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A simple model of dark matter contains a light Dirac field charged under a hidden U(1) gauge symmetry. When a chiral matter content in a strong dynamics satisfies the t'Hooft anomaly matching condition, a massless baryon is a natural candidate of the light Dirac field. One realization is the same matter content as the standard SU(5)$\times$U(1)$_{(B-L)}$ grand unified theory. We propose a chiral [SU(5)$\times$U(1)]$^4$ gauge theory as a unified model of the SM and DM sectors. The low-energy dynamics, which was recently studied, is governed by the hidden U(1)$_4$ gauge interaction and the third-family U(1)$_{(B-L)_3}$ gauge interaction. This model can realize self-interacting dark matter and alleviate the small-scale crisis of collisionless cold dark matter in the cosmological structure formation. The model can also address the semi-leptonic $B$-decay anomaly reported by the LHCb experiment., 15 pages, 2 figures

We consider the L-R symmetric composite model for quarks and leptons where constituent preons possessing some local SU(N)MF metaflavor symmetry are bound by the chiral SO(n)L×SO(n)R gauge metacolor forces. The strengthening of the 't Hooft's anomaly matching condition, when the massless fermion composites are required to complete a single representation of the SU(N)MF rather than some set of its representations, allows to fix the number of basic metaflavors N. Particularly, just eight left-handed and eight right-handed preons and their composites preserving the global chiral symmetry SU(8)L×SU(8)R are turned out to underlie the physical world at small distances that uniquely identifies the local metaflavor symmetry SU(8)MF as its effective unified symmetry. We next show that the spontaneous L-R symmetry violation caused by the simultaneously emerged composite scalars reduces this initially vectorlike SU(8)MF theory down to the conventional SU(5) GUT with an extra local family symmetry SU(3)F and three standard families of quarks and leptons. Though the tiny confinement scale for universal preons composing both quarks and leptons makes it impossible to directly confirm their composite nature, simultaneous emergence of several extra SU(5)×SU(3)F multiplets of heavy composite fermions may help with a model verification. Generally, they may be located at scales from O(100) TeV up to the Planck mass scale depending on an interplay between the compositeness scale and scale of the family symmetry SU(3)F. Some of them through a natural see-saw mechanism provide the physical neutrino masses which, in contrast to conventional picture, appear to follow an inverted family hierarchy. Others mix with ordinary quark-lepton families in a way that there may arise a marked violation of unitarity in the CKM matrix for leptons.

A symmetry-twisted boundary condition of the path integral provides a suitable framework for the semi-classical analysis of nonperturbative quantum field theories (QFTs), and we reinterpret it from the viewpoint of the Hilbert space. An appropriate twist with the unbroken symmetry can potentially produce huge cancellations among excited states in the state-sum, without affecting the ground states; we call this effect "quantum distillation". Quantum distillation can provide the underlying mechanism for adiabatic continuity, by preventing a phase transition under $S^1$ compactification. We revisit this point via the 't Hooft anomaly matching condition when it constrains the vacuum structure of the theory on $\mathbb{R}^d$ and upon compactification. We show that there is a precise relation between the persistence of the anomaly upon compactification, the Hilbert space quantum distillation, and the semi-classical analysis of the corresponding symmetry-twisted path integrals. We motivate quantum distillation in quantum mechanical examples, and then study its non-trivial action in QFT, with the example of the 2D Grassmannian sigma model $\mathrm{Gr}(N,M)$. We also discuss the connection of quantum distillation with large-$N$ volume independence and flavor-momentum transmutation., 29 pages, 2 figures

