Fayet Iliopoulos Research Articles

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.

Nonlinear [formula omitted] supersymmetry, effective actions and moduli stabilization

Nonlinear supersymmetry is used to compute the general form of the effective D-brane action in type I string theory compactified to four dimensions in the presence of internal magnetic fields. In particular, the scalar potential receives three contributions: (1) a nonlinear part of the D-auxiliary component, associated to the Dirac–Born–Infeld action; (2) a Fayet–Iliopoulos (FI) D-term with a moduli-dependent coefficient; (3) a D-auxiliary independent (but moduli dependent) piece from the D-brane tension. Minimization of this potential leads to three general classes of vacua with moduli stabilization: (i) supersymmetric vacua allowing in general FI terms to be cancelled by non-trivial vacuum expectation values (VEV's) of charged scalar fields; (ii) anti-de Sitter vacua of broken supersymmetry in the presence of a non-critical dilaton potential that can be tuned at arbitrarily weak string coupling; (iii) if the dilaton is fixed in a supersymmetric way by three-form fluxes and in the absence of charged scalar VEV's, one obtains non-supersymmetric vacua with positive vacuum energy.

Fayet-Iliopoulos terms in AdS/CFT with flavour

We construct the gravity dual of a field theory with flavour in which there are Fayet-Iliopoulos (FI) terms present. For this purpose we turn on a constant Kalb-Ramond B field in four internal space directions of AdS_5 x S^5 together with a D7 brane probe wrapping AdS_5 x S^3. The B field induces noncommutativity on the four internal directions of the D7 brane probe perpendicular to the AdS boundary. We argue on general grounds that the moduli space of the Higgs part of mixed Coulomb-Higgs states in the dual field theory at the boundary is described by the ADHM equations for noncommutative instantons on the four internal directions of the D7 brane probe. In particular, the global symmetries match. The FI term arises as the holographic dual of an anti-selfdual B field. We discuss possible applications for this construction.

Small extra dimensions from the interplay of gauge and supersymmetry breaking

Higher-dimensional theories provide a promising framework for unified extensions of the supersymmetric Standard Model. Compactifications to four dimensions often lead to U ( 1 ) symmetries beyond the Standard Model gauge group, whose breaking scale is classically undetermined. Without supersymmetry breaking, this is also the case for the size of the compact dimensions. Fayet–Iliopoulos terms generically fix the scale M of gauge symmetry breaking. The interplay with supersymmetry breaking can then stabilize the compact dimensions at a size 1 / M , much smaller than the inverse supersymmetry breaking scale 1 / μ . We illustrate this mechanism with an SO ( 10 ) model in six dimensions, compactified on an orbifold.

Metastable vacua in perturbed Seiberg–Witten theories. Part 2: Fayet–Iliopoulos terms and Kähler normal coordinates

We show that the perturbation of an N = 2 supersymmetric gauge theory by a superpotential linear in the Kähler normal coordinates of the Coulomb branch, discussed in [H. Ooguri, Y. Ookouchi, C.S. Park, Metastable vacua in perturbed Seiberg–Witten theories, arXiv: 0704.3613 [hep-th]], is equivalent to the perturbation by Fayet–Iliopoulos terms. It follows that the would-be meta-stable vacuum at the origin of the normal coordinates in fact preserves N = 1 supersymmetry unless the superpotential is truncated to a finite-degree polynomial of the adjoint scalar fields. We examine the criteria for supersymmetry breaking under a perturbation by Fayet–Iliopoulos terms and present a general classification of non-supersymmetric critical points. In some explicit examples, we are also able to study local stability of these points and demonstrate that, if the perturbation is chosen appropriately, they indeed correspond to supersymmetry-breaking vacua. Relations of these constructions to flux compactifications and geometric meta-stability are also discussed.

