We study the concomitant breaking of spatial translations and dilatations in Ginzburg-Landau-like models, where the dynamics responsible for the symmetry breaking is described by an effective Mexican hat potential for spatial gradients. We show that there are fractonic modes with either subdimensional propagation or no propagation altogether, namely, immobility. Such class of effective field theories encompasses instances of helical superfluids and meta-fluids, where fractons can be connected to an emergent symmetry under higher moment charges, leading in turns to the trivialization of some elastic coefficients. The introduction of a finite charge density alters the mobility properties of fractons and leads to a competition between the chemical potential and the superfluid velocity in determining the gap of the dilaton. The mobility of fractons can also be altered at zero density upon considering additional higher-derivative terms.
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…
We consider theories of fractons with $N$ fields. These theories have exotic spacetime symmetries, including a conserved dipole moment. Using collective fields we solve these models to leading order in large $N$. The large $N$ solution reveals that these models are strongly correlated, and that interactions generate a momentum-dependent self-energy. Dipole symmetry is spontaneously broken throughout the phase diagram of these models, leading to a low-energy Goldstone description of what we dub "dipole superfluids."
We present an effective field theory for the nonlinear fluctuating hydrodynamics of a single conserved charge with or without time-reversal symmetry, based on the Martin-Siggia-Rose formalism. Applying this formalism to fluids with only charge and multipole conservation, and with broken time-reversal symmetry, we predict infinitely many new dynamical universality classes, including some with arbitrarily large upper critical dimensions. Using large scale simulations of classical Markov chains, we find numerical evidence for a breakdown of hydrodynamics in quadrupole-conserving models with broke…
We study models with fracton-like order based on $\mathbb{Z}_2$ lattice gauge theories with subsystem symmetries in $d=2$ and $d=3$ spatial dimensions. The $3d$ model reduces to the $3$-dimensional Toric Code when subsystem symmetry is broken, giving an example of a subsystem symmetry enriched topological phase (SSET). Although not topologically protected, its ground state degeneracy has as leading contribution a term which grows exponentially with the square of the linear size of the system. Also, there are completely mobile gauge charges living along with immobile fractons. Our method shows …
Fractons are particles with restricted mobility. We give a symmetry-based derivation of effective field theories of gapless phases with fractonic topological defects, such as solids and supersolids, using a coset construction. The resulting theory is identified as the Cosserat elasticity theory, which reproduces the conventional symmetric elasticity theory at low energies. The construction can be viewed as a dynamical realization of the inverse Higgs mechanism. We incorporate topological defects such as dislocations and disclinations, which are nontrivially related by the Bianchi identities of…
We construct infinite families of new universality classes of fracton hydrodynamics with momentum conservation, both with multipole conservation laws and/or subsystem symmetry. We explore the effects of broken inversion and/or time-reversal symmetry at the ideal fluid level, along with momentum relaxation. In the case of one-dimensional multipole-conserving models, we write down explicit microscopic Hamiltonian systems realizing these new universality classes. All of these hydrodynamic universality classes exhibit instabilities and will flow to new non-equilibrium fixed points. Such fixed poin…
The spontaneous breaking of boost invariance is ubiquitous in nature, yet the associated Goldstone bosons are nowhere to be seen. We discuss why some subtleties are to be expected in the Goldstone phenomenon for spontaneously broken boosts, and derive the corresponding quantum mechanical, non-perturbative Goldstone theorem. Despite similarities with more standard Goldstone theorems, we show by examples that ours can be obeyed by quite unusual spectra of low-energy excitations. In particular, for non-relativistic Fermi liquids, we prove that it is obeyed by the particle-hole continuum. To the b…
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.
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.
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 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.
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 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.
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.
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 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.
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…
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 study p-string condensation mechanisms for fracton phases from the viewpoint of higher-form symmetry, focusing on the examples of the X-cube model and the rank-two symmetric-tensor U(1) scalar charge theory. This work is motivated by questions of the relationship between fracton phases and continuum quantum field theories, and also provides general principles to describe p-string condensation independent of specific lattice model constructions. We give a perspective on higher-form symmetry in lattice models in terms of cellular homology. Applying this perspective to the coupled-layer constr…
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.
