We consider a gauge-Higgs system on a fuzzy 2-sphere and study the topological structure of gauge configurations, when the U(2) gauge symmetry is spontaneously broken to U(1) times U(1) by the vev of the Higgs field. The topology is classified by the index of the Dirac operator satisfying the Ginsparg-Wilson relation, which turns out to be a noncommutative analog of the topological charge introduced by 't Hooft. It can be rewritten as a form whose commutative limit becomes the winding number of the Higgs field. We also study conditions which assure the validity of the formulation, and give a generalization of the admissibility condition. Finally we explicitly calculate the topological charge of a one-parameter family of configurations.
We consider a U(2) Yang-Mills theory on M x S_F^2 where M is an arbitrary noncommutative manifold and S_F^2 is a fuzzy sphere spontaneously generated from a noncommutative U(N) Yang-Mills theory on M, coupled to a triplet of scalars in the adjoint of U(N). Employing the SU(2)-equivariant gauge field constructed in arXiv:0905.2338, we perform the dimensional reduction of the theory over the fuzzy sphere. The emergent model is a noncommutative U(1) gauge theory coupled adjointly to a set of scalar fields. We study this model on the Groenewald-Moyal plane and find that, in certain limits, it admi…
We propose gauge-Higgs unification in fuzzy extra dimensions as a possible solution to the Higgs naturalness problem. In our approach, the fuzzy extra dimensions are created spontaneously as a vacuum solution of certain four-dimensional gauge theory. As an example, we construct a model which has a fuzzy torus as its vacuum. The Higgs field in our model is associated with the Wilson loop wrapped on the fuzzy torus. We show that the quadratic divergence in the mass of the Higgs field in the one-loop effective potential is absent. We then argue based on symmetries that the quantum corrections to …
We consider certain vacua of four-dimensional SU(N) gauge theory with the same field content as the N=4 supersymmetric Yang-Mills theory, resulting from potentials which break the N=4 supersymmetry as well as its global SO(6) symmetry down to SO(3) x SO(3). We show that the theory behaves at intermediate scales as Yang-Mills theory on M^4 x S^2 x S^2, where the extra dimensions are fuzzy spheres with magnetic fluxes. We determine in particular the structure of the zero modes due to the fluxes, which leads to low-energy mirror models.
Local gauge symmetries cannot break spontaneously, according to Elitzur's theorem, but this leaves open the possibility of breaking some global subgroup of the local gauge symmetry, which is typically the gauge symmetry remaining after certain (e.g. Coulomb or Landau) gauge choices. We show that in an SU(2) gauge-Higgs system such symmetries do indeed break spontaneously, but the location of the breaking in the phase diagram depends on the choice of global subgroup. The implication is that there is no unique broken gauge symmetry, but rather many symmetries which break in different places. The…
We study the spontaneous symmetry breaking of O(3) scalar field on a fuzzy sphere $S_F^2$. We find that the fluctuations in the background of topological configurations are finite. This is in contrast to the fluctuations around a uniform configuration which diverge, due to Mermin-Wagner-Hohenberg-Coleman theorem, leading to the decay of the condensate. Interesting implications of enhanced topological stability of the configurations are pointed out.
We utilize Coleman's theorem and show that quantum chromodynamics based on asymptotic freedom and confinement must have chiral symmetry realized as a spontaneously broken symmetry.
We find new spontaneously generated fuzzy extra dimensions emerging from a certain deformation of $N=4$ supersymmetric Yang-Mills (SYM) theory with cubic soft supersymmetry breaking and mass deformation terms. First, we determine a particular four dimensional fuzzy vacuum that may be expressed in terms of a direct sum of product of two fuzzy spheres, and denote it in short as $S_F^{2\, Int}\times S_F^{2\, Int}$. The direct sum structure of the vacuum is revealed by a suitable splitting of the scalar fields in the model in a manner that generalizes our approach in \cite{Seckinson}. Fluctuations…
Conformal Field Theories (CFTs) have rich dynamics in heavy states. We describe the constraints due to spontaneously broken boost and dilatation symmetries in such states. The spontaneously broken boost symmetries require the existence of new low-lying primaries whose scaling dimension gap, we argue, scales as $O(1)$. We demonstrate these ideas in various states, including fluid, superfluid, mean field theory, and Fermi surface states. We end with some remarks about the large charge limit in 2d and discuss a theory of a single compact boson with an arbitrary conformal anomaly.
It was suggested by Sugimoto that there is a new supersymmetry breaking mechanism by an orientifold plane which is oppositely charged as the usual one. Here we prove the trace formula for this system to show that the supersymmetry is broken not explicitly but spontaneously. We also discuss the possibility of interpreting the orientifold plane as an intrinsic object of the superstring theory.