Metastable vacuum in spontaneously brokenN=2supersymmetric gauge theory

We consider an $\mathcal{N}=2$ supersymmetric $SU(2)\ifmmode\times\else\texttimes\fi{}U(1)$ gauge theory with ${N}_{f}=2$ massless flavors and a Fayet-Iliopoulos (FI) term. In the presence of the FI term, supersymmetry is spontaneously broken at tree level (on the Coulomb branch), leaving a pseudoflat direction in the classical potential. This vacuum degeneracy is removed once quantum corrections are taken into account. Because of the $SU(2)$ gauge dynamics, the effective potential exhibits a local minimum at the dyon point, where not only supersymmetry but also $U(1{)}_{R}$ symmetry is broken, while a supersymmetric vacuum would be realized toward infinity with the runaway behavior of the potential. This local minimum is found to be parametrically long-lived. Interestingly, from a phenomenological point of view, in this metastable vacuum the massive hypermultiplets inherent in the theory play the role of the messenger fields in the gauge mediation scenario, when the standard model gauge group is embedded into their flavor symmetry.

Geometric transitions and D-term SUSY breaking

We propose a new way of using geometric transitions to study metastable vacua in string theory and certain confining gauge theories. The gauge theories in question are N = 2 supersymmetric theories deformed to N = 1 by superpotential terms. We first geometrically engineer supersymmetry-breaking vacua by wrapping D5 branes on rigid 2-cycles in non-compact Calabi–Yau geometries, such that the central charges of the branes are misaligned. In a limit of slightly misaligned charges, this has a gauge theory description, where supersymmetry is broken by Fayet–Iliopoulos D-terms. Geometric transitions relate these configurations to dual Calabi–Yaus with fluxes, where H RR , H NS and dJ are all non-vanishing. We argue that the dual geometry can be effectively used to study the resulting non-supersymmetric, confining vacua.

New model of [formula omitted] superconformal mechanics

Using an N=4, d=1 superfield approach, we construct an N=8 supersymmetric action of the self-interacting off-shell N=8 multiplet (1,8,7). This action is found to be invariant under the exceptional N=8,d=1 superconformal group F(4) with the R-symmetry subgroup SO(7). The general N=8 supersymmetric (1,8,7) action is a sum of the superconformal action and the previously known free bilinear action. We show that the general action is also superconformal, but with respect to redefined superfield transformation laws. The scalar potential can be generated by two Fayet–Iliopoulos N=4 superfield terms which preserve N=8 supersymmetry but break the superconformal and SO(7) symmetries.

The common origin of linear and nonlinear chiral multiplets in [formula omitted] mechanics

Elaborating on previous work [F. Delduc, E. Ivanov, Nucl. Phys. B 753 (2006) 211, hep-th/0605211; F. Delduc, E. Ivanov, Nucl. Phys. B 770 (2007) 179, hep-th/0611247], we show how the linear and nonlinear chiral multiplets of N = 4 supersymmetric mechanics with the off-shell content ( 2 , 4 , 2 ) can be obtained by gauging three distinct two-parameter isometries of the “root” ( 4 , 4 , 0 ) multiplet actions. In particular, two different gauge groups, one Abelian and one non-Abelian, lead, albeit in a disguised form in the second case, to the same (unique) nonlinear chiral multiplet. This provides an evidence that no other nonlinear chiral N = 4 multiplets exist. General sigma model type actions are discussed, together with the restricted potential terms coming from the Fayet–Iliopoulos terms associated with Abelian gauge superfields. As in our previous work, we use the manifestly supersymmetric language of N = 4 , d = 1 harmonic superspace. A novel point is the necessity to use in parallel the λ and τ gauge frames, with the “bridges” between these two frames playing a crucial role. It is the N = 4 harmonic analyticity which, though being non-manifest in the τ frame, gives rise to both linear and nonlinear chirality constraints.

P-term potentials from 4-D supergravity

P-term inflation arises in some models of brane inflation. Within N = 2 supersymmetry the scalar potential contains a vector of Fayet-Iliopoulos (FI) terms ξi. Depending on the direction of this vector it is possible to get D-term and F-term inflation or a mix of these models. In this paper we review the problems of embedding the P-term model in supergravity and show how these can be solved by considering the truncation from an N = 2 theory to N = 1. We show that with a simple gauging the scalar potential can include F-term or D-term parts but not both. The gauging can be altered so that both F-terms and D-terms containing FI constants can be included. In all cases we display the inflationary trajectory and, if it exists, the supersymmetric minimum.