We study the non-local regularization for the case of a spontaneously broken abelian gauge theory in the R_xi gauge with an arbitrary gauge parameter xi. We consider a simple abelian-Higgs model with chiral couplings as an example. We show that if we apply the nonlocal regularization procedure [to construct a nonlocal theory with finite mass parameter ] to the spontaneously broken R_xi gauge Lagrangian, using the quadratic forms as appearing in this Lagrangian, we find that a physical observable in this model, an analogue of the muon anomalous magnetic moment, evaluated to order O[g^{2}] does …
We derive positivity bounds on EFT coefficients in theories where boosts are spontaneously broken. We employ the analytic properties of the retarded Green's function of conserved currents (or of the stress-energy tensor) and assume the theory becomes conformal in the UV. The method is general and applicable to both cosmology and condensed matter systems. As a concrete example, we look at the EFT of conformal superfluids which describes the universal low-energy dynamics of CFT's at large chemical potential and we derive inequalities on the coefficients of the operators, in three dimensions, at …
In the framework of the gauge symmetry ${SU(2)}_{\tiny{CMB}}\times {SU(2)}_{\tiny{e}}\times {SU(2)}_{\tinyμ}\times {SU(2)}_{\tinyτ}$ we provide a microscopic argument why a spontaneously broken, local Z$_2$ symmetry surviving the 1$^{\tiny{st}}$ order phase transition to the confining phase of one of the SU(2) factors generates two stable spin-1/2 excitations of vastly different mass. A mixture of Fermi-Dirac and Bose-Einstein distributions with the former favored by a factor two over the latter is obtained by applying inequivalent, local-in-Euclidean-time Z$_2$ transformations to one and the …
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.
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.
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.
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.
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.
Rational counterterms are a key ingredient for the automation of loop calculations through numerical methods. Building on the recently established properties of rational terms of UV origin at two loops, in this paper we present a systematic method for the determination of rational counterterms within spontaneously broken theories. In particular we introduce a generalised vev-expansion approach that makes it possible to obtain the rational counterterms of UV origin for a spontaneously broken theory by means of calculations in the unbroken phase. The drastic simplifications that result from the …
We analyze the vacuum structure of spontaneously broken N=2 supersymmetric gauge theory with the Fayet-Iliopoulos term. Our theory is based on the gauge group SU(2) \times U(1) with N_f=1,2 massless quark hypermultiplets having the same U(1) charges. In the classical potential, there are degenerate vacua even in the absence of supersymmetry. It is shown that this vacuum degeneracy is smoothed out, once quantum corrections are taken into account. In N_f=1 case, the effective potential is found to be so-called runaway type, and there is neither well-defined vacuum nor local minimum. On the other…
We consider low energy processes described by the N=2 supercurrent on its partially (to N=1) and spontaneously broken vacuum and the attendant Nambu-Goldstone fermion (NGF), which the presence of the electric and magnetic Fayet-Iliopoulos (FI) terms is responsible for. We show suppressions of amplitudes decaying into the NGF as its momentum becomes small. In the lagrangian realization (namely, the model of arXiv:hep-th/0409060) of the conserved supercurrent, the NGF resides in the overall U(1), which is nonetheless not decoupled, and interacts with the SU(N) sector through nonderivative as wel…
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.
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…
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.
A generalization of the standard electroweak model to noncommutative spacetime would involve a product gauge group which is spontaneously broken. Gauge interactions in terms of physical gauge bosons are canonical with respect to massless gauge bosons as required by the exact gauge symmetry, but not so with respect to massive ones; and furthermore they are generally asymmetric in the two sets of gauge bosons. On noncommutative spacetime this already occurs for the simplest model of U(1) x U(1). We examine whether the above feature in gauge interactions can be perturbatively maintained in this m…
We explore the possibility that scale symmetry is a quantum symmetry that is broken only spontaneously and apply this idea to the Standard Model (SM). We compute the quantum corrections to the potential of the higgs field ($ϕ$) in the classically scale invariant version of the SM ($m_ϕ=0$ at tree level) extended by the dilaton ($σ$). The tree-level potential of $ϕ$ and $σ$, dictated by scale invariance, may contain non-polynomial effective operators, e.g. $ϕ^6/σ^2$, $ϕ^8/σ^4$, $ϕ^{10}/σ^6$, etc. The one-loop scalar potential is scale invariant, since the loop calculations manifestly preserve t…
We consider an N=2 supersymmetric SU(2) \times 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 pseudo-flat direction in the classical potential. This vacuum degeneracy is removed once quantum corrections are taken into account. Due to 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 …
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 investigate fermion production in the background of Minkowski space solutions to the equations of motion of $SU(2)$ gauge theory spontaneously broken via the Higgs mechanism. First, we attempt to evaluate the topological charge $Q$ of the solutions. We find that for solutions $Q$ is not well-defined as an integral over all space-time. Solutions can profitably be characterized by the (integer-valued) change in Higgs winding number $ΔN_H$. We show that solutions which dissipate at early and late times and which have nonzero $ΔN_H$ must have at least the sphaleron energy. We show that if we co…
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…
