Here we study two important properties of $2+1$ dimensional QCD -- confinement and pseudoscalar glueball spectrum -- with holographic approach. We consider the low energy decoupled geometry of the isotropic non-susy D$2$ brane. We find the corresponding gauge theory is similar to the $2+1$-dim Yang-Mills theory with the running coupling $λ^2$. At the extremal limit (i.e. BPS limit), this gauge theory reduces to the super-YM theory. From the Nambu-Goto action of a test string, the potential of a \qq pair located on the boundary is calculated. At large \qq separation it gives the tension $σ$ of the QCD flux-tube. The parametric dependencies of $σ$ is shown pictorially. It is found that $σ$ is a monotonically increasing function of the effective coupling $λ^2$. In comparison, $\sqrtσ/g_\text{YM}^2N_c$ is found to match accurately with the previous results. In the next part, we consider fluctuation of the axion field in the aforementioned gravity background. From the linearized field equation of the fluctuation we calculate the mass spectrum of $0^{-+}$ numerically using the WKB approximation. The pseudoscalar mass is found to be related to the string tension approximately as $M_{0^{-+}}/\sqrtσ\approx 3(n+2)$ for first three energy states, $n=0,\,1,\,2$.
We discuss the $0^{+-}$ singlet sector of glueballs in the Klebanov-Strassler theory. We report the results of a numerical study of the linearized equations in the Klebanov-Strasller background and make a comparison with the spectrum of the scalar sector. While for four towers of the total six towers of massive pseudoscalar states our results match the spectrum of the corresponding towers of scalars, the values for the remaining two towers diverge with those of the scalars. We discuss possible interpretations of this divergence.
In this paper we describe a pseudoscalar subsector of the Klebanov-Strassler model. This subsector completes the holographic reconstruction of the spectrum of the lowest-lying glueball states, which are singlet under the global symmetry group $SU(2)\times SU(2)$. We derive the linearized supergravity equations for the pseudoscalar fluctuations and analyze their spectrum. The system of equation is shown to be compatible with six eigenmodes, as expected from supersymmetry. Our numerical analysis allows to reliably extract four of the corresponding towers. Their values match well the eigenvalues …
Here we analyse the low energy confining phase of the $2+1$ dimensional quenched QCD-like theory in anisotropic non-supersymmetric D$2$ brane background with the holographic approach. Two key features of QCD -- flux-tube tension and mass spectrum of pseudoscalar glueball are studied. The non-supersymmetric D$2$ branes with anisotropy in time direction are considered as the gravity theory. Tuning the anisotropic parameter, we get the Hawking-Page transition in the gravity background. On the dual theory, this refers the confinement-deconfinement phase transition. Using the Wilson loop, the linea…
We provide results for the spectrum of scalar and pseudoscalar glueballs in pure Yang-Mills theory using a parameter-free fully self-contained truncation of Dyson-Schwinger and Bethe-Salpeter equations. The only input, the scale, is fixed by comparison with lattice calculations. We obtain ground state masses of $1.9\,\text{GeV}$ and $2.6\,\text{GeV}$ for the scalar and pseudoscalar glueballs, respectively, and $2.6\,\text{GeV}$ and $3.9\,\text{GeV}$ for the corresponding first excited states. This is in very good quantitative agreement with available lattice results. Furthermore, we predict ma…
We revisit the $U(1)_A$ anomaly in the holographic model of low-energy QCD by Witten, Sakai, and Sugimoto, presenting a new and direct derivation of the Witten-Veneziano mechanism for generating the mass of the $η'$ through an anomalous mixing of the Ramond-Ramond $C_1$ field with the singlet component of the pseudoscalar mesons. The latter turns out to have a kinetic mixing with the normalizable modes of the $C_1$ field representing pseudoscalar glueballs, yielding additional vertices for their production and their decay that dominate over those of the unmixed case considered previously in th…
