We examine generalized O'Raifeartaigh models that feature multiple tree-level flat directions and only contain fields with R-charges 0 or 2. We show that spontaneous R-breaking at up to one-loop order is impossible in such theories. Specifically, we prove that the R-symmetric origin of field space is always a local minimum of the one-loop Coleman-Weinberg potential, generalizing an earlier result for the case of a single flat direction. This result has consequences for phenomenology and helps elucidate the behavior of various models of dynamical SUSY breaking.
We classify possible types of pseudomoduli which arise when supersymmetry is dynamically broken in infrared-free low-energy theories. We show that, even if the pseudomoduli potential is generated only at higher loops, there is a regime where the potential can be simply determined from a combination of one-loop running data. In this regime, we compute whether the potential for the various types of pseudomoduli is safe, has a dangerous runaway to the UV cutoff of the low-energy theory, or is incalculable. Our results are applicable to building new models of supersymmetry breaking. We apply the r…
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 o…
We analyze two loop quantum corrections for pseudomoduli in O'Raifeartaigh like models. We argue that R-symmetry can be spontaneously broken at two loop in non supersymmetric vacua. We provide a basic example with this property. We discuss on phenomenological applications.
We present an inflationary scenario based on a phenomenologically viable model with direct gauge mediation of low-scale supersymmetry breaking. Inflation can occur in the supersymmetry-breaking hidden sector. Although the reheating temperature from the inflaton decay is so high that the gravitino problem seems to be severe, late time entropy production from the decay of the pseudomoduli field associated with the supersymmetry breaking can dilute gravitinos sufficiently. We show that gravitinos are also produced from the pseudomoduli decay and there is a model parameter space where gravitinos c…
We study the D-term effect on runaway directions of the F-term scalar potential. A minimal renormalizable model is presented where supersymmetry is broken without any pseudomoduli. The model is applied to the hidden sector of gauge mediation for spontaneously breaking R symmetry and generating nonvanishing gaugino masses at the one-loop order.
We present gauge theory completions of Wess-Zumino models admitting supersymmetry breaking vacua with spontaneously broken R-symmetry. Our models are simple deformations of generalized ITIY models, a supersymmetric theory with gauge group Sp(N), N+1 flavors plus singlets, with a modified tree level superpotential which explicitly breaks (part of) the global symmetry. Depending on the nature of the deformation, we obtain effective O'Raifeartaigh-like models whose pseudomoduli space is locally stable in a neighborhood of the origin of field space, or in a region not including it. Hence, once emb…
It is proposed that an event that constitutes a quantum measurement corresponds to the spontaneous breaking of a symmetry in the measuring device over time.
A nonperturbative approach for spontaneous symmetry breaking is proposed. It is based on some properties of interacting field operators. As the consequences an additional terms like to m^2 A^2 appears in the initial Lagrangian.
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.
We show how translational invariance can be broken by the vacuum that drives the spontaneous symmetry breaking of extra-dimensional extensions of the Standard Model, when delta-like interactions between brane and bulk scalar fields are present. We explicitly build some examples of vacuum configurations, which induce the spontaneous symmetry breaking, and have non trivial profile in the extra coordinate.
We present a new picture of global symmetry breaking in quantum field theory and propose a novel realization of symmetry breaking phenomena in terms of the conserved charge associated with its symmetry. In particular, the fermion condensate of the vacuum state is examined when the spontaneous chiral symmetry breaking takes place. It is shown that the fermion condensate of the vacuum vanishes if the system is solved exactly, and therefore we cannot make use of the Goldstone theorem. As a perfect example, we present the Bethe ansatz vacuum of the Thirring model which shows the spontaneous chiral…
Non-Abelian discrete family symmetries play a pivotal role in the formulation of models with tri-bimaximal lepton mixing. We discuss how to obtain symmetries such as A4, semidirect product of Z7 and Z3, and Delta(27) from an underlying SU(3) gauge symmetry. Higher irreducible representations are required to achieve the spontaneous breaking of the continuous group. We present methods of identifying the required vacuum alignments and discuss in detail the symmetry breaking potentials.
