Nambu-Goldstone Research Articles

Non-Abelian chiral soliton lattice in rotating QCD matter: Nambu-Goldstone and excited modes

The ground state of QCD with two flavors at a finite baryon chemical potential under rapid rotation is a chiral soliton lattice (CSL) of the η meson, consisting of a stack of sine-Gordon solitons carrying a baryon number, due to the anomalous coupling of the η meson to the rotation. In a large parameter region, the ground state becomes a non-Abelian CSL, in which due to the neutral pion condensation each η soliton decays into a pair of non-Abelian sine-Gordon solitons carrying S2 moduli originated from Nambu-Goldstone (NG) modes localized around it, corresponding to the spontaneously broken vector symmetry SU(2)V. There, the S2 modes of neighboring solitons are anti-aligned, and these modes should propagate in the transverse direction of the lattice due to the interaction between the S2 modes of neighboring solitons. In this paper, we calculate excitations including gapless NG modes and excited modes around non-Abelian and Abelian (η) CSLs, and find three gapless NG modes with linear dispersion relations (type-A NG modes): two isospinons (S2 modes) and a phonon corresponding to the spontaneously broken vector SU(2)V and translational symmetries around the non-Abelian CSL, respectively, and only a phonon for the Abelian CSL because of the recovering SU(2)V. We also find in the deconfined phase that the dispersion relation of the isospinons becomes of the Dirac type, i.e. linear even at large momentum.

Nambu-goldstone Modes in Two Segregated Bose-einstein Condensates Limited by Two Hard Walls

The Nambu-Goldstone (NG) modes in the system of two segregated Bose-Einstein condensates (BECs) limited by two hard walls are studied by means of the Gross-Pitaevskii (GP) theory. Based on the double-parabola approximation (DPA) combining with the Bogoliubov-de Gennes (BdG) equations we found four NG modes that proves the failure of the Watanabe-Brauner counting rule and, furthermore, their dispersion relations depend explicitly on the geometrical structure.
 
 

Dynamics of strongly-coupled chiral gauge theories

We study the dynamics of SU(N) chiral gauge theories with massless fermions belonging to various combinations of the symmetric, antisymmetric or fundamental representations. We limit ourselves to the gauge-anomaly-free and asymptotically free systems. These theories have a global symmetry group with the associated ’t Hooft anomaly-matching conditions severely limiting the possible RG flows. Recent developments on the applications of the generalized symmetries and the stronger requirement of the matching of the mixed anomalies also give further indications on the possible IR dynamics. In vectorlike theories such as the quantum chromodynamics (QCD), gauge-invariant “quark-antiquark” condensates form and characterize the IR dynamics, and the anomaly matching involves the Nambu-Goldstone (NG) bosons. In some other special cases, such as the Bars-Yankielowicz (BY) or Georgi-Glashow (GG) models, a hypothetical solution was proposed in the literature, with no global symmetry breaking and with some simple set of composite massless fermions saturating all the anomalies. For the BY and GG systems, actually, a more plausible candidate for their IR physics is the dynamical Higgs phase, with a few simple bi-fermion color-flavor locked condensates, breaking the color and flavor symmetries, partially or totally. Remarkably, the ’t Hooft anomaly-matching (and generalized anomaly-matching) conditions are automatically satisfied in this phase. Another interesting possibility, occurring in some chiral gauge theories, is dynamical Abelianization, familiar from N = 2 supersymmetric gauge theories. We explore here even more general types of possible IR phases than the ones mentioned above, for wider classes of models. With the help of large-N arguments we look for IR free theories, whereas the MAC (maximal attractive channel) criterion might suggest some simple bi-fermion condensates characterizing the IR dynamics of the systems. In many cases the low-energy effective theories are found to be described by quiver-like gauge theories, some of the (nonAbelian) gauge groups are infrared-free while some others might be asymptotically free.

