We present a class of models in which the dark matter stabilization symmetry is generated by spontaneous symmetry breaking. These models naturally correlate the dark and electroweak symmetry breaking scales. The result is a generic mechanism linking the annihilation cross section for thermally populated dark matter with the weak scale. The thermal relic abundance, sensitivity to major precision electroweak observables and additional LHC signatures are also presented.
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 intro…
In this talk I review the issues of supersymmetry breaking and radion stabilization in a five dimensional theory compactified on the Z_2 orbifold. Supersymmetry breaking by Scherk-Schwarz boundary conditions is interpreted as spontaneous breaking of local supersymmetry by the Hosotani mechanism. The auxiliary field responsible for spontaneous supersymmetry breaking is inside the five-dimensional off-shell minimal supergravity multiplet. Different ways of fixing the supersymmetry breaking order parameter are analyzed. In the presence of supersymmetry breaking the one-loop effective potential fo…
My recent fit of the light scalar mesons is discussed in the light of the U3 x U3 linear sigma model. The argument for why there exists a light and broad sigma meson is explained in more detail, and the mechanism of spontaneous symmetry breaking is discussed.
We study a supersymmetric field theory in six dimensions compactified on the orbifold T^2/Z_2 with two Wilson lines. After supersymmetry breaking, the Casimir energy fixes the shape moduli at fixed points in field space where the symmetry of the torus lattice is enhanced. Localized Fayet-Iliopoulos terms stabilize the volume modulus at a size much smaller than the inverse supersymmetry breaking scale. All moduli masses are smaller than the gravitino mass.
We emphasize that the stabilizing symmetry for dark matter (DM) particles does not have to be the commonly used parity (Z_2) symmetry. We therefore examine the potential of the colliders to distinguish models with parity stabilized DM from models in which the DM is stabilized by other symmetries. We often take the latter to be a Z_3 symmetry for illustration. We focus on signatures where a single particle, charged under the DM stabilization symmetry decays into the DM and Standard Model (SM) particles. Such a Z_3-charged "mother" particle can decay into one or two DM particles along with the s…
One common way to define spontaneous symmetry breaking involves explicit symmetry breaking. This definition can be used in any approach to Effective Field Theory, from perturbation theory to lattice simulations. It allows us to study the spontaneous breakdown of global symmetries without assuming that the local gauge symmetry is spontaneously broken. This is important since perturbation theory is insufficient to study extended Higgs sectors: it is insufficient to predict the physical spectrum of the SU(5) Grand Unified Theory (Georgi-Glashow) or to predict the spontaneous breakdown of global s…
Many popular models of new physics beyond the Standard Model use a parity to stabilize weakly interacting, dark matter candidates. We examine the potential for the CERN Large Hadron Collider to distinguish models with parity stabilized dark matter from models in which the dark matter is stabilized by other symmetries. In this letter, we focus on signatures involving long-lived particles and large amounts of missing transverse energy. To illustrate these signatures, we consider three models from the literature which are representative of a more general class of models with non-traditional stabi…
It is well known that a tachyonic mode appears in the spectrum of Yang--Mills theory with a static uniform magnetic field, and that the free energy has an (unstable) minimum at finite magnetic field. It is argued that spontaneous generation of magnetic field does not take place at high temperature due to nonperturbative magnetic screening. Furthermore, the dispersion relation for gauge field fluctuations in an external magnetic field at high temperature is solved. The lowest energy mode is stable against spontaneous generation of magnetic fields since it acquires a thermal mass. However, the r…
We examine the potential of using colliders to distinguish models with parity (Z_2) stabilized dark matter (DM) from models in which the DM is stabilized by other symmetries, taking the latter to be a Z_3 symmetry for illustration. The key observation is that a heavier mother particle charged under a Z_3 stabilization symmetry can decay into one or two DM particles along with Standard Model (SM) particles. This can be contrasted with the decay of a mother particle charged under a parity symmetry; typically, only one DM particle appears in the decay chain. In arXiv:1003.0899, some of us studied…
To obtain natural inflation with large tensor-to-scalar ratio in string framework, we need a special moduli stabilization mechanism which can separate the masses of real and imaginary components of Kähler moduli at different scales, and achieve a trans-Planckian axion decay constant from sub-Planckian axion decay constants. In this work, we stabilize the matter fields by F-terms and the real components of Kähler moduli by D-terms of two anomalous $U(1)_X\times U(1)_A$ symmetries strongly at high scales, while the corresponding axions remain light due to their independence on the Fayet-Iliopoul…