The top-down holographic Witten-Sakai-Sugimoto model for low-energy QCD, augmented by finite quark masses, has recently been found to be able to reproduce the decay pattern of the scalar glueball candidate f0(1710) on a quantitative level. In this Letter we show that this model predicts a narrow pseudoscalar glueball heavier than the scalar glueball and with a very restricted decay pattern involving eta or eta' mesons. Production should be either in pairs or in association with eta(') mesons. We discuss the prospect of discovery in high-energy hadron collider experiments through central exclus…
Here, we calculate the pseudo-scalar glueball mass at finite temperature from the holographic QCD in $3+1$ dimensions. The decoupled geometry of the non-supersymmetric (non-susy) D$3$ brane at the finite temperature which is the solution of the type-II supergravity is considered as the dual theory of QCD. We calculate the mass spectrum from the axion fluctuation in this gravity background using WKB approximations. Approximating the WKB equation for various orders of mass, we derive the analytical expressions of the mass spectrum of $0^{-+}$ at the finite temperature. Finally we evaluate the ma…
We generalize the dispersive approach to axial anomaly by A.D. Dolgov and V.I. Zakharov to a non-Abelian case with arbitrary photon virtualites. We derive the anomaly sum rule for the singlet current and obtain the $π^0,η,η'\rightarrowγγ^*$ transition form factors. Using them, we established the behavior of a nonperturbative gluon matrix element $\langle 0 |G\tilde{G} |γγ^*(q^2) \rangle$ in both spacelike and timelike regions. We found a significant contribution of the non-Abelian axial anomaly to the processes with one virtual photon, comparable to that of the electromagnetic anomaly. The dua…
The holographic Witten-Sakai-Sugimoto model is an almost parameter-free approximation to large-N QCD with chiral quarks that in a number of cases gives surprisingly good quantitative results for light meson physics. It also allows for predictions of the decay rates of glueballs into pseudoscalar and vector mesons through the coupling of modes on the flavor branes to the massive gravitational modes in the bulk. Including effects from finite quark masses leads to an enhancement of the decay of scalar glueballs into heavier pseudoscalars in good agreement with the decay pattern observed for the s…
We point out that perturbation theory in conjunction with the renormalization group (RG) puts a severe constraint on the structure of the large-N non-perturbative glueball propagators in SU(N) pure YM, in QCD and in n=1 SUSY QCD with massless quarks, or in any confining asymptotically-free gauge theory massless in perturbation theory. For the scalar and pseudoscalar glueball propagators in pure YM and QCD with massless quarks we check in detail the RG-improved estimate to the order of the leading and next-to-leading logarithms by means of a remarkable three-loop computation by Chetyrkin et al.…
We prove an asymptotic structure theorem for glueball and meson propagators of any spin in large-N QCD and in n=1 SUSY QCD with massless quarks, that determines asymptotically the residues of the poles of the propagators in terms of their anomalous dimensions and of the spectral density of the masses. The asymptotic theorem follows by the severe constraints on the propagators in large-N QCD with massless quarks, or in any large-N confining asymptotically-free gauge theory massless in perturbation theory, that arise by perturbation theory in conjunction with the renormalization group and by the…
Glueballs and fractional anomalous determinants at nonzero $θ$, and the decays of the X(2370)
Jan Kochanowski University（扬·科哈诺夫斯基大学）；Goethe-University（歌德大学）；University of Pittsburgh（匹兹堡大学）；HUN-REN Wigner Research Centre for Physics（匈牙利研究与创新网络维格纳物理研究中心）；University of Wroclaw（弗罗茨瓦夫大学）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Justus Liebig University Giessen（吉森尤斯图斯·李比希大学）；Helmholtz Research Academy Hesse for FAIR (HFHF)（黑森亥姆霍兹FAIR研究院）
A method for computing the low-energy non-perturbative properties of SUSY GFT, starting from the microscopic lagrangian model, is presented. The method relies on covariant SUSY Feynman graph techniques, adapted to low energy, and Renormalization-Group-improved perturbation theory. We apply the method to calculate the glueball superpotential in N=1 SU(2) SYM and obtain a potential of the Veneziano-Yankielowicz type.