The Narain lattice construction of string compactifications is generalized to include spontaneously broken supersymmetry. Consistency conditions from modular invariance and Lorentz symmetry are solved in full generality. This framework incorporates models where supersymmetry breaking is inversely proportional to the radii of compact dimensions. The enhanced lattice description, however, might allow for models with a different geometrical or even non-geometrical interpretation.
A generalization of the Akulov-Volkov effective Lagrangian governing the self interactions of the Nambu-Goldstone fermions associated with spontaneously broken extended supersymmetry as well as their coupling to matter is presented and scrutinized. The resulting currents associated with R-symmetry, supersymmetry and space-time translations are constructed and seen to form a supermultiplet structure.
Using lattice simulations of a one-component $(λΦ^4)_4$ theory, we have measured the energy spectrum $ω({\mathbf{k}})$ in the broken phase at various lattice sizes. Our data show that the energy-gap $ω(0)$ is {\it not} the `Higgs mass' $M_h$ but an infrared-sensitive quantity that becomes smaller and smaller by increasing the lattice size and may even vanish in the infinite-volume limit.
The proof given in the paper was incomplete due to an omission in the proof of Lemma 2. A corrected and improved version of the paper is in arXiv:0902.2486.
By using zero-norm states in the spectrum, we explicitly demonstrate the existence of an infinite number of high energy symmetry structures of the closed bosonic string theory. Each symmetry transformation (except those generated by massless zero-norm states) relates infinite particles with different masses, thus they are broken spontaneously at the Planck scale as previously conjectured by Gross and Evans and Ovrut. As an application, the results of Das and Sathiapalan which claim that sigma-midel is nonperturbatively nonrenormalizable are reproduced from a stringy symmetry argument point of …
Noncommutative geometry(NCG) on the discrete space successfully reproduces the Higgs mechanism of the spontaneously broken gauge theory, in which the Higgs boson field is regarded as a kind of gauge field on the discrete space. We could construct the generalized differential geometry(GDG) on the discrete space $M_4\times Z_N$ which is very close to NCG in case of $M_4\times Z_2$. GDG is a direct generalization of the differential geometry on the ordinary manifold into the discrete one. In this paper, we attempt to construct the BRST invariant formulation of spontaneously broken gauge theory ba…
We discuss the generalization to global gauge anomalies of the familiar procedure for the cancellation of local gauge anomalies in effective theories of spontaneously broken symmetries. We illustrate this mechanism in a recently proposed six-dimensional extension of the standard model.
Gauge fixing and the observable fields for both abelian and non-abelian gauge theories with spontaneous breaking of gauge symmetry are studied. We explicitly show that it is possible to globally fix the gauge in the broken sector and hence construct physical fields even in the non-abelian theory. We predict that any high temperature restoration of gauge symmetry will be accompanied by a confining transition.
We consider a relativistic effective field theory of vector boson whose vacuum exhibits spontaneous breaking of Lorentz invariance. We argue that a simple model of this type, considered recently by Kraus and Tomboulis, is obstructed from having a consistent ultraviolet completion according to the diagnostic recently suggested by Adams, Arkani-Hamed, Dubovsky, Nicolis, and Rattazzi.
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.
We argue that orientable open string theory without GSO projection has N=2 space-time supersymmetry in a spontaneously broken phase. The arguments are presented both in Neveu-Schwarz-Ramond and Green-Schwarz formulations. The formal but explicit supersymmetry transformation law for string field is given in the framework of Witten's open string field theory. Our results support a fundamental assumption which lies behind the topological construction of stable D-branes starting from the unstable systems of D9-branes.
We study the solution to the Slavnov-Taylor (ST) identities in spontaneously broken effective gauge theories for a non-Abelian gauge group. The procedure to extract the $β$-functions of the theory in the presence of (generalized) non-polynomial field redefinitions is elucidated.
We present a Z_2 x Z_2 four dimensional orientifold in which supersymmetry is broken by a temperature-like Scherk-Schwarz mechanism. As usual in this type of models, at the tree-level the breaking affects only the branes tangent to the direction involved by the SS deformation, and it can propagate only through radiative corrections to other sectors, where the gauge group is broken. The result is a non-chiral model with gauge group Usp(16)^2 x Usp(8)^4.