We study the compatibility of spontaneous breaking of parity and successful cosmology in a left-right symmetric model where supersymmetry breaking is achieved in metastable vacua. We show that domain walls formed due to this breaking can be removed due to Planck scale suppressed terms, provided the parity breaking scale $M_R$ is constrained to remain smaller than $10^{10}-10^{11}$ GeV. Ensuring metastability is achieved naturally even if the entire mechanism operates at low scales, within a few orders of magnitude of the TeV scale. Taking $M_R$ as high as permitted, close to the acceptable reh…
The convexity of a scalar effective potential is a well known property, and, in the situation of spontaneous symmetry breaking, leads to the so-called Maxwell construction, characterised by a flat effective potential between the minima of the bare potential. Simple derivations are given here, which show how linear effective potentials arise from non-trivial saddles points which dominate the partition function, for a self-interacting scalar field and for a Yukawa model.
We study spontaneous supersymmetry breaking in N=2 globally supersymmetric theories describing a system of abelian vector multiplets. We find that the most general form of the action admits, in addition to the usual Fayet-Iliopoulos term, a magnetic Fayet-Iliopoulos term for the auxiliary components of dual vector multiplets. In a generic case, N=2 supersymmetry is broken down spontaneously to N=1. In some cases however, the scalar potential can drive the theory towards a N=2 supersymmetric ground state where massless dyons condense in the vacuum.
A promising approach to the Standard Model flavor puzzle is based on the idea that the $SU(3)^3$ quark-flavor symmetry is spontaneously broken by vacuum expectation values of `Yukawa fields' which minimize the symmetry invariant scalar potential at configurations corresponding to the observed quark masses and mixing angles. We show that this approach provides a simple and elegant explanation for CP conservation in strong interactions.
A very simple mechanism is proposed that stabilizes the orbifold geometry within the context of the Randall-Sundrum proposal for solving the hierarchy problem. The electroweak TeV scale is generated from the Planck scale by spontaneous breaking of the orbifold symmetry
I summarize the development of the ideas of Spontaneous symmetry breaking in the 1960s with an outline of the Guralnik, Hagen, Kibble (GHK) paper and include comments on the relationship of this paper to those of Brout, Englert and Higgs. I include some pictures from my "physics family album which might be of some amusement value".
I discuss historical material about the beginning of the ideas of spontaneous symmetry breaking and particularly the role of the Guralnik, Hagen Kibble paper in this development. I do so adding a touch of some more modern ideas about the extended solution-space of quantum field theory resulting from the intrinsic nonlinearity of non-trivial interactions.
We study two-dimensional QED with unequal charges at finite temperature, and show that there is a phase with a spontaneously broken $Z_n$ symmetry. In spite of this, we were not able to establish the presence of domain walls. The relevance for QCD in higher dimensions is discussed.
Elitzur's theorem stating the impossibility of spontaneous breaking of local symmetries in a gauge theory is reexamined. The existing proofs of this theorem rely on gauge invariance as well as positivity of the weight in the Euclidean partition function. We examine the validity of Elitzur's theorem in gauge theories for which the Euclidean measure of the partition function is not positive definite. We find that Elitzur's theorem does not follow from gauge invariance alone. We formulate a general criterion under which spontaneous breaking of local symmetries in a gauge theory is excluded. Final…
For spontaneous breaking of global or gauge symmetry, it is superfluous to assume that the vacuum expectation value of the scalar field manifesting the symmetry is nonvanishing. The vacuum with spontaneous symmetry breaking simply corresponds to nonzero number of particles of one or more components of the real scalar field.
In non-Abelian field theories with q-symmetry groups the massive particles have a non-local interpretation with a stringlike spectrum. It is shown that a massless vector similarly acquires a tower of masses by spontaneous symmetry breaking.
The simple examples of spontaneous breaking of various symmetries for the scalar theory with fundamental mass have been considered. Higgs generalizations on "fundamental mass" were introduced into the theory on a basis of the five-dimensional de Sitter space.
The concept of spontaneous symmetry breaking (SSB) generally lacks a simple and intuitive introduction in the literature. This gap is filled by defining SSB in a universal context beyond its usual applications in physics and by discussing some very simple, but stunning examples of the phenomenon.
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.
The personal and scientific history of the discovery of spontaneous symmetry breaking in gauge theories is outlined and its scientific content is reviewed
We show that one can obtain naturally the Cornell confining potential from the spontaneous symmetry breaking of scale invariance in gauge theory. At the classical level a confining force is obtained and at the quantum level, using a gauge invariant but path-dependent variables formalism, the Cornell confining potential is explicitly obtained.