We study the supersymmetric spontaneous symmetry breaking of SO(10) into SU(3)xSU(2)xU(1) for the most physically interesting cases of SU(5) or flipped SU(5)xU(1) intermediate symmetries. The first case is more easily realized while the second one requires a fine-tuning condition on the parameters of the superpotential. This is because in the case of SU(5) symmetry there is at most one singlet of the residual symmetry in each SO(10) irreducible representation. We also point out on more general grounds in supersymmetric GUT's that some intermediate symmetries can be exactly realized and others …
We discuss the breaking of $SO(3)$ down to finite family symmetries such as $A_4$, $S_4$ and $A_5$ using supersymmetric potentials for the first time. We analyse in detail the case of supersymmetric $A_4$ and its finite subgroups $Z_3$ and $Z_2$. We then propose a supersymmetric $A_4$ model of leptons along these lines, originating from $SO(3)\times U(1)$, which leads to a phenomenologically acceptable pattern of lepton mixing and masses once subleading corrections are taken into account. We also discuss the phenomenological consequences of having a gauged $SO(3)$, leading to massive gauge bos…
We study moduli stabilization with F-term uplifting. As a source of uplifting F-term, we consider spontaneous supersymmetry breaking models, e.g. the Polonyi model and the Intriligator-Seiberg-Shih model. We analyze potential minima by requiring almost vanishing vacuum energy and evaluate the size of modulus F-term. We also study soft SUSY breaking terms. In our scenario, the mirage mediation is dominant in gaugino masses. Scalar masses can be comparable with gaugino masses or much heavier, depending on couplings with spontaneous supersymmetry breaking sector.
In a class of supersymmetric flavor models predictions are based on residual symmetries of some subsectors of the theory such as those of the charged leptons and neutrinos. However, the vacuum expectation values of the so-called flavon fields generally modify the Kähler potential of the setting, thus changing the predictions. We derive simple analytic formulae that allow us to understand the impact of these corrections on the predictions for the masses and mixing parameters. Furthermore, we discuss the effects on the vacuum alignment and on flavor changing neutral currents. Our results can als…
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.
Within multi-Higgs-doublet models, one can impose symmetries on the Higgs potential, either discrete or continuous, that mix several doublets. In two-Higgs-doublet model any such symmetry can be conserved or spontaneously violated after the electroweak symmetry breaking (EWSB), depending on the coefficients of the potential. With more than two doublets, there exist symmetries which are always spontaneously violated after EWSB. We discuss the origin of this phenomenon and show its similarity to geometric frustration in condensed-matter physics.
Goldstone's theorem states that there is a massless mode for each broken symmetry generator. It has been known for a long time that the naive generalization of this counting fails to give the correct number of massless modes for spontaneously broken spacetime symmetries. We explain how to get the right count of massless modes in the general case, and discuss examples involving spontaneously broken Poincare and conformal invariance.
Many models of beyond Standard Model physics connect flavor symmetry with a discrete group. Having this symmetry arise spontaneously from a gauge theory maintains compatibility with quantum gravity and can be used to systematically prevent anomalies. We minimize a number of Higgs potentials that break gauge groups to discrete symmetries of interest, and examine their scalar mass spectra.
We study the spontaneous breaking of discrete symmetries in theories with broken gauge symmetry. The intended application is to CP breaking in theories with gauged flavor symmetries, but the analysis described here is preliminary. We dispense with matter fields and take the gauge theory to be weakly coupled and broken spontaneously by unspecified, short-distance forces. We develop an effective-field-theory description of the resultant low energy theory, and ask whether this theory by itself can describe the subsequent breaking of discrete symmetries. We conclude that this can happen depending …
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…
The symmetry breaking pattern of QCD features two seemingly disconnected phenomena: the spontaneous breakdown of the Z(3) center symmetry in the deconfinement transition of pure-gauge QCD, and the spontaneous breaking of chiral SU(N_f)xSU(N_f) symmetry in the limit of N_f massless quark flavours. The dynamical entanglement of these symmetries is displayed in the framework of a schematic model (the PNJL model) in comparison with results from Lattice QCD. Extensions to non-zero baryon chemical potential are discussed.