Minimal Nambu-Goldstone-Higgs model in supersymmetric SU(5) revisited

We revisit the minimal Nambu-Goldstone (NG) Higgs supersymmetric (SUSY) SU(5) grand unified model and study its phenomenological implications. The Higgs sector of the model possesses a global SU(6) symmetry, which is spontaneously broken and results in the Higgs doublets of the minimal SUSY Standard Model (MSSM) as NG chiral superfields. Therefore, the model naturally leads to light Higgs doublets and solves the doublet-triplet splitting problem. Because of the SU(6) symmetry, the couplings of the Higgs sector are tightly restricted, and thus the model is more predictive than the minimal SUSY SU(5). We determine all the grand-unified-theory parameters via the matching conditions of the gauge coupling constants at the unification scale and calculate proton lifetime, confronting this with current experimental bounds. We discuss that this model is incompatible with the constrained MSSM, whilst it has a large viable parameter space in the high-scale SUSY scenario. The perturbativity condition on the trilinear coupling of the adjoint Higgs field imposes an upper (lower) limit on the wino (gluino) mass, implying a hierarchical mass pattern for these gauginos. Future proton-decay searches can probe a large part of the parameter space, especially if the SUSY-breaking scale is $\lesssim 100$~TeV.

Unstable Nambu-Goldstone modes

Nambu-Goldstone (NG) modes for 0-form and higher-form symmetries can become unstable in the presence of background fields. Examples include the instability of a photon with a time-dependent axion background or with a chirality imbalance, known as the chiral plasma instability, and the instability of a dynamical axion with a background electric field. We show that all these phenomena can be universally described by a symmetry algebra for 0-form and higher-form symmetries. We prove a counting rule for the number of unstable NG modes in terms of correlation functions of broken symmetry generators. Based on our unified description, we further give a simple new example where one of the NG modes associated with the spontaneous 0-form symmetry breaking $U(1) \times U(1) \to \{1\}$ becomes unstable.

On commutator-based linearization of vector-spinor nonlinear supersymmetry and Rarita–Schwinger fields

In this paper, we discuss the linearization of vector-spinor (spin-3/2) nonlinear supersymmetry (vsNLSUSY) transformations for both [Formula: see text] and [Formula: see text]-extended SUSY in flat spacetime based on the commutator algebra by using functionals (composites) of spin-3/2 Nambu–Goldstone (NG) fermions, which are expressed as simple products of powers of the spin-3/2 NG fermions and a fundamental determinant in the vsNLSUSY theory. We define basic component fields by means of those functionals in a linearized vsSUSY theory including spin-3/2 fields, general auxiliary ones and a [Formula: see text]-term. The general forms of linear (rigid) vsSUSY transformations for the component fields are determined uniquely from the commutator-based linearization procedure. By considering appropriate recombinations of the functionals of the spin-3/2 NG fermions for [Formula: see text] SUSY, we find that variations of the recombinations under the vsNLSUSY transformations include linear spin-1/2 SUSY ones of spin-[Formula: see text] fields with [Formula: see text] gauge invariance. The spinorial gauge invariance of the Rarita–Schwinger action in the linearization process is also discussed together with the [Formula: see text] gauge invariance.

Effective field theory of fluctuating wall in open systems: from a kink in Josephson junction to general domain wall

We investigate macroscopic behaviors of fluctuating domain walls in nonequilibrium open systems with the help of the effective field theory based on symmetry. Since the domain wall in open systems breaks the translational symmetry, there appears a gapless excitation identified as the Nambu-Goldstone (NG) mode, which shows the non-propagating diffusive behavior in contrast to those in closed systems. After demonstrating the presence of the diffusive NG mode in the (2+1)-dimensional dissipative Josephson junction, we provide a symmetry-based general analysis for open systems breaking the one-dimensional translational symmetry. A general effective Lagrangian is constructed based on the Schwinger-Keldysh formalism, which supports the presence of the gapless diffusion mode in the fluctuation spectrum in the thin wall regime. Besides, we also identify a term peculiar to the open system, which possibly leads to the instability in the thick-wall regime or the nonlinear Kardar-Parisi-Zhang coupling in the thin-wall regime although it is absent in the Josephson junction.

