Chiral Flavor Symmetry Research Articles

Mirror dualities with four supercharges

We consider 3d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 non-abelian Hanany-Witten brane setups with chiral flavor symmetry. We propose that the associated field theories are quivers with improved bifundamentals, instead of standard bifundamentals. The improved bifundamental is a strongly coupled SCFT that carries one more U(1) global symmetry than the standard bifundamental. As a consequence, our proposal overcomes the long standing challenge of associating to each N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 brane setup a gauge theory with the full rank global symmetry, allowing the study of all the usual supersymmetric observables, such as superconformal index, sphere partition function, chiral ring and moduli space. The construction passes many non-trivial tests, for instance we algorithmically prove that any two improved quivers associated to S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{S} $$\\end{document}-dual brane setups are infrared dual. The 3dN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 mirror dualities can be uplifted to 4d dualities with 4d improved bifundamentals connecting USp(2N) nodes.

CKM and PMNS mixing matrixes from SO(2) flavor symmetry

The relation between quark masses and CKM mixing is studied based on an approximate chiral flavor symmetry of quark mass matrix. In mass hierarchy limit, the mass ratio effect on CKM mixing is suppressed, which separates mass hierarchy and quark flavor mixing into two independent problems. We show that CKM mixing is dominated by two left-handed symmetries while mass hierarchy only provides slight corrections. The same mixing structure is generalized to lepton sector with extended Dirac neutrinos. The common flavor mixing provides a novel comprehension on the relation between quark CKM mixing and lepton PMNS mixing.

Chiral composite asymmetric dark matter

The asymmetric dark matter (ADM) scenario solves the baryon-dark matter coincidence problem when the dark matter (DM) mass is of mathcal{O}(1) GeV. Composite ADM models based on QCD-like strong dynamics are particularly motivated since the strong dynamics naturally provides the DM mass of mathcal{O}(1) GeV and the large annihilation cross-section simultaneously. In those models, the sub-GeV dark photon often plays an essential role in transferring the excessive entropy in the dark sector into the visible sector, i.e., the Standard Model sector. This paper constructs a chiral composite ADM model where the U(1)D gauge symmetry is embedded into the chiral flavor symmetry. Due to the dynamical breaking of the chiral flavor symmetry, the model naturally provides the masses of the dark photon and the dark pions in the sub-GeV range, both of which play crucial roles for a successful ADM model.

Dynamical generation of field mixing via flavor vacuum condensate

In this paper we study dynamical chiral symmetry breaking of a generic quantum field theoretical model with global chiral flavor symmetry. By purely algebraic means we analyze the vacuum structure for different symmetry breaking schemes and show explicitly how the ensuing non-trivial flavor vacuum condensate characterizes the phenomenon of field mixing. In addition, with the help of Ward-Takahashi identities we demonstrate the emergence of a correct number of Nambu-Goldstone modes in the physical spectrum.

Dynamical generation of three flavor mixing

In this paper we study patterns of dynamical symmetry breaking for a class of models characterized by SU(3)V × SU(3)A × U(1)V chiral-flavor symmetry. In particular, we show how dynamical mixing generation implies the existence of exotic condensates on vacuum, mixing fermion and antifermions with different flavors. By means of Ward–Takahashi identities we also derive Haag expansions for Nambu–Goldstone fields.

Patterns of symmetry breaking in chiral QCD

We consider $SU(N)$ Yang-Mills theory with massless chiral fermions in a complex representation of the gauge group. The main emphasis is on the so-called hybrid psi-chi-eta model. The possible patterns of realization of the continuous chiral flavor symmetry are discussed. We argue that the chiral symmetry is broken in conjunction with a dynamical Higgsing of the gauge group (complete or partial) by bi-fermion condensates. As a result a color-flavor locked symmetry is preserved. The 't Hooft anomaly matching proceeds via saturation of triangles by massless composite fermions or, in a mixed mode, i.e., also by the "weakly" coupled fermions associated with dynamical Abelianization, supplemented by a number of Nambu-Goldstone mesons. Gauge-singlet condensates are of the multifermion type and, though it cannot be excluded, the chiral symmetry realization via such gauge invariant condensates is more contrived (requires a number of four-fermion condensates simultaneously and, even so, problems remain), and less plausible. We conclude that in the model at hand, chiral flavor symmetry implies dynamical Higgsing by bifermion condensates.