Spontaneous collapse models aim at solving the measurement problem of quantum mechanics by introducing collapse of wave function as an ontologically objective mechanism that suppresses macroscopic superpositions. In particular, the strength of collapse depends on the mass of the system. Flavor oscillating systems such as neutral mesons feature superpositions of states of different masses and, hence, could be used to test the validity of spontaneous collapse models. Recently, it has been shown that the mass-proportional CSL model causes exponential damping of the neutral meson oscillations whic…
We propose a dark matter (DM) scenario in an extension of a left-right symmetric model with a gauge-singlet scalar field. The gauge-singlet scalar can automatically become a DM candidate, provided that both P and CP symmetries are only broken spontaneously. Thus no extra discrete symmetries are needed to make the DM candidate stable. After constraining the model parameters from the observed relic DM density we make predictions for direct detection experiments. We show that for some parameter range, the predicted WIMP-nucleon elastic scattering cross section can reach the current experimental u…
We argue that in certain models with family symmetries the implementation of the alignment mechanism for the supression of the flavor changing neutral currents requires mass matrices with holomorphic zeros in the down quark sector. Holomorphic zeros typically open flat directions that potentially spoil the uniqueness of the supersymmetric vacuum. We then present an anomalous U(1) model without holomorphic zeros in the quark sector that can reproduce the fermion mass hierarchies, provided that $\tanβ$ is of order one. To avoid undesired flavor changing neutral currents we propose a supersymmetr…
We construct a model of spontaneous CP violation in E6 supersymmetric grand unified theory. In the model, we employ an SU(2)F flavor symmetry and an anomalous U(1)A symmetry. The SU(2)F flavor symmetry is introduced to provide the origin of hierarchical structures of Yukawa coupling and to ensure the universality of sfermion soft masses. The anomalous U(1)A symmetry is introduced to realize the doublet-triplet mass splitting, to provide the origin of hierarchical structures of Yukawa couplings, and to solve the mu problem. In the model, CP is spontaneously broken by the SU(2)F breaking in orde…
It has been long known that when spacetime symmetry is spontaneously broken, some of the broken generators may not give rise to independent gapless, Nambu-Goldstone excitations. We provide two complementary viewpoints of this phenomenon. On the one hand, we show that the corresponding field degrees of freedom have the same symmetry transformation properties as massive, matter fields. The "inverse Higgs constraints", sometimes employed to eliminate these modes from the theory, are reinterpreted as giving a field parametrization that makes these transformation properties manifest. On the other h…
We systematically investigate possibilities of realizing the spontaneous CP violation in Type IIB flux compactifications on toroidal orientifolds. Our detailed analysis leads to the presence of flat directions at degenerate CP-breaking and -conserving vacua for a generic choice of three-form fluxes, indicating that flux compactifications are not sufficient to realize the spontaneous CP violation. Furthermore, the four-dimensional CP can be embedded into the duality symmetries, namely modular symmetries for a particular choice of fluxes.
We propose a flavor model where both CP and flavor symmetries are broken at the supersymmetric level. The model is an effective SU(5) theory based on a U(2) horizontal symmetry. The minimum of the supersymmetric scalar potential can be solved to yield a realistic pattern of charged fermion masses. The Higgs sector contains a symmetric, an antisymmetric and two vector fields, plus their U(2) conjugates. These Higgs fields are the only fields strictly required to break the flavor and CP symmetries and generate masses for all charged fermions including the up-quark. The model predicts the existen…
In this paper we consider dissipative hydrodynamic equations for systems with continuous broken symmetries. We first present the case of superfluidity, in which the symmetry U(1) is broken and then generalize to the chiral symmetry $SU(2)_L \times SU(2)_R$. The corresponding new transport coefficients are introduced.
We study the impact of a set of horizontal symmetries on the requirements for producing the baryon asymmetry of the universe via leptogenesis. We find that Abelian horizontal symmetries lead to a simple description of the parameters describing leptogenesis in terms of the small expansion parameter that arises from spontaneous symmetry breaking. If the family symmetry is made discrete, then an enhancement in the amount of leptogenesis can result.
Discrete Abelian symmetries ($\mathbb{Z}_N$) are a common "artifact" of beyond the standard model physics models. They provide different avenues for constructing consistent scenarios for lepton and quark mixing patterns, radiative neutrino mass generation as well as dark matter stabilization. We argue that these symmetries can arise from the spontaneous breaking of the Abelian $U(1)$ factors contained in the global flavor symmetry transformations of the gauge invariant kinetic Lagrangian. This will be the case provided the ultra-violet completion responsible for the Yukawa structure involves s…
We discuss O'Raifeartaigh models with general R-charge assignments, introduced by Shih to break R-symmetry spontaneously. We argue that most of these models have runaway directions related to the R-symmetry. In addition, we study the simplest model with a U(N) global symmetry and show that in a range of parameters R-symmetry is spontaneously broken in a metastable vacuum.