With the elements of the Doplicher, Fredenhagen and Roberts (DFR) noncommutative formalism, we have constructed the standard electroweak model. To accomplish this task we have begun with the WM-product basis group of symmetry. We have introduced the spontaneous symmetry breaking and the hypercharge in DFR framework. The electroweak symmetry breaking was analyzed and the masses of the new bosons were computed.
We study models of spontaneous N=2 -> N=1 supergravity breaking in three space-time dimensions and discuss the topological Higgs- and super-Higgs mechanism which generates the masses for the spin-3/2 gravitino multiplet. The resulting N=1 spectrum and its effective action is analysed.
We show that in supersymmetric pure Yang Mills theories with arbitrary simple gauge group, the spontaneous breaking of chiral fermionic and bosonic charge by the associated gaugino and gauge boson condensates implies the spontaneous breaking of supersymmetry by the condensate of the underlying Lagrangian density. The explicit breaking of the restricted fermionic charge through the chiral anomaly is deferred to a secondary stage in the elimination of infrared singularities or long range forces.
The theory of symmetry breaking in presence of gauge fields is presented, following the historical track. Particular emphasis is placed upon the underlying concepts.
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.
Generic partial supersymmetry breaking of $N=2$ supergravity with zero vacuum energy and with surviving unbroken arbitrary gauge groups is exhibited. Specific examples are given.
I will discuss spontaneous conformal symmetry breaking in the strongly $γ$-deformed limit of the $\mathcal N=4$ supersymmetric Yang-Mills theory known as~\emph{Fishnet Conformal Field Theory}.
The spontaneous breaking of of translational invariance in non-commutative self-interacting scalar field theory in two dimensions is investigated by effective action techniques. The analysis confirms the existence of the stripe phase, already observed in lattice simulations, due to the non-local nature of the non-commutative dynamics.
We analyze the mechanism of spontaneous symmetry breaking of scale invariance in Galilean invariant field theories. We show that the existence of a dynamic gapless dilaton mode depends on whether the $U(1)$ particle number or the Galilean boost symmetry are spontaneously broken. When both scale and particle number symmetries are spontaneously broken there is one propagating gapless Nambu-Goldstone mode. Its dispersion relation is linear if the chemical potential is nonzero and quadratic otherwise. We discuss the reversibility of RG flows in such theories.
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.
We give a basic review of some recent developments in local supersymmetry breaking in 4-dimensional effective theories coming from compactifications of string and M-theory in the presence of non-trivial form and geometrical fluxes.
A possible mechanism for the spontaneous breaking of SUSY, based on the presence of vacuum condensates, is reviewed. Such a mechanism could occur in many physical examples, both at the fundamental and emergent level, and would be formally analogous to spontaneous SUSY breaking at finite temperature in the TFD formalism, in which case it can be applied as well. A possible experimental setup for detecting such a breaking through measurement of the Anandan-Aharonov invariants associated with vacuum condensates in an optical lattice model is proposed.
The prediction of a massless boson after the spontaneous chiral symmetry breaking in the classic paper of Nambu and Jona-Lasinio (NJL) is shown to be wrong. Their mistake is due to a carelessly employed perturbative vacuum when evaluating the boson mass by summing up one loop Feynman diagrams. With the proper symmetry broken vacuum, one obtains a finite boson mass depending on the coupling constant $G$.
In this paper we consider the Spontaneous Symmetry Breaking Mechanism (SSBM) in the Standard Model of particles in the unitary gauge. We show that the computation usually presented of this mechanism can be conveniently performed in a slightly different manner. As an outcome, the computation we present can change the interpretation of the SSBM in the Standard Model, in that it decouples the SU(2)-gauge symmetry in the final Lagrangian instead of breaking it.
One kind of spontaneous (2+1)-dimensional Lorentz symmetry breaking is discussed. The symmetry breaking pattern is $SO(2,1)\rightarrow SO(1,1)$. Using the coset construction formalism, we derive the Goldstone covariant derivative and the associated covariant gauge field. Finally, the two-derivative low-energy effective action of the Nambu-Goldstone bosons is obtained.
We discuss some issues related to spontaneous N=2-> N=1 supersymmetry breaking. In particular, we state a set of geometrical conditions which are necessary that such a breaking occurs. Furthermore, we discuss the low energy N=1 effective Lagrangian and show that it satisfies non-trivial consistency conditions which can also be viewed as conditions on the geometry of the scalar manifold.
We study the vacuum condensate characterizing many physical phenomena. We show that such a condensate may leads to non-trivial components of the dark energy and of the dark matter and may induces the spontaneous supersymmetry breaking, in a supersymmetric context. In particular, we consider the condensate induced by thermal states, fields in curved space-time and mixed particles.