We discuss consequences of the 't Hooft anomaly matching condition for Quantum Chromodynamics (QCD) with massless fundamental quarks. We derive the new discrete 't Hooft anomaly of massless QCD for generic numbers of color $N_\mathrm{c}$ and flavor $N_\mathrm{f}$, and an exotic chiral-symmetry broken phase without quark-bilinear condensate is ruled out from possible QCD vacua. We show that the $U(1)_\mathrm{B}$ baryon number symmetry is anomalously broken when the $(\mathbb{Z}_{2N_\mathrm{f}})_\mathrm{A}$ discrete axial symmetry and the flavor symmetry are gauged. In the ordinary chiral symmetry breaking, the Skyrmion current turns out to reproduce this 't Hooft anomaly of massless QCD. In the exotic chiral symmetry breaking, however, the anomalous breaking of $U(1)_\mathrm{B}$ does not take the correct form, and it is inconsistent with anomaly matching. This no-go theorem is based only on symmetries and anomalies, and thus has a wider range of applicability to the QCD phase diagram than the previous one obtained by QCD inequalities. Lastly, as another application, we check that duality of $\mathcal{N}=1$ supersymmetric QCD with $N_\mathrm{f}\ge N_\mathrm{c}+1$ satisfies the new anomaly matching., 28 pages;(v2) minor updates;(v3) ref added, appendix added

We explore 4-dimensional SU(N) gauge theory with a Weyl fermion in an irreducible self-conjugate representation. This theory, in general, has a discrete chiral symmetry. We use 't Hooft anomaly matching condition of the center symmetry and the chiral symmetry, and find constraints on the spontaneous chiral symmetry breaking in the confining phase. The domain-walls connecting different vacua are discussed from the point of view of the 't Hooft anomaly. We consider the SU(6) gauge theory with a Weyl fermion in the rank 3 anti-symmetric representation as an example. It is argued that this theory is likely to be in the confining phase. The chiral symmetry $\mathbb{Z}_6$ should be spontaneously broken to $\mathbb{Z}_2$ under the assumption of the confinement, although there cannot be any fermion bilinear condensate in this theory., Comment: 14 pages, no figure. v2: typos corrected. Comments and references added. v3: Discussion on domain-walls added, commens added. v4: minor change

Based on Son-Yamamoto relation obtained for transverse part of triangle axial anomaly in ${\rm QCD}_4$, we derive its analog in two-dimensional system. It connects the transverse part of mixed vector-axial current two-point function with diagonal vector and axial current two-point functions. Being fully non-perturbative, this relation may be regarded as anomaly matching for conductivities or certain transport coefficients depending on the system. We consider the holographic RG flows in holographic Yang-Mills-Chern-Simons theory via the Hamilton-Jacobi equation with respect to the radial coordinate. Within this holographic model it is found that the RG flows for the following relations are diagonal: Son-Yamamoto relation and the left-right polarization operator. Thus the Son-Yamamoto relation holds at wide range of energy scales., Comment: 22 pages, 4 figures

The chiral anomaly provides a smoking-gun evidence of a new confining gauge theory. Motivated by a reported event excess in a diphoton invariant mass distribution at the LHC, we discuss a scenario that a pseudo-Nambu-Goldstone (pNG) boson of a new QCD-like theory is produced by gluon fusion and decays into a pair of the standard model gauge bosons. Despite the strong dynamics, the production cross section and the decay widths are determined by anomaly matching condition. The excess can be explained by the pNG boson with mass of around 750 GeV. The model also predicts exotic hadrons such as a color octet scalar and baryons. Some of them are within the reach of the LHC experiment., 7 pages, 2 figures, typos fixed, figure 1 added, and journal version

A conservation law is one of the most fundamental properties in nature, but a certain class of conservation "laws"' could be spoiled by intrinsic quantum mechanical effects, so-called quantum anomalies. Profound properties of the anomalies have deepened our understanding in quantum many body systems. Here, we investigate quantum anomaly effects in quantum phase transitions between competing orders and striking consequences of their presence. We explicitly calculate topological nature of anomalies of non-linear sigma models (NLSMs) with the Wess-Zumino-Witten (WZW) terms. The non-perturbative nature is directly related with the 't Hooft anomaly matching condition : anomalies are conserved in renormalization group flow. By applying the matching condition, we show massless excitations are enforced by the anomalies in a whole phase diagram in sharp contrast to the case of the Landau-Ginzburg-Wilson theory which only has massive excitations in symmetric phases. Furthermore, we find non-perturbative criteria to characterize quantum phase transitions between competing orders. For example, in 4D, we show the two competing order parameter theories, CP(1) and the NLSM with WZW, describe different universality class. Physical realizations and experimental implication of the anomalies are also discussed., Comment: Published version