We formulate a framework to determine the mass of glueball states of Landau gauge Yang-Mills theory in the continuum. To this end we derive a Bethe-Salpeter equation for two gluon bound states including the effects of Faddeev-Popov ghosts. We construct a suitable approximation scheme such that the interactions in the bound state equation match a corresponding successful approximation of the Dyson-Schwinger equations for the Landau gauge ghost and gluon propagators. Based upon a recently obtained solution for the propagators in the complex momentum plane we obtain results for the mass of the sc…
We study the theta dependence of the glueball spectrum in a strongly coupled cousin of large N gluodynamics defined via the AdS/CFT correspondence. By explicitly diagonalizing the 10d gravity equations in the presence of the RR 3-form and 1-form fluxes we found a mixing pattern for the lowest-spin lightest glueballs. The mixing between the scalar and pseudoscalar states is not suppressed, suggesting that the CP-odd effects persist in the large N theory. As a consequence, the lightest mass eigenstate ceases to be a parity eigenstate. We found the former as a linear combination of a scalar and p…
We review the determinations of the pseudoscalar glueball and eventual radial excitation of the η' masses and decay constants from QCD spectral sum rules (QSSR). The glueball mass is (2.05+-0.19) which one can compare with the eventual experimental candidate X(1835), while the η(1400) is likely a radial excitation of the η'-meson. Their effects on the estimates of U(1)_A topological susceptibility and its slope as well as the impact of the latter in the estimate of the spin of the proton is discussed. We predict the singlet polarized parton distributions to be a^0(Q^2=4 GeV^2)=0.32+-0.02, whic…
The Veneziano-Yankielowicz glueball superpotential for an arbitrary N=1 SUSY pure gauge theory with classical gauge group is derived using an approach following recent work of Dijkgraaf, Vafa and others. These non-perturbative terms, which had hitherto been included by hand in the above approach, are thus seen to arise naturally, and the approach is rendered self-contained. By minimising the glueball superpotential for theories with fundamental matter added, the expected vacuum structure with gaugino condensation and chiral symmetry breaking is obtained. Various possible extensions are also di…
Predictions of glueball decay rates in the holographic Witten-Sakai-Sugimoto model for low-energy QCD can be uniquely extended to include finite quark masses up to an as yet undetermined parameter in the coupling of glueballs to the nonanomalous part of the pseudoscalar mass terms. The assumption of a universal coupling of glueballs to mass terms of the full nonet of pseudoscalar mesons leads to flavor asymmetries in the decay rates of scalar glueballs that agree well with experimental data for the glueball candidate $f_0(1710)$ and implies a vanishing decay rate into $ηη'$ pairs, for which on…
In the pure large-N Yang-Mills theory there is a quasi-BPS sector that is exactly solvable at large N. It follows an exact beta function and the glueball spectrum in this sector. The main technical tool is a new holomorphic loop equation for quasi-BPS Wilson loops, that occurs as a non-supersymmetric analogue of Dijkgraaf-Vafa holomorphic loop equation for the glueball superpotential of n=1 SUSY gauge theories. The new holomorphic loop equation is localized, i.e. reduced to a critical equation, by a deformation of the loop that is a vanishing boundary in homology, somehow in analogy with Witte…
We set up an infrared-based moment problem to obtain estimates of the masses of the scalar, pseudoscalar and tensor glueballs in Euclidean Yang-Mills theories using the Refined Gribov-Zwanziger (RGZ) version of the Landau gauge, which takes into account nonperturbative physics related to gauge copies. Employing lattice input for the mass scales of the RGZ gluon propagator, the lowest order moment problem approximation gives the values m_{0++}\approx 1.96 GeV, m_{2++} \approx 2.04 GeV and m_{0-+}\approx 2.19 GeV in the SU(3) case, all within a 20% range of the corresponding lattice values. We a…
It is well-known that the non-supersymmetric D3 brane (a cousin of BPS D3 brane) including its black version of type IIB string theory has a decoupling limit, where the decoupled geometry is the gravity dual of a non-supersymmetric, non-conformal (finite temperature) quantum field theory having some properties similar to QCD. Using the ideas of AdS/CFT we study some non-perturbative aspects of this quantum field theory. Since in this case we have a Yang-Mills theory (no quarks) with running coupling (non-constant dilaton), we compute the gluon condensate in this theory as a function of tempera…
We use an analogy between the Yang-Mills theory Hamiltonian and the matrix model description of the closed bosonic membrane theory to calculate the spectrum of glueballs in the large $N_c$ limit. Some features of the Yang-Mills theory vacuum, such as the screening of the topological charge and vacuum topological susceptibility are discussed. We show that the topological susceptibility has different properties depending on whether it is calculated in the weak coupling or strong coupling regimes of the theory. A mechanism of the formation of the pseudoscalar glueball state within pure Yang-Mills…
We study non-spinning Q-balls and boson stars in 4-dimensional Anti-de Sitter (AdS) space-time. We use an exponential scalar field potential that appears in gauge-mediated supersymmetry (SUSY) breaking in the minimal supersymmetric extension of the Standard Model (MSSM). We investigate the dependence of the charge and mass of these non-topological solitons on the negative cosmological constant, the frequency that appears in the periodic time-dependence as well as on the ratio between the SUSY breaking scale and the Planck mass. Next to fundamental solutions without nodes in the scalar field fu…
We find an asymptotic solution for two- and three-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-$N$ $QCD$, in terms of glueball and meson propagators, by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap. The asymptotically-free bootstrap exploits the lowest-order conformal invariance of connected correlators of gauge invariant composite operators in perturbation theory, the renormalization-group improvement, and a recently-proved asymptotic structure theorem for glueball and meson propagators, that…
Democracy among the same type of particles is a useful paradigm in studying masses and interactions of particles with supersymmetry(SUSY) or without SUSY. This simple idea predicts the presence of massless particles. We attempt to use one of these massless pseudoscalar particles as generating the cosmological dark energy(DE) potential. To achieve the extremely shallow potential of DE, the pseudoscalar boson is required not to couple to the QCD anomaly. So, we consider two pseudoscalars, one coupling to the QCD anomaly (i.e. QCD axion) and the other not coupling to the QCD anomaly. To obtain th…
We study $\mathcal{N}=1$ supersymmetric Yang-Mills theory (SYM) on the lattice. The non-perturbative nature of supersymmetric field theories is still largely unknown. Similarly to QCD, SYM is confining and contains strongly bound states. Applying the variational method together with different smearing techniques we extract masses of the lightest bound states such as gluino-glue, glueball and mesonic states. As these states should form supermultiplets, this study allows to check whether SYM remains supersymmetric also on the quantum level.