Frohlich, Morchio and Strocchi long ago proved that Lorentz invariance is spontaneously broken in QED because of infrared effects. We develop a simple model where consequences of this breakdown can be explicitly and easily calculated. For this purpose, the superselected U(1) charge group of QED is extended to a superselected "Sky" group containing direction-dependent gauge transformations at infinity. It is the analog of the Spi group of gravity. As Lorentz transformations do not commute with Sky, they are spontaneously broken. These abelian considerations and model are extended to non-Abelian…
We discuss spontaneous symmetry breakdown (SSB) of both global and local scale symmetries in scalar-tensor gravity with two scalar fields, one of which couples nonminimally to scalar curvature while the other is a normal scalar field. In case of a global scale symmetry, by moving from the Jordan frame to the Einstein frame, a normal scalar field becomes massive while the dilaton remains massless after the SSB. In case of a local scale symmetry, we take a gauge fixing condition for the local scale invariance, $a R + b ϕ^2 = k$, which was found in our previous study of a Weyl's quadratic gravity…
We show that a momentum operator of a translational symmetry may not commute with an internal symmetry operator in the presence of a topological soliton in non-relativistic theories. As a striking consequence, there appears a coupled Nambu-Goldstone mode with a quadratic dispersion consisting of translational and internal zero modes in the vicinity of a domain wall in an O(3) sigma model, a magnetic domain wall in ferromagnets with an easy axis.
An SU(2) lattice gauge theory with two doublets of complex scalar fields is considered. All continuous symmetries are identified and, using the nonperturbative methods of lattice field theory, the phase diagram is mapped out by direct numerical simulation. Two-doublet models contain phase transitions that separate qualitatively distinct regions of the parameter space. In some regions global symmetries are spontaneously broken. For some special choices of the model parameters, the symmetry-breaking order parameter is calculated. The pattern of symmetry breaking is verified further through obser…
In gauge theories, spontaneous breaking of the centre symmetry provides a precise definition of deconfinement. In large-$N$ gauge theories, evidence has emerged recently that between confined and deconfined phases a partially-deconfined phase can appear, in which only a subset of colours deconfine. In the partially-deconfined phase, the centre symmetry is spontaneously broken, raising the question of whether an order parameter exists that can distinguish completely- and partially-deconfined phases. We present two examples in gauge theories of global symmetries that are spontaneously broken in …
For relativistic quantum field theories, we consider Lorentz breaking, spatially homogeneous field configurations or states that evolve in time along a symmetry direction. We dub this situation "spontaneous symmetry probing" (SSP). We mainly focus on internal symmetries, i.e. on symmetries that commute with the Poincare group. We prove that the fluctuations around SSP states have a Lagrangian that is explicitly time independent, and we provide the field space parameterization that makes this manifest. We show that there is always a gapless Goldstone excitation that perturbs the system in the d…
We argue that the non-observability of the spontaneous breakdown of Lorentz symmetry (SBLS) caused by the vacuum expectation values of vector fields could provide the origin of all internal symmetries observed. Remarkably, the application of this principle to the most general relativistically invariant Lagrangian, with arbitrary couplings for all the fields involved, leads by itself to the appearance of a symmetry and, what is more, to the massless vector field(s) gauging this symmetry. A simple model for the SBLS based on massive vector and real scalar field interactions is considered; it is …
In this note we show that the cosmological domain wall and the de Sitter quantum breaking problems complement each other in theories with discrete symmetries that are spontaneously broken at low energies. Either the symmetry is exact and there is a domain wall problem, or it is approximate and there exists an inconsistent de Sitter minimum. This leaves no room for many extension of the Standard Model based on such discrete symmetries. We give some examples that include NMSSM, spontaneous CP violation at the weak scale and some versions of the Peccei-Quinn scenario with discrete symmetries.