We study the global anomaly matching condition in N=1 supersymmetric gauge theories. The condition provides an extra test, apart from the 't Hooft anomaly matching condition, to the validity of low energy descriptions in terms of gauge invariant composites or electric–magnetic duality.

We discuss that the deviation of the Kugo-Ojima color confinement parameter $u(0)$ from -1 in the case of quenched lattice simulation and the consistency with -1 in the case of full QCD simulation could be attributed to the boundary condition defined by fermions inside the region of $r, 3 pages 2 figures, submitted to the SCGT09 proceedings

A new approach towards the composite structure of quarks and leptons in the context of the higher dimensional unified theories is proposed. Owing to the certain strong dynamics, much like an ordinary QCD, every possible vectorlike multiplets of composites appear in higher dimensional bulk space-time, however, through a proper Sherk-Schwarz compactification only chiral set of composite quarks and leptons survive as the massless states in four dimensions. In this scenario restrictions related with the 't Hooft's anomaly matching condition are turned out to be avoided and, as a result, the composite models look rather simple and economic. We demonstrate our approach by an explicit construction of model of preons and their composites unified in the supersymmetric SU(5) GUT in five space-time dimensions. The model predicts exactly three families of the composite quarks and leptons being the triplets of the chiral horizontal symmetry SU(3)_h which automatically appears in the composite spectrum when going to ordinary four dimensions., Comment: 13 pages, tcilatex, no figures, v2 - misprints corrected

Seiberg duality in supersymmetric gauge theories is the claim that two different theories describe the same physics in the infrared limit. However, one cannot easily work out physical quantities in strongly coupled theories and hence it has been difficult to compare the physics of the electric and magnetic theories. In order to gain more insight into the equivalence of two theories, we study the ''e{sup +}e{sup -}'' cross sections into ''hadrons'' for both theories in the superconformal window. We describe a technique which allows us to compute the cross sections exactly in the infrared limit. They are indeed equal in the low-energy limit and the equality is guaranteed because of the anomaly matching condition. The ultraviolet behavior of the total ''e{sup +}e{sup -}'' cross section is different for the two theories. We comment on proposed nonsupersymmetric dualities. We also analyze the agreement of the ''{gamma}{gamma}'' and ''WW'' scattering amplitudes in both theories, and in particular try to understand if their equivalence can be explained by the anomaly matching condition.

We formulate ``Witten'' matching conditions for confining gauge theories. The conditions are analogous to 't Hooft's, but involve Witten's global SU(2) anomaly. Using a group theoretic result of Geng, Marshak, Zhao and Okubo, we show that if the fourth homotopy group of the flavor group $H$ is trivial ($\Pi_4(H) = 0$) then realizations of massless composite fermions that satisfy the 't Hooft conditions also satisfy the Witten conditions. If $\Pi_4 (H)$ is nontrivial, the new matching conditions can yield additional information about the low energy spectrum of the theory. We give a simple physical proof of Geng, et. al.'s result., Comment: 11 pages, LaTex, all macros included

The question of the anomalies in the effective theory of heavy quarks is investigated at two different levels. Firstly, it is shown that none of the symmetries of this effective theory contains an anomaly. The existence of a new `$ \gamma _ 5 $'-symmetry is pointed out and shown to be also anomaly free. Secondly, it is shown that the chiral anomaly of QCD is not reproduced in the effective lagrangian for the heavy quarks, thus contradicting 't Hooft's anomaly matching condition. Finally, the effective theory of heavy quarks is derived from the QCD lagrangian in such a way that the terms leading to the anomaly are included. For this derivation the generating functional method is used., Comment: 16 pages, UB-ECM-PF-92/15

We investigate unified preon models based onSU9 andSU10 gauge groups. Using the anomaly matching condition, we obtain unique generation numbers 6 and 8, respectively. These are independent of preon configurations.