Effective Lagrangian for Nambu-Goldstone modes in nonequilibrium open systems

We develop the effective field theory of diffusive Nambu-Goldstone (NG) modes associated with spontaneous internal symmetry breaking taking place in nonequilibrium open systems. The effective Lagrangian describing semi-classical dynamics of the NG modes is derived and matching conditions for low-energy coefficients are also investigated. Due to new terms peculiar to open systems, the associated NG modes show diffusive gapless behaviors in contrast to the propagating NG mode in closed systems. We demonstrate two typical situations relevant to the condensed matter physics and high-energy physics, where diffusive type-A or type-B NG modes appear.

Perfect Transmission and Perfect Reflection of Bogoliubov Quasiparticles in a Dynamically Unstable Bose–Einstein Condensate

The Nambu–Goldstone (NG) mode in a Bose–Einstein condensate (BEC) transmits a potential barrier with probability 1 in the zero-energy limit, which is known as the anomalous tunneling. In this paper, we investigate the tunneling properties of quasiparticles in a dynamically unstable BEC. We prepare a multicomponent BEC (binary and spin-1 BECs) in a dynamically unstable state and solve the tunneling problem of the spin-wave excitation from the condensate. We find that the perfect transmission occurs even when the BEC is dynamically unstable if the spin-wave mode is the NG mode. Here, the mode that exhibits the perfect transmission is the dynamically unstable spin-wave, which is a pure-imaginary-eigenvalue solution of the Bogoliubov–de Gennes equation. Hence, we should take the zero-energy limit not along the real axis but along the imaginary axis. We also demonstrate the existence of the perfect reflection of a dynamically unstable mode at the point where the imaginary part of the eigenvalue takes its maximum. In this case, the incident and reflected waves destructively interfere, and the amplitude of the quasiparticle wave function is strongly suppressed. We numerically confirm that the perfect reflection is a generic nature of dynamically unstable modes and not related to the NG mode. A possible experimental scheme to observe the tunneling properties is discussed on the basis of real-time dynamics obtained by solving the time-dependent Gross–Pitaevskii equation.

Counting Nambu-Goldstone Modes of Higher-Form Global Symmetries.

We discuss the counting of Nambu-Goldstone (NG) modes associated with the spontaneous breaking of higher-form global symmetries. Effective field theories of NG modes are developed based on symmetry-breaking patterns, using a generalized coset construction for higher-form symmetries. We derive a formula of the number of gapless NG modes, which involves expectation values of the commutators of conserved charges, possibly of different degrees.

Exceptional nonrelativistic effective field theories with enhanced symmetries

We initiate the classification of nonrelativistic effective field theories (EFTs) for Nambu-Goldstone (NG) bosons, possessing a set of redundant, coordinate-dependent symmetries. Similarly to the relativistic case, such EFTs are natural candidates for “exceptional” theories, whose scattering amplitudes feature an enhanced soft limit, that is, scale with a higher power of momentum at long wavelengths than expected based on the mere presence of Adler’s zero. The starting point of our framework is the assumption of invariance under spacetime translations and spatial rotations. The setup is nevertheless general enough to accommodate a variety of nontrivial kinematical algebras, including the Poincaré, Galilei (or Bargmann) and Carroll algebras. Our main result is an explicit construction of the nonrelativistic versions of two infinite classes of exceptional theories: the multi-Galileon and the multi-flavor Dirac-Born-Infeld (DBI) theories. In both cases, we uncover novel Wess-Zumino terms, not present in their relativistic counterparts, realizing nontrivially the shift symmetries acting on the NG fields. We demonstrate how the symmetries of the Galileon and DBI theories can be made compatible with a nonrelativistic, quadratic dispersion relation of (some of) the NG modes.

Emergence of the Unconventional Type-II Nambu-Goldstone Modes with Topological Origin in Bose Superfluids.

The Nambu-Goldstone (NG) modes in a nonrelativistic system can be classified into two types from their characteristic features: being of either an odd (type I) or an even (type II) power energy-momentum dispersion. Conventionally, the type-II NG modes may universally arise from spontaneous breaking of noncommutative symmetry pairs. Here, we predict a novel type of quadratically dispersed NG modes that emerges in mixed s and p band Bose superfluids in an optical lattice and, unlike the conventional type-II NG modes, cannot be solely interpreted with the celebrated symmetry-based argument. Instead, we show that the existence of such modes has a profound connection to the topological transition on projective complex order-parameter space. The detection scheme is also proposed. Our Letter reveals a new universal mechanism for emergence of type-II NG modes, which bridges intrinsically the Landau symmetry-breaking and topological theories.