Constraints on low energy QCD parameters from eta rightarrow 3pi and pi pi scattering

The eta ,rightarrow ,3pi decays are a valuable source of information on low energy QCD. Yet they were not used for an extraction of the three flavor chiral symmetry breaking order parameters until now. We use a Bayesian approach in the framework of resummed chiral perturbation theory to obtain constraints on the quark condensate and pseudoscalar decay constant in the chiral limit. We compare our results with recent CHPT and lattice QCD fits and find some tension, as the eta ,rightarrow ,3pi data seem to prefer a larger ratio of the chiral order parameters. The results also disfavor a very large value of the pseudoscalar decay constant in the chiral limit, which was found by some recent work. In addition, we present results of a combined analysis including eta ,rightarrow ,3pi decays and pi pi scattering and though the picture does not changed appreciably, we find some tension between the data we use. We also try to extract information on the mass difference of the light quarks, but the uncertainties prove to be large.

Dp-brane Dynamics and Thermalization in Type IIB Ben Ami-Kuperstein-Sonnenschein Models

We extend and complete our analysis arXiv:1608.02380 and study the induced world volume metrics and Hawking temperatures of all type IIB rotating probe Dp-branes, dual to the temperature of different flavors at finite R-charge, in the Ben Ami–Kuperstein–Sonnenschein holographic models including the effects of spontaneous conformal and chiral flavor symmetry breakdown. The model embeds type IIB probe flavor Dp-branes into the Klebanov-Witten gravity dual of conformal gauge theory, with the embedding parameter, given by the minimal radial extension of the probes, dual to the IR scale of conformal and chiral flavor symmetry breakdown. We show that when the minimal extension is positive definite, the induced world volume metrics of type IIB rotating probe branes admit thermal horizons and Hawking temperatures despite the absence of black holes in the bulk subject to the world volume and topology of the nontrivial internal cycle wrapped by the probe. We also derive the energy–stress tensor of the thermal probes and study their backreaction and energy dissipation. We show that at the IR scale the backreaction is nonnegligible and find the energy can flow from the probes to the bulk, dual to the energy dissipation from the flavor sectors into the gauge theory.

D7-brane dynamics and thermalization in the Kuperstein–Sonnenschein model

We study the temperature of rotating probe D7-branes, dual to the temperature of flavored quarks, in the Kuperstein–Sonnenschein holographic model including the effects of spontaneous breakdown of the conformal and chiral flavor symmetry. The model embeds probe D7-branes into the Klebanov–Witten gravity dual of conformal gauge theory, with the embedding parameter, given by the minimal radial extension of the probe, setting the IR scale of conformal and chiral flavor symmetry breakdown. We show that when the minimal extension is positive definite and additional spin is turned on, the induced world volume metrics on the probe admit thermal horizons and Hawking temperatures despite the absence of black holes in the bulk. We find the scale and behavior of the temperature in flavored quarks are controlled dramatically by the IR scale of symmetry breaking, and by the strength and sort of external fields. We also derive the energy-stress tensor of the rotating probe and study its backreaction and energy dissipation. We show that at the IR scale the backreaction is nonnegligible and find the energy can flow from the probe to the bulk, dual to the energy dissipation from the flavor sector into the gauge theory.

Is the relaxion an axion?

We consider the recently proposed cosmological relaxation mechanism where the hierarchy problem is ameliorated, and the electroweak (EW) scale is dynamically selected by a slowly rolling axion field. We argue that, in its simplest form, the construction breaks a gauge symmetry that always exists for pseudo-Nambu-Goldstone bosons (in particular the axion). The small parameter in the relaxion model is therefore not technically natural as it breaks a gauge symmetry rather than global symmetries only. The consistency of the theory generically implies that the cutoff must lie around the electroweak scale, but not qualitatively higher. We discuss several ways to evade the above conclusion. Some of them may be sufficient to increase the cutoff to the few-TeV range (and therefore may be relevant for the little-hierarchy problem). To demonstrate the ideas in a concrete setting we consider a model with a familon, the Nambu-Goldstone boson of a spontaneously broken chiral flavor symmetry. The model has some interesting collider-physics aspects and contains a viable weakly interacting dark matter candidate.