We have constructed a version of the chiral three-preon model E6 × SO(10) that satisfies the condition of asymptotic freedom in the metacolor and composite color-flavor sectors. The construction is based on the global color-flavor symmetry group SU(18). By applying the 't Hooft anomaly matching condition to the subgroup SU(16) × SU(2) of SU(18), together with a few physical constraints, we obtain a unique solution that gives rise to precisely three generations of the spinorial representation 16 of SO(10) without exotics. Except for N = 18, no solution exists for the global color-flavor group satisfying metacolor asymptotic freedom (N < 22) when SU(N) breaks to SU(16) × SU(N − 16).

A study is made of the properties of a susy preonic model. Constraints such as the 't Hooft anomaly matching condition, supersymmetry, conservation of electric charge and the assumption that only a single left-handed and a single right-handed fermion doublet is present are imposed. Applications to β-decay, Cabibbo-allowed and Cabibbo-suppressed processes are considered. Finally predictions for changes in the proton and neutron x-distribution are given.

In a simplified model lagrangian of 3 quarks with an SU(2) L gauging of chiral SU(3) L × SU(3) R to introduce W-bosons, we analyse certain complications associated with the low-energy theorem including axial weak fields. We first show that the low-energy amplitude is independent of the form of the quark-level anomalous identity, whether in the covariant form or the consistent form. However, the interplay of the short-distance dynamics (anomalous identity) and the long-distance dynamics (low-energy theorem) becomes involved in the presence of axial fields. We then discuss what kinds of conditions single out the gauged Wess-Zumino term as a low-energy effective action. The connection of the low-energy theorem with the 't Hooft anomaly matching condition is also discussed.

We discuss the recent proposal of arXiv:1608.05351 about generalization of the RTT relation to network matrix models. We show that the RTT relation in these models is modified by a nontrivial, but essentially abelian anomaly cocycle, which we explicitly evaluate for the free field representations of the quantum toroidal algebra. This cocycle is responsible for the braiding, which permutes the external legs in the q-deformed conformal block and its 5d/6d gauge theory counterpart, i.e. the non-perturbative Nekrasov functions. Thus, it defines their modular properties and symmetry. We show how to cancel the anomaly using a construction somewhat similar to the anomaly matching condition in gauge theory. We also describe the singular limit to the affine Yangian (4d Nekrasov functions), which breaks the spectral duality., Comment: 21 pages

A properly called “naturalness” is imposed on gauge theories. It is an order-of-magnitude restriction that must hold at all energy scales μ. To construct models with complete naturalness for elementary particles one needs more types of confining gauge theories besides quantum chromodynamics. We propose a search program for models with improved naturalness and concentrate on the possibility that presently elementary fermions can be considered as composite. Chiral symmetry must then be responsible for the masslessness of these fermions. Thus we search for QCD-like models where chiral symmetry is not or only partly broken spontaneously. They are restricted by index relations that often cannot be satisfied by other than unphysical fractional indices. This difficulty made the author’s own search unsuccessful so far. As a by-product we find yet another reason why in ordinary QCD chiral symmetry must be broken spontaneously.

We have constructed a version of the chiral three-preon model E6 ⊗ SO(10) based on the global color-flavor symmetry group SU(18). By applying the 't Hooft anomaly matching condition to the subgroup SU(16)×SU(2) of SU(18) together with a few physical constraints, we obtain a unique solution that gives rise to three generations of the spinorial representation 16 of SO(10) without exotics. Except for N = 18, no solution at all exists for the global color-flavor group SU(N) (16 < N < 22) when SU(N) breaks to SU(16)×SU(N−16).