We study the possibility of spontaneous CP violation in string models with the dilaton field stabilized at a phenomenologically acceptable value. We consider three mechanisms to stabilize the dilaton: multiple gaugino condensates, a nonperturbative Kahler potential, and a superpotential based on S-duality, and analyze consequent CP phases in the soft SUSY breaking terms. Due to non-universality forced upon the theory by requiring a non-trivial CKM phase, the EDM problem becomes more severe. Even if there are no complex phases in the VEVs of the SUSY breaking fields, the electric dipole moments…
We calculate and explore the moduli potential for M-Theory compactified on G_2-manifolds in which the superpotential is dominated by a single membrane instanton term plus one from an asymptotically free hidden sector gauge interaction. We show that all moduli can be stabilized and that hidden sector gauge symmetries can be Higgsed at a high scale. We then compute the spectrum of superpartner masses at the GUT scale and evolve it to the electroweak scale. We find a spectrum which is very similar to the G_2-MSSM with light gauginos - accessible at the LHC - and a neutral wino dark matter candida…
We reconsider the origin of CP violation in fundamental theory. Existing string models of spontaneous CP violation make ambiguous predictions, due to the arbitrariness of CP transformation and the apparent non-invariance of the results under duality. We find an unambiguous modular CP invariance condition, applicable to predictive models of spontaneous CP violation, which circumvents these problems; it strongly constrains CP violation by heterotic string moduli. The dilaton is also evaluated as a source of CP violation, but is likely experimentally excluded. We consider the prospects for explai…
Neutrino oscillations in a hot and dense astrophysical environment such as a core-collapse supernova pose a challenging, seven-dimensional flavor transport problem. To make the problem even more difficult (and interesting), neutrinos can experience collective oscillations through nonlinear refraction in the dense neutrino medium in this environment. Significant progress has been made in the last decade towards the understanding of collective neutrino oscillations in various simplified neutrino gas models with imposed symmetries and reduced dimensions. However, a series of recent studies seem t…
String gas cosmology is an approach towards studying the effects of superstring theory on early universe cosmology which is based on new symmetries and new degrees of freedom of string theory. Within this context, it appears possible to stabilize the moduli which describe the size and shape of the extra spatial dimensions without the need of introducing many extra tools such as warping and fluxes. In this lecture, the recent progress towards moduli stabilization in string gas cosmology is reviewed, and outstanding problems for the scenario are discussed.
We continue to explore the consequences of the recently discovered Minkowski space structure of the Higgs potential in the two-Higgs-doublet model. Here, we focus on the vacuum properties. The search for extrema of the Higgs potential is reformulated in terms of 3-quadrics in the 3+1-dimensional Minkowski space. We prove that 2HDM cannot have more than two local minima in the orbit space and that a twice-degenerate minimum can arise only via spontaneous violation of a discrete symmetry of the Higgs potential. Investigating topology of the 3-quadrics, we give concise criteria for existence of n…
This theoretical particle physics thesis is an investigation into old and new symmetries of Nature. Known symmetries and conservation laws serve as a guide for dark and visible sector model building. New symmetries of Nature are proposed, broken and subsequently reinstated at high temperatures in order to discover well-motivated particle physics models for cosmological observations implying the existence of a dark sector. Candidate processes for creation of a non-primordial matter/antimatter asymmetry result from out of equilibrium spontaneous breaking of these symmetries in the early Universe…
We consider a 3-brane embedded in 5-dimensional space time characterized by a Gaussian warp factor, for which the four-dimensional effective theory for brane fluctuation (branons) is unstable. We show that radiative corrections arising from fermions living on the brane, and therefore coupled to branons, stabilize the system by generating dynamically a spontaneous symmetry breaking for the branon field. The price to pay, for the corresponding mechanism to be consistent, is to have a large number of fermion flavours, and we discuss the fat brane scenario as an interpretation for the dressed bran…
We analyze patterns of remnant discrete symmetries that arise from U(1)^N theories by spontaneous breaking. We describe a simple, geometrical way to understand these patterns and provide methods for identifying the discrete symmetries and bringing them to the simplest possible form. Applications in GUT and string model building are briefly discussed.
Outer automorphisms of symmetries ("symmetries of symmetries") in relativistic quantum field theories are studied, including charge conjugation (C), space-reflection (P) , and time-reversal (T) transformations. The group theory of outer automorphisms is pedagogically introduced and it is shown that CP transformations are special outer automorphisms of the global, local, and space-time symmetries of a theory. It is shown that certain discrete groups allow for a group theoretical prediction of parameter independent CP violating complex phases with fixed geometrical values. The remainder of this …