Position space formulation for Dirac fermions on honeycomb lattice

We study how to construct Dirac fermion defined on the honeycomb lattice in position space. Starting from the nearest neighbor interaction in tight binding model, we show that the Hamiltonian is constructed by kinetic term and second derivative term of three flavor Dirac fermions in which one flavor has a mass of cutoff order and the other flavors are massless. In this formulation, the structure of the Dirac point is simplified so that its uniqueness can be easily shown even if we consider the next-to-nearest neighbor interaction. We also show that there is a hidden exact U(1) symmetry (flavor–chiral symmetry) at finite lattice spacing, which protects the masslessness of the Dirac fermion, and discuss the analogy with the staggered fermion formulation.

A holographic quantum Hall ferromagnet

A detailed numerical study of a recent proposal for exotic states of the D3-probe D5 brane system with charge density and an external magnetic field is presented. The state has a large number of coincident D5 branes blowing up to a D7 brane in the presence of the worldvolume electric and magnetic fields which are necessary to construct the holographic state. Numerical solutions have shown that these states can compete with the the previously known chiral symmetry breaking and maximally symmetric phases of the D3-D5 system. Moreover, at integer filling fractions, they are incompressible with integer quantized Hall conductivities. In the dual superconformal defect field theory, these solutions correspond to states which break the chiral and global flavor symmetries spontaneously. The region of the temperature-density plane where the D7 brane has lower energy than the other known D5 brane solutions is identified. A hypothesis for the structure of states with filling fraction and Hall conductivity greater than one is made and tested by numerical computation. A parallel with the quantum Hall ferromagnetism or magnetic catalysis phenomenon which is observed in graphene is drawn. As well as demonstrating that the phenomenon can exist in a strongly coupled system, this work makes a number of predictions of symmetry breaking patterns and phase transitions for such systems.

Lattice formulation of 2D = (2,2) SQCD and twisted supercharges

We discuss on two kinds of lattice formulation of two-dimensional = (2, 2) supersymmetric QCD preserving one of its supercharges. The preserved supercharge is of the same form obtained by topological twist. One formulation is based on A model twist, and the other is based on B model twist. For the A model twist case, by employing the Ginsparg-Wilson operator, the lattice model can be constructed for general number of flavors of fundamental and anti-fundamental matter multiplets under the gauge group G = U(N) or SU(N). It preserves both of one supercharge (Q) and chiral flavor symmetry of matter multiplets. Furthermore, superpotential can be introduced with exact holomorphic or anti-holomorphic structure on lattice. For the B model twist case, the lattice action takes a simpler form compared with the A model twist case, because the admissibility condition is not required to the formulation. It can be applied to a restricted cases of G = U(N) and of fundamental matters or anti-fundamental matters only.

A novel (2+1)-dimensional model of chiral symmetry breaking

We propose a new model of flavour chiral symmetry breaking in a (2+1)-dimensional defect gauge theory of strongly coupled fermions by introducing probe D5/anti-D5-flavour branes on the conifold. After working out the flavour brane embeddings at zero temperature, we thoroughly investigate the spectra of small fluctuations on the world volume of the flavour branes (meson spectrum) and conclude that they are free of tachyons. Thus the proposed probe brane embedding is stable. Moreover, we introduce finite temperature and an external magnetic field and study the thermodynamics of the resulting configurations. Namely, we compute the free energies, entropies, heat capacities and magnetisations. The results are used to establish a detailed phase diagram of the model. We find that the effect of magnetic catalysis of chiral symmetry breaking is realised in our model and show that the meson-melting phase transition coincides with the chiral symmetry breaking phase transition. Furthermore, we show that the model is in a diamagnetic phase.

A holographic model of heavy-light mesons

We construct a holographic model of heavy-light mesons by extending the AdS/QCD to incorporate the behavior of the heavy quark limit. In that limit, the QCD dynamics is governed by the light quark and the heavy quark simply plays the role of a static color source. The heavy quark spin symmetry can be treated as a global symmetry in the AdS bulk. As a consequence, the heavy-light mesons are mapped to "fermions" in the AdS theory. The light flavor chiral symmetry is naturally built in by this construction, and its breaking produces the splitting of the parity-doubled heavy-light meson states. The scaling dependences of physical quantities on the heavy quark mass in the heavy quark effective theory are reproduced. The mass spectra and decay constants of the B and D mesons can be well fit by suitable choices of model parameters. The couplings between the heavy-light mesons and the pions are also calculated. The holographic model may capture the essence of the long distance effects of QCD and can serve as a useful tool for studying the non-perturbative hadronic matrix elements involving heavy-light mesons.