We consider D-dimensional Lovelock gravity with only one term of higher-order Lovelock Lagrangian densities, and show that a product of Minkowski space-time and n-spheres is its vacuum solution. The most interesting feature of our model is that the spontaneous compactification of the extra dimensions results in reproduction of the Einstein gravity with no cosmological constant.
We consider the question which potentials in the action of a (1+1) dimensional scalar field theory allowing for spontaneous symmetry breaking have quantum fluctuations corresponding to reflectionless scattering data. The general problem of restoration from known scattering data is formulated and a number of explicit examples is given. Only certain sets of reflectionless scattering data correspond to symmetry breaking and all restored potentials are similar either to the Phi**4-model or to the sine-Gordon model.
We show that a system of bosons in a T=0 quantum field theory can present metastable ground states with spontaneous symmetry breaking, even in the absence of an imaginary mass term. This gives a natural explanation to the Davis-Shellard background field \exp(-i ω_0 t) and adds a new degree of freedom in boson systems, with possible applications in cosmology, condensed matter and high energy physics.
A model describing the $N=2$ supergravity interaction with vector and linear multiplets is constructed. It admits the introduction of the spontaneous breaking of supersymmetry with arbitrary scales, one of which may be equal to zero, which corresponds to partial super-Higgs effect ($N=2 \rightarrow N=1$). A cosmological term is automatically equal to zero.
We exploit boundary term to preserve the supersymmetric gauge invariance of Bagger--Lambert--Gustavsson (BLG) theory. The fermionic rigid BRST and anti-BRST symmetries are studied in linear and non-linear gauges. Remarkably, for Delbourgo-Jarvis-Baulieu-Thierry-Mieg (DJBTM) type gauge the spontaneous breaking of BRST symmetry occurs in the BLG theory. The responsible guy for such spontaneous breaking is ghost-anti-ghost condensation. Further, we discuss the ghost-anti-ghost condensates in the modified maximally Abelian (MMA) gauge in the BLG theory.
O'Raifeartaigh models with general R-charge assignments can have vacua where both supersymmetry and R-symmetry are spontaneously broken. Most of these vacua are metastable because the potential shows a runaway behaviour. We explain the relation between runaway directions and R-symmetry.
We show that one can obtain naturally the confinement of static charges from the spontaneous symmetry breaking of scale invariance in a gauge theory. At the classical level a confining force is obtained and at the quantum level, using a gauge invariant but path-dependent variables formalism, the Cornell confining potential is explicitly obtained. Our procedure answers completely to the requirements by 't Hooft for ''perturbative confinement''.
In this paper we consider the problem of spontaneous supersymmetry breaking in $N=4$ supergravity interacting with vector multiplets. We start with the ordinary version of such model with the scalar field geometry $SU(1,1)/U(1)\otimes SO(6,m)/SO(6)\otimes SO(m)$. Then we construct a dual version of this theory with the same scalar field geometry, which corresponds to the interaction of arbitrary number of vector multiplets with the hidden sector, admitting spontaneous supersymmetry breaking without a cosmological term. We show that supersymmetry breaking is still possible in the presence of ma…
We consider the modified superfield constraints with constant terms for the D=3, N=2 Goldstone-Maxwell gauge multiplet which contains Goldstone fermions, real scalar and vector fields. The partial spontaneous breaking N=2 to N=1 is possible for the non-minimal self-interaction of this modified gauge superfield including the linear Fayet-Iliopoulos term. The dual description of the partial breaking in the model of the self-interacting Goldstone chiral superfield is also discussed.
We propose a new spontaneous supersymmetry breaking mechanism, in which extra compact dimensions play an important role. To illustrate our mechanism, we study a simple model consisting of two chiral superfields, where one spatial dimension is compactified on a circle $S^1$. It is shown that supersymmetry is spontaneously broken irrespective of the radius of the circle, and also that the translational invariance for the $S^1$-direction and a global symmetry are spontaneously broken when the radius becomes larger than a critical radius. These results are expected to be general features of our me…
We determine the static potential for a heavy quark-antiquark pair from the spontaneous symmetry breaking of scale invariance in a non-Abelian gauge theory. Our calculation is done within the framework of the gauge-invariant, path-dependent, variables formalism. The result satisfies the 't Hooft basic criterion for achieving confinement.