The Galilei group involves mass as a central charge. We show that the associated superselection rule is incompatible with the observed phenomenology of superfluid helium 4: this is recovered only under the assumption that mass is spontaneously broken. This remark is somewhat immaterial for the real world, where the correct space-time symmetries are encoded by the Poincaré group, which has no central charge. Yet it provides an explicit example of how superselection rules can be experimentally tested. We elaborate on what conditions must be met for our ideas to be generalizable to the relativist…
We first review the representations of the six-dimensional (2,0) superalgebra on a free tensor multiplet and on a free string. We then construct a supersymmetric Lagrangian describing a free tensor multiplet. (It also includes a decoupled anti self-dual part of the three-form field strength.) This field theory is then rewritten in variables appropriate for analyzing a situation where the R-symmetry is spontaneously broken by the vacuum expectation values of the scalar moduli fields. Finally, we construct a supersymmetric and kappa-symmetric action for a free string.
We quantize the spontaneously broken abelian U(1) Higgs model by using the improved BFT and BFV formalisms. We have constructed the BFT physical fields, and obtain the first class observables including the Hamiltonian in terms of these fields. We have also explicitly shown that there are exact form invariances between the second class and first class quantities. Then, according to the BFV formalism, we have derived the corresponding Lagrangian having U(1) gauge symmetry. We also discuss at the classical level how one easily gets the first class Lagrangian from the symmetry-broken second class …
I review recent work on computing radiative corrections to non-abelian gauge couplings in four-dimensional heterotic vacua with spontaneously broken supersymmetry. The prototype models can be considered as K3 surfaces with additional Scherk-Schwarz fluxes inducing the spontaneous $\mathcal{N}=2 \to \mathcal{N}=0$ breaking. Remarkably, although the gauge thresholds are no longer BPS protected and receive contributions also from the excitations of the RNS sector, their difference is still exactly computable and universal. Based on a talk presented at the DISCRETE 2014 conference at King's Colleg…
In the framework of standard electrodynamics with linear local response, we construct a model that provides spontaneously broken transparency. The functional dependence of the medium parameter turns out to be of the Higgs type.
We consider a complex scalar $Φ^4 $ theory with spontaneously broken global U(1) symmetry, minimally coupling to perturbatively quantized Einstein gravity which is treated as an effective theory at the energy well below the Planck scale. Both the lowest order pure real scalar correction and the gravitational correction to the renormalization of the Higgs sector in this model have been investigated. Our results show that the gravitational correction renders the renormalization of the Higgs sector in this model inconsistent while the pure real scalar correction to it leads to a compatible renorm…
We propose a mechanism to break the translational invariance of compactified space spontaneously. As a simple model, we study a real $ϕ^4$ model compactified on $M^{D-1}\otimes S^1$ in detail, where we impose a nontrivial boundary condition on $ϕ$ for the $S^1$-direction. It is shown that the translational invariance for the $S^1$-direction is spontaneously broken when the radius $R$ of $S^1$ becomes larger than a critical radius $R^*$ and also that the model behaves like a $ϕ^4$ model on a single kink background for $R \to \infty$. It is pointed out that spontaneous breakdown of translational…
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.
We present a spontaneously broken N=2 supergravity model that reduces in the flat limit to a globally supersymmetric N=2 system with explicit soft supersymmetry breaking terms. These soft terms generate a mass O(100 GeV) for mirror quarks and leptons, while leaving the physical fermions light, thereby overcoming one of the major obstacles towards the construction of a realistic N=2 model of elementary interactions.
In a wide class of three-dimensional Abelian gauge theories with a bare Chern-Simons term, the Lorentz invariance is spontaneously broken by dynamical generation of a non-vanishing magnetic field. A detailed computation of an energy density of the true vacuum is given. The originally massive photon becomes massless, fulfilling the role of a Nambu-Goldstone boson associated with the spontaneous breaking of the Lorentz invariance.
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 report on some recent investigations of the structure of the four dimensional gauged supergravity Lagrangian which emerges from flux and Scherk-Schwarz compactifications in higher dimensions. Special attention is given to the gauge structure of M-theory compactified on a seven torus with 4-form and geometrical (spin connection) fluxes turned on. A class of vacua, with flat space-time and described by ``no-scale'' supergravity models, is analyzed.
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.
Callan-Symanzik and renormalization group equation are discussed for the $U(1)$-axial model and it is shown that the symmetric model is not the asymptotic version of the spontaneously broken one due to mass logarithms in the $β$-functions. The Callan-Symanzik equation of the standard model is seen to have the same form as the one of the simple model.
We describe a stabilization mechanism for fuzzy $S^4_N$ in the Euclidean IIB matrix model due to vacuum energy in the presence of a positive mass term. The one-loop effective potential for the radius contains an attractive contribution attributed to supergravity, while the mass term induces a repulsive contribution for small radius due to SUSY breaking. This leads to a stabilization of the radius. The mechanism should be pertinent to recent results on the genesis of 3+1-dimensional space-time in the Minkowskian IIB model.