As shown in arXiv:hep-th/0405282, the warped deformed conifold has two bosonic massless modes, a pseudoscalar and a scalar, that are dual to the phase and the modulus of the baryonic condensates in the cascading gauge theory. We reconsider the scalar mode sector, mixing fluctuations of the NS-NS 2-form and the metric, and include non-zero 4-d momentum $k_μ$. The resulting pair of coupled equations produce a discrete spectrum of $m_4^2=- k_μ^2$ which is interpreted as the spectrum of $J^{PC}= 0^{+-}$ glueballs in the gauge theory. Similarly, we derive the spectrum of certain pseudoscalar glueba…
The large-$N_c$ orientifold planar equivalence between $\mathcal{N}=1$ SUSY Yang-Mills theory and ordinary 1-flavor QCD suggests that low-energy quark-gluon dynamics in QCD should be constrained by the supersymmetry of the parent theory. One SUSY relic expected from orientifold equivalence is the approximate degeneracy of the scalar and pseudoscalar mesons in 1-flavor QCD. Here we study the role of the $q\bar{q}$ annihilation (hairpin) contributions to the meson correlators. These annihilation terms induce mass shifts of opposite sign in the scalar and pseudoscalar channels, making degeneracy …
We study N=1 supersymmetric U(N) gauge theories coupled to an adjoint chiral field with superpotential. We consider the full supersymmetric moduli space of these theories obtained by adding all allowed chiral operators. These include higher-dimensional operators that introduce a field-dependence for the gauge coupling. We show how Feynman diagram/matrix model/string theoretic techniques can all be used to compute the IR glueball superpotential. Moreover, in the limit of turning off the superpotential, this leads to a deformation of N=2 Seiberg-Witten theory. In the case where the superpotentia…
We consider a model of brane world gravity in the context of non-conformal non-SUSY matter. In particular we modify the earlier strong coupling solution to the glueball spectrum in an $AdS^7$ Black Hole by introducing a Randall-Sundrum Planck brane as a UV cut-off. The consequence is a new normalizable zero mass tensor state, which gives rise to an effective Einstein-Hilbert theory of gravity, with exponentially small corrections set by the mass gap to the discrete glueball spectrum. However the simplest microscopic theory for the Planck brane is found to have a tachyonic instability in the ra…
The local SUSY symmetry of the loop dynamics of QCD is found. The remarkable thing is, there is no einbein-gravitino on this theory, which makes it a 1D topological supergravity, or locally SUSY quantum mechanics. Using this symmetry, we derive the large $N_c$ loop equation in momentum superloop space. Introducing as before the position operator $\Xμ$ we argue that the superloop equation is equivalent to invariance of correlation functions of products of these operators with respect to certain quadrilinear transformation. The applications to meson and glueball sectors as well as the chiral sym…
We study instanton contributions to the superpotential of local F-theory compactifications which could potentially be used to engineer models of dynamical supersymmetry breaking. These instantons correspond to Euclidean 3-branes which form a threshold bound state with spacetime filling 7-branes. In certain cases, their contributions to the effective 4d superpotential can be determined in both perturbative string theory as well as directly via the topologically twisted theory on the 3-brane worldvolume, and in all cases we observe an exact match between these results. We further present an inst…
We discuss the instability of the Veneziano-Yankielowicz effective action (or its supersymmetric ground-state) with respect to higher order derivative terms. As such terms must be present in an effective action, the V-Y action alone cannot describe the dynamics of SYM consistently. We introduce an extension of this action, where all instabilities are removed by means of a much richer structure of the Kaehler potential. We demonstrate that the dominant contributions to the effective potential are determined by the non-holomorphic part of the action and we prove that the non-perturbative ground-…