Neutral kaon mixing beyond the standard model withnf=2+1chiral fermions

We compute the hadronic matrix elements of the four-quark operators needed for the study of ${K}^{0}\ensuremath{-}{\overline{K}}^{0}$ mixing beyond the Standard Model (SM). We use ${n}_{f}=2+1$ flavors of domain-wall fermion that exhibit good chiral-flavor symmetry. The renormalization is performed nonperturbatively through the RI-MOM scheme and our results are converted perturbatively to $\overline{\mathrm{MS}}$. The computation is performed on a single lattice spacing $a\ensuremath{\sim}0.086$ with a lightest unitary pion mass of 290 MeV. The various systematic errors, including the discretization effects, are estimated and discussed. Our results confirm a previous quenched study, where large ratios of non-SM to SM matrix elements were obtained.

Non-Abelian gauged Nambu–Jona-Lasinio models on the lattice

We use Monte Carlo simulation to probe the phase structure of a $SU(2)$ gauge theory containing ${N}_{f}$ Dirac fermion flavors transforming in the fundamental representation of the group and interacting through an additional four-fermion term. Pairs of physical flavors are implemented using the two tastes present in a reduced staggered fermion formulation of the theory. The resultant lattice theory is invariant under a set of shift symmetries which correspond to a discrete subgroup of the continuum chiral-flavor symmetry. The pseudoreal character of the representation guarantees that the theory has no sign problem. For the case of ${N}_{f}=4$ we observe a crossover in the behavior of the chiral condensate for strong four-fermi coupling associated with the generation of a dynamical mass for the fermions. At weak gauge coupling this crossover is consistent with the usual continuous phase transition seen in the pure (ungauged) Nambu--Jona-Lasinio model. However, if the gauge coupling is strong enough to cause confinement, we observe a much more rapid crossover in the chiral condensate consistent with a first order phase transition.

Scalar and vector mesons of flavor chiral symmetry breaking in the Klebanov-Strassler background

Recently, Dymarsky, Kuperstein and Sonnenschein constructed an embedding of flavor D7- and anti-D7-branes in the Klebanov-Strassler geometry that breaks the supersymmetry of the background, yet is stable. In this article, we study in detail the spectrum of vector mesons in this new model of flavor chiral symmetry breaking and commence an analytical analysis of the scalar mesons in this setup.

Chiral symmetry breaking with non-SUSY D7-branes in ISD backgrounds

Supersymmetric probe branes satisfy the κ-symmetry condition which ensures that the action is minimized with respect to both variations of the embedding and of the world-volume gauge field. We observe that the κ-symmetry condition for a D7-brane in an imaginary self-dual (ISD) background can be generalized yielding minimization of the action with respect to variations of the gauge field only but not of the embedding. This provides a new way to construct non-BPS solutions for D7-branes once the embedding extremizes the geometrical volume of the brane. We then apply this method to the Klebanov-Strassler background and find a new D7−7 brane configuration that realizes the spontaneous breaking of flavor chiral symmetry as evidenced by the Goldstone boson identified in the spectrum. This result generalizes our previous construction for the Klebanov-Witten model. We compare our setup with the Sakai-Sugimoto model and discuss possible applications to QCD-like physics.

Ginsparg–Wilson formulation of 2D [formula omitted] SQCD with exact lattice supersymmetry

In this paper, we introduce the overlap Dirac operator, which satisfies the Ginsparg–Wilson relation, to the matter sector of two-dimensional N = ( 2 , 2 ) lattice supersymmetric QCD (SQCD) with preserving one of the supercharges. It realizes the exact chiral flavor symmetry on the lattice, to make possible to define the lattice action for general number of the flavors of fundamental and anti-fundamental matter multiplets and for general twisted masses. Furthermore, superpotential terms can be introduced with exact holomorphic or anti-holomorphic structure on the lattice. We also consider the lattice formulation of matter multiplets charged only under the central U ( 1 ) (the overall U ( 1 ) ) of the gauge group G = U ( N ) , and then construct lattice models for gauged linear sigma models with exactly preserving one supercharge and their chiral flavor symmetry.