We analyze the moduli space of spontaneously broken N=8 supergravity theories in 4 dimensions with classical Minkowski vacua. We find that all the known classical vacua, as well as the several new ones we construct here, can be connected by sending some of the moduli to their boundary values. We also show that Cremmer-Scherk-Schwarz models can be viewed as special limits of more general CSO* gaugings, which allow for non-Abelian residual symmetries on the vacuum. Finally, we find that all the classical Minkowski vacua with fully broken supersymmetry found so far are unstable with respect to 1-…
We examine the renormalizability problem of spontaneously broken non-Abelian gauge theory on noncommutative spacetime. We show by an explicit analysis of the U(2) case that ultraviolet divergences can be removed at one loop level with the same limited number of renormalization constants as required on commutative spacetime. We thus push forward the efforts towards constructing realistic models of gauge interactions on noncommutative spacetime.
We examine Dashen's phenomenon in the Leutwyler--Smilga regime of QCD with any number of colors and quarks in either the fundamental or adjoint representations of the gauge group. In this limit, the theories only depend on simple combinations of quark masses, volume, chiral condensate and vacuum angle. Based upon this observation, we derive simple expressions for the chiral condensate and the topological density and show that they are in fact related. By examining the zeros of the various partition functions, we elucidate the mechanism leading to Dashen's phenomena in QCD.
In spontaneously broken supergravity with non-flat potential the vanishing of the cosmological constant is usually associated with a non-trivial balancing of two opposite-sign contributions. We make the simple observation that, in an appropriately defined expansion of the superfield action in inverse powers of $M_P$, this tuning corresponds to the absence of two specific operators. It is then tempting to speculate what kind of non-standard symmetry or structural principle might underlie the observed extreme smallness of the corresponding coefficients in the real world. Independently of such sp…
We extend our previous results on the evolution of quantum fermi fields in Minkowski gauge field backgrounds to the case of spontaneously broken gauge theories. We obtain a selection rule which relates the amount of fermion number violation to the change in Higgs winding number of the configuration. This selection rule is applicable to any classical solution which dissipates at both early and late times.
Starting from the standard Lagrangian for a SU(2) x U(1) gauge theory plus a Higgs field we derive the corresponding "maximal helicity violating" (MHV) Lagrangian. From this MHV Lagrangian one deduces simple diagrammatic rules for the calculation of multi-particle scattering amplitudes. We arrive at the MHV Lagrangian by a canonical change of the field variables in the light-cone gauge. We comment on the modifications which occur in a spontaneously broken gauge theory as compared to a pure (unbroken) Yang-Mills theory.
This paper revisits the nonlinear realization of spontaneously broken N=1 supersymmetry. It is shown that the constrained superfield formalism can be reinterpreted in the language of standard realization of nonlinear supersymmetry via a new and simpler route. Explicit formulas of actions are presented for general renormalizable theories with or without gauge interactions. The nonlinear Wess-Zumino gauge is discussed and relations are pointed out for different definitions of gauge fields. In addition, a general procedure is provided to deal with theories of arbitrary Kahler potentials.
The vanishing of the electromagnetic field, for purely electric configurations of spontaneously broken Abelian models, is established in the domain of outer communications of a static asymptotically flat black hole. The proof is gauge invariant, and is accomplished without any dependence on the model. In the particular case of the Abelian Higgs model, it is shown that the only solutions admitted for the scalar field become the vacuum expectation values of the self-interaction.
The Ward identities involving the currents associated to the spontaneously broken scale and special conformal transformations are derived and used to determine, through linear order in the two soft-dilaton momenta, the double-soft behavior of scattering amplitudes involving two soft dilatons and any number of other particles. It turns out that the double-soft behavior is equivalent to performing two single-soft limits one after the other. We confirm the new double-soft theorem perturbatively at tree-level in a $D$-dimensional conformal field theory model, as well as nonperturbatively by using …
A spontaneously broken SU(2) theory is the simplest generalization of the Abelian Higgs model, containing three equally massive vector bosons and a single Higgs scalar. A strictly diagrammatic proof is presented of the tree-level unitarity of this model in the unitary gauge, i.e. employing only physical fields. A new Ward-like identity is used to show that the high-energy behaviour of all amplitudes cannot be more than quadratic; the use of generating functions for all off-shell amplitudes then leads to the unitarity proof.
We construct, numerically, stationary and spherically symmetric nontopological soliton solutions in the system composed of a complex scalar field, a U(1) gauge field, and a complex Higgs scalar field that causes spontaneous symmetry braking. It is shown that the charge of the soliton is screened by counter charge everywhere.
