We study cosmological constraints on dark pure Yang-Mills sectors. Dark glueballs are overproduced for large regions of ultraviolet parameter space. The problem may be alleviated in two ways: via a large preferential reheating into the visible sector, motivating certain inflation or modulus decay models, or via decays into axions or moduli, which are strongly constrained by nucleosynthesis and $ΔN_{\text{eff}}$ bounds. String models frequently have multiple hidden Yang-Mills sectors, which are subject to even stronger constraints due to the existence of multiple dark glueballs.
Dark gauge sectors and axions are well-motivated in string theory. We demonstrate that if a confining gauge sector gives rise to dark glueballs that are a fraction of the dark matter, and the associated axion has a decay constant near the string scale, then this axion is ultralight and naturally realizes the fuzzy