Deformation of Dijkgraaf–Vafa relation via spontaneously broken [formula omitted] supersymmetry

It is known that the fermionic shift symmetry of the N=1, U(N) gauge model with a superpotential of an adjoint chiral superfield is replaced by the second (spontaneously broken) supersymmetry in the N=2, U(N) gauge model with a prepotential and Fayet–Iliopoulos parameters. Based on a diagrammatic analysis, we demonstrate how the well-known form of the effective superpotential in the former model is modified in the latter. A set of two equations on the one-point functions stating the Konishi anomaly is modified accordingly.

A KIND OF PREDICTION FROM STRING PHENOMENOLOGY: EXTRA MATTER AT LOW ENERGY

We review the possibility that the Supersymmetric Standard Model arises from orbifold constructions of the E8×E8 Heterotic Superstring, and the phenomenological properties that such a model should have. In particular, trying to solve the discrepancy between the unification scale predicted by the Heterotic Superstring (≈g GUT × 5.27 × 1017 GeV ) and the value deduced from LEP experiments (≈2 × 1016 GeV ), we will predict the presence at low energies of three families of Higgses and vector-like colour triplets. Our approach relies on the Fayet–Iliopoulos breaking, and this is also a crucial ingredient, together with having three Higgs families, to obtain in these models an interesting pattern of fermion masses and mixing angles at the renormalizable level. Namely, after the gauge breaking some physical particles appear combined with other states, and the Yukawa couplings are modified in a well-controlled way. On the other hand, dangerous flavour-changing neutral currents may appear when fermions of a given charge receive their mass through couplings with several Higgs doublets. We will address this potential problem, finding that viable scenarios can be obtained for a reasonable light Higgs spectrum.

Partial breaking of [formula omitted] supersymmetry and decoupling limit of Nambu–Goldstone fermion in [formula omitted] gauge model

We study the N = 1 U ( N ) gauge model obtained by spontaneous breaking of N = 2 supersymmetry. The Fayet–Iliopoulos term included in the N = 2 action does not appear in the resulting N = 1 action and the superpotential is modified to break discrete R symmetry. We take a limit in which the Kähler metric becomes flat and the superpotential preserves non-trivial form. The Nambu–Goldstone fermion is decoupled from other fields but the resulting action is still N = 1 supersymmetric. It shows the origin of the fermionic shift symmetry in N = 1 U ( N ) gauge theory.

Moduli corrections to D-term inflation

We present a D-term hybrid inflation model, embedded in supergravity with moduli stabilization.Its novel features allow us to overcome the serious challenges of combiningD-term inflation and moduli fields within the same string motivatedtheory. One salient point of the model is the positive definite upliftingD-term arising from the moduli stabilization sector. By coupling thisD-term to the inflationary sector, we generate an effective Fayet–Iliopoulos term. Moduli correctionsto the inflationary dynamics are also obtained. Successful inflation is achieved for a limitedrange of parameter values with spectral index compatible with the WMAP3 data. CosmicD-term strings are also formed at the end of inflation; these are no longerBogomol’nyi–Prasad–Sommerfeld (BPS) objects. The properties of the strings are studied.

Precision Sparticle Predictions and Anomaly Mediation

We consider the sparticle spectra that arise when anomaly mediation is the source of supersymmetry-breaking and the tachyonic slepton problem is solved by a Fayet-Iliopoulos (FI) D -term. We also show how this can lead to a minimal viable extension of anomaly mediation, in which the gauge symmetry associated with this D -term is broken at very high energies, leaving as its footprint in the low energy theory only the required D -terms and seesaw neutrino masses.