Starting with a N=4 supersymmetric Yang-Mills theory in four dimensions with gauge group SU(3N) we perform an orbifold projection leading to a N=1 supersymmetric SU(N)^3 Yang-Mills theory with matter supermultiplets in bifundamental representations of the gauge group, which is chiral and anomaly free. Subsequently, we search for vacua of the projected theory which can be interpreted as spontaneously generated twisted fuzzy spheres. We show that by adding the appropriate soft supersymmetry breaking terms we can indeed reveal such vacua. Three cases are studied, where the gauge group is spontane…
Color/kinematics duality and the double-copy construction have proved to be systematic tools for gaining new insight into gravitational theories. Extending our earlier work, in this paper we introduce new double-copy constructions for large classes of spontaneously-broken Yang-Mills-Einstein theories with adjoint Higgs fields. One gauge-theory copy entering the construction is a spontaneously-broken (super-)Yang-Mills theory, while the other copy is a bosonic Yang-Mills-scalar theory with trilinear scalar interactions that display an explicitly-broken global symmetry. We show that the kinemati…
We consider the matter induced part of the effective superpotential of N=2, U(N) gauge model in which N=2 supersymmetry is spontaneously broken to N=1, by using the properties of the chiral ring and the generalized Konishi anomaly equations derived in our previous paper arXiv:0704.1060. It is shown that the effective superpotential is related to the planar free energy of the matrix model by a formula which consists of two parts -- the well-known part due to Dijkgraaf-Vafa and the part that acts as a deformation of the couplings. These couplings are those of the original bare prepotential in th…
The methods of non-linear realizations have proven to be powerful in studying the low energy physics resulting from spontaneously broken internal and spacetime symmetries. In this paper, we reconsider how these techniques may be applied to the case of spontaneously broken gauge theories, concentrating on Yang-Mills theories. We find that coset methods faithfully reproduce the description of low energy physics in terms of massive gauge bosons and discover that the Stückelberg replacement commonly employed when treating massive gauge theories arises in a natural manner. Uses of the methods are c…
Conformal invariance is spontaneously broken in many physical systems leading to the appearance of a single massless Goldstone mode in the spectrum, the dilaton. The dilaton soft limit is shown to generically encode the action of both the dilatation and the special conformal transformation on observables. For massive on-shell legs these take the form of sub-leading soft theorems. At loop level, we show how anomalous dimensions for coupling constants and fields can be included. We illustrate the general analysis with a variety of formal and phenomenological applications.
In the ``Type-II'' regime, $m_{\rm Higgs}\gap m_{\rm gauge}$, the finite-temperature phase transition in spontaneously-broken gauge theories (including the standard model) must be be studied using a renormalization group treatment. Previous studies within the $(4-\ep)$-expansion suggest a 1st-order transition in this regime. We use analogies with experimentally accessible phase transitions in liquid crystals, and theoretical investigations of superconductor phase transitions to argue that, in this range, the critical behavior of a large class of gauge-Higgs-fermion systems changes from 1st to …
We construct a purely fermionic system with spontaneously broken supersymmetry that shares the common feature with a fracton phase of matter. Our model is gapless due to the Nambu-Goldstone mechanism. It shows a ground-state degeneracy with the "Area-law" entropy due to fermionic subsystem symmetries. In the strongly coupled limit, it becomes a variant of the Nicolai model, and the ground-state degeneracy shows the "Volume-law" entropy. Gauging the fermionic subsystem symmetry has an t'Hooft anomaly by itself, but the would-be gauged theory may possess a fermionic defect that is immobile in ce…
In this paper we investigate the canonical quantization of a non-Abelian topologically massive Chern-Simons theory in which the gauge fields are minimally coupled to a multiplet of scalar fields in such a way that the gauge symmetry is spontaneously broken. Such a model produces the Chern-Simons-Higgs mechanism in which the gauge excitations acquire mass both from the Chern-Simons term and from the Higgs-Kibble effect. The symmetry breaking is chosen to be only partially broken, in such a way that in the broken vacuum there remains a residual non-Abelian symmetry. We develop the canonical oper…
We perform a comprehensive study of on-shell recursion relations for Born amplitudes in spontaneously broken gauge theories and identify the minimal shifts required to construct amplitudes with a given particle content and spin quantum numbers. We show that two-line or three-line shifts are sufficient to construct all amplitudes with five or more particles, apart from amplitudes involving longitudinal vector bosons or scalars, which may require at most five-line shifts. As an application, we revisit selection rules for multi-boson amplitudes using on-shell recursion and little-group transforma…
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 …