Thouless-Valatin moment of inertia and removal of the spurious mode in the linear response theory

Symmetry breaking at the mean-field level leads to an appearance of a symmetry restoring Nambu-Goldstone (NG) mode in the linear response theory. These modes represent a special kind of collective motion of the system. However, they can interfere with the calculated intrinsic physical excitations and, hence, they are often called as spurious modes. I discuss translational and rotational NG mode and the inertia parameter associated with these modes, by using the finite amplitude method formalism. I will also discuss how to remove spurious mode from the calculated transition strength function.

Cosmic string in Abelian-Higgs model with enhanced symmetry \u2014 Implication to the axion domain-wall problem

In our previous work, we found new types of the cosmic string solutions in the Abelian-Higgs model with an enhanced U(1) global symmetry. We dubbed those solutions as the compensated/uncompensated strings. The compensated string is similar to the conventional cosmic string in the Abrikosov-Nielsen-Olesen (ANO) string, around which only the would-be Nambu-Goldstone (NG) boson winds. Around the uncompensated string, on the other hand, the physical NG boson also winds, where the physical NG boson is associated with the spontaneous breaking of the enhanced symmetry. Our previous simulation in the 2+1 dimensional spacetime confirmed that both the compensated/uncompensated strings are formed at the phase transition of the symmetry breaking. Non-trivial winding of the physical NG boson around the strings potentially causes the so-called axion domain- wall problem when the model is applied to the axion model. In this paper, we perform simulation in the 3+1 dimensional spacetime to discuss the fate of the uncompensated strings. We observe that the evolution of the string-network is highly complicated in the 3+1 dimensional simulation compared with that seen in the previous simulation. Despite such complications, we find that the number of the uncompensated strings which could cause can be highly suppressed at late times. Our observation suggests that the present setup can be applied to the axion model without suffering from the axion domain-wall problem.

Spin excitations in dipolar spin-1 condensates

We investigate the low-lying spin excitation of a trapped dipolar spin-1 condensate with antiferromagnetic spin-exchange interactions by numerically solving the Bogoliubov--de Gennes equations. We explore the behavior of the excited modes with different dipolar interaction strength and in different trap geometries. We also discuss the origin of the Nambu-Goldstone (NG) zero modes in different phases by analyzing the broken continuous symmetries of the ground-state wave function. In particular, we find a quasi-NG mode in the antiferromagnetic phase. These studies lead to the discovery of an unusual quantum phase and the exact critical trap aspect ratio for one of the phase transitions.

Role of Nambu-Goldstone modes in the fermionic-superfluid point contact

In fermionic superfluids that are charge neutral, Nambu-Goldstone (NG) modes also known as Anderson-Bogoliubov modes emerge as a result of spontaneous symmetry breaking. Here, we discuss DC transport properties of such NG modes through a quantum point contact. We show that contrary to a naive view that enhancement of the phase stiffness may suppress transport of the NG modes, there must be an anomalous contribution that survives at low temperature. This contribution originates from the conversion process between the condensate and NG mode. We find that within the BCS regime the anomalous contribution is enhanced with increasing channel transmittance and attractive interaction, and leads to a temperature-dependent Lorenz number and absence of the bunching effect in current noise.

Bino-wino coannihilation as a prediction in the E7 unification of families

We study the phenomenological consequences of the supersymmetric (SUSY) E7/SU(5) × U(1)3 non-linear sigma model coupled to supergravity, where the three gen- erations of quark and lepton chiral multiplets appear as (pseudo) Nambu Goldstone (NG) multiplets, that is, the origin of the three families is explained. To break SUSY, we intro- duce a SUSY breaking field charged under some symmetry avoiding the Polonyi problem. The gaugino mass spectrum is almost uniquely determined when one requires the electroweak vacuum to be (meta)stable: it would be a miracle that the mass difference between the bino and wino turns out to be within mathcal{O} (1)% at the low energy. Thus, a bino-wino coannihilation is naturally predicted, which can explain the correct relic abundance of dark matter. Moreover, we find that the bottom-tau Yukawa couplings and the gauge couplings are unified up to mathcal{O} (1)% in most of the viable region. This scenario can be fully tested at the LHC and future collider experiments since the gauginos and some of the pseudo-NG bosons are light. An axion-like multiplet, which can be identified with the QCD axion, is also predicted.

