bar{T})$ and the superpotential as a sum of a constant and a linear term, we find that viable inflation is possible for $3\leqα\leqα_{\rm max}$ where $α_{\rm max}\approx 7.235$. Observations of the amplitude of primordial scalar perturbations fix the SUSY breaking scale in o…
SUSY breaking without messenger fields is proposed. We assume that our world is on a wall and SUSY is broken only by the coexistence of another wall with some distance from our wall. The Nambu-Goldstone fermion is localized on the distant wall. Its overlap with the wave functions of physical fields on our wall gives the mass splitting of physical fields on our wall thanks to a low-energy theorem. We propose that this overlap provides a practical method to evaluate mass splitting in models with SUSY breaking due to the coexisting walls.
We discuss the structure of the soft supersymmetry breaking terms in a MSSM like model, which can be derived from D7-branes with chiral matter fields from 2-form f-fluxes and supersymmetry breaking from 3-form G-fluxes.
A cardinal principle of any theory of spontaneous (${\cal N}=1$) supersymmetry breaking, is that the order parameter is a linear combination of the F and D terms. Also as long as the supersymmetry of the action is preserved at the quantum level, this principle should be valid after the appropriate corrections are incorporated into the Kaehler potential, the superpotential, and the gauge coupling functions that define the theory. The claim that in AMSB there is an extra term for the gaugino mass that is proportional to the gravitino mass, is then equivalent to the statement that quantum effects…
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…
We propose a new chiral model of metastable supersymmetry breaking in the conformal window via chiral/nonchiral Seiberg duality, which is focused on Spin(7)/SU(N_f-4) duality in this letter. Following the approach of Intriligator-Seiberg-Shih model, a small mass perturbation in the nonchiral theory leads to supersymmetry breaking by rank condition in the chiral dual description.
We study gauge mediation in a wide class of O'Raifeartaigh type models where supersymmetry breaking metastable vacuum is created by gravity and/or quantum corrections. We examine their thermal evolution in the early universe and the conditions under which the susy breaking vacuum can be selected. It is demonstrated that thermalization typically makes the metastable supersymmetry breaking cosmologically disfavoured but this is not always the case. Initial conditions with the spurion displaced from the symmetric thermal minimum and a small coupling to the messenger sector can result in the reali…
The electroweak (EW) symmetry breaking in the simplest supersymmetric (SUSY) extensions of the standard model (SM), i.e. minimal and next-to-minimal supersymmetric standard models (MSSM and NMSSM), is considered. The spectrum of the Higgs particles, upper bound on the mass of the lightest Higgs boson and little hierarchy problem are discussed. The breakdown of gauge symmetry and Higgs phenomenology within the E6 inspired SUSY models with extra U(1)' factor are briefly reviewed.
We modify the first ISS model (hep-th/0602239) by gauging a diagonal flavour symmetry. We add additional multiplets transforming as fundamentals and anti-fundamentals under the gauged flavour group. Their number is chosen such that the microscopic theory is asymptotically free whereas in the Seiberg dual (w.r.t. the colour group) it changes to an infrared free theory. Non perturbative effects within the flavour group can correct the location of the supersymmetric vacuum. Statements about meta-stability of the susy breaking vacuum would require a two loop calculation. For general couplings, the…
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