Linearizing N=3 nonlinear supersymmetry in two dimensions

Abstract We investigate for N = 3 supersymmetry (SUSY) in D = 2 the algebraic relation between the Volkov–Akulov (VA) model of nonlinear (NL) SUSY and a (renormalizable) SO(3) vector supermultiplet of linear (L) SUSY. We derive SUSY and SO(3) invariant relations between component fields of the vector supermultiplet and Nambu–Goldstone fermions of the VA model at leading orders by using three arbitrary dimensionless parameters which can be recasted as the vacuum expectation values of auxiliary fields in the vector supermultiplet. Two different irreducible representations of SO(3) super-Poincare symmetry which appear in the same massless state are compatible with each other in the linearization of NL SUSY. The equivalence of a NL SUSY VA action to a free L SUSY action containing the Fayet–Iliopoulos D term which indicates a spontaneously SUSY breaking is also discussed explicitly according to the SUSY invariant relations.

Gauging [formula omitted] supersymmetric mechanics

We argue that off-shell dualities between d = 1 supermultiplets with different sets of physical bosonic components and the same number of fermionic ones are related to gauging some symmetries in the actions of the supermultiplets with maximal sets of physical bosons. Our gauging procedure uses off-shell superfields and so is manifestly supersymmetric. We focus on N = 4 supersymmetric mechanics and show that various actions of the multiplet ( 3 , 4 , 1 ) amount to some gauge choices in the gauged superfield actions of the linear or nonlinear ( 4 , 4 , 0 ) multiplets. In particular, the conformally invariant ( 3 , 4 , 1 ) superpotential is generated by the Fayet–Iliopoulos term of the gauge superfield. We find a new nonlinear variant of the multiplet ( 4 , 4 , 0 ) , such that its simplest superfield action produces the most general 4-dim hyper-Kähler metric with one triholomorphic isometry as the bosonic target metric. We also elaborate on some other instructive examples of N = 4 superfield gaugings, including a non-Abelian gauging which relates the free linear ( 4 , 4 , 0 ) multiplet to a self-interacting ( 1 , 4 , 3 ) multiplet.

Formula omitted]-term hybrid inflation with electroweak-scale lepton number violation

We study F-term hybrid inflation in a novel supersymmetric extension of the SM with a subdominant Fayet–Iliopoulos D-term. We call this particular form of inflation, in short, FD-term hybrid inflation. The proposed model ties the μ-parameter of the MSSM to an SO(3)-symmetric Majorana mass mN, through the vacuum expectation value of the inflaton field. The late decays of the ultraheavy particles associated with the extra U(1) gauge group, which are abundantly produced during the preheating epoch, could lower the reheat temperature even up to 1 TeV, thereby avoiding the gravitino overproduction problem. The baryon asymmetry in the Universe can be explained by thermal electroweak-scale resonant leptogenesis, in a way independent of any pre-existing lepton- or baryon-number abundance. Further cosmological and particle-physics implications of the FD-term hybrid model are briefly discussed.

Brane world effective actions for D-branes with fluxes

We develop systematic string techniques to study brane world effective actions for models with magnetized (or equivalently intersecting) D-branes. In particular, we derive the dependence on all NS–NS moduli of the kinetic terms of the chiral matter in a generic non-supersymmetric brane configurations with non-commuting open string fluxes. Near a N = 1 supersymmetric point the effective action is consistent with a Fayet–Iliopoulos supersymmetry breaking and the normalization of the scalar kinetic terms is nothing else than the Kähler metric. We also discuss, from a stringy perspective, D and F term breaking mechanisms, and how, in this generic set up, the Kähler metric enters in the physical Yukawa couplings.

Partial supersymmetry breaking and [formula omitted][formula omitted] gauge model with hypermultiplets in harmonic superspace

We provide a manifestly N = 2 supersymmetric formulation of the N = 2 U ( N c ) gauge model constructed in terms of N = 1 superfields in hep-th/0409060. The model is composed of N = 2 vector multiplets in harmonic superspace and can be viewed as the N = 2 U ( N c ) Yang–Mills effective action equipped with the electric and magnetic Fayet–Iliopoulos terms. We generalize this gauge model to an N = 2 U ( N c ) QCD model by introducing N = 2 hypermultiplets in harmonic superspace which include both the fundamental representation of U ( N c ) and the adjoint representation of U ( N c ) . The effect of the magnetic Fayet–Iliopoulos term is to shift the auxiliary field by an imaginary constant. Examining vacua of the model, we show that N = 2 supersymmetry is spontaneously broken down to N = 1 .