Crawling technicolor

We analyze the Callan-Symanzik equations when scale invariance at a nontrivial infrared (IR) fixed point $\alpha^{}_{\mathrm{IR}}$ is realized in the Nambu-Goldstone (NG) mode. As a result, Green's functions at $\alpha^{}_{\mathrm{IR}}$ do not scale in the same way as for the conventional Wigner-Weyl (WW) mode. This allows us to propose a new mechanism for dynamical electroweak symmetry breaking where the running coupling $\alpha$ "crawls" towards (but does not pass) $\alpha^{}_{\mathrm{IR}}$ in the exact IR limit. The NG mechanism at $\alpha^{}_{\mathrm{IR}}$ implies the existence of a massless dilaton $\sigma$, which becomes massive for IR expansions in $\epsilon \equiv \alpha^{}_{\mathrm{IR}} - \alpha$ and is identified with the Higgs boson. Unlike "dilatons" that are close to a WW-mode fixed point or associated with a Coleman-Weinberg potential, our NG-mode dilaton is genuine and hence naturally light. Its (mass)$^2$ is proportional to $\epsilon \beta'(4+\beta')F_\sigma^{-2} \langle\hat{G}^2\rangle_{\text{vac}}$, where $\beta'$ is the (positive) slope of the beta function at $\alpha^{}_{\mathrm{IR}}$, $F_\sigma$ is the dilaton decay constant and $\langle\hat{G}^2\rangle_{\text{vac}}$ is the technigluon condensate. Our effective field theory for this works because it respects Zumino's consistency condition for dilaton Lagrangians. We find a closed form of the Higgs potential with $\beta'$-dependent deviations from that of the Standard Model. Flavor-changing neutral currents are suppressed if the crawling region $\alpha \lesssim \alpha^{}_{\mathrm{IR}}$ includes a sufficiently large range of energies above the TeV scale. In Appendix A, we observe that, contrary to folklore, condensates protect fields from decoupling in the IR limit.

Pion and kaon structure at the electron-ion collider

Understanding the origin and dynamics of hadron structure and in turn that of atomic nuclei is a central goal of nuclear physics. This challenge entails the questions of how does the roughly 1 GeV mass-scale that characterizes atomic nuclei appear; why does it have the observed value; and, enigmatically, why are the composite Nambu-Goldstone (NG) bosons in quantum chromodynamics (QCD) abnormally light in comparison? In this perspective, we provide an analysis of the mass budget of the pion and proton in QCD; discuss the special role of the kaon, which lies near the boundary between dominance of strong and Higgs mass-generation mechanisms; and explain the need for a coherent effort in QCD phenomenology and continuum calculations, in exa-scale computing as provided by lattice QCD, and in experiments to make progress in understanding the origins of hadron masses and the distribution of that mass within them. We compare the unique capabilities foreseen at the electron-ion collider (EIC) with those at the hadron-electron ring accelerator (HERA), the only previous electron-proton collider; and describe five key experimental measurements, enabled by the EIC and aimed at delivering fundamental insights that will generate concrete answers to the questions of how mass and structure arise in the pion and kaon, the Standard Model's NG modes, whose surprisingly low mass is critical to the evolution of our Universe.

Triangle anomalies and nonrelativistic Nambu-Goldstone modes of generalized global symmetries

In massless QCD coupled to QED in an external magnetic field, a photon with the linear polarization in the direction of the external magnetic field mixes with the charge neutral pion through the triangle anomaly, leading to one gapless mode with the quadratic dispersion relation $\omega \sim k^2$ and one gapped mode. We show that this gapless mode can be interpreted as the so-called type-B Nambu-Goldstone (NG) mode associated with the spontaneous breaking of generalized global symmetries and that its presence is solely dictated by the anomalous commutator in the symmetry algebra. We also argue a possible realization of such nonrelativistic NG modes in 3-dimensional Dirac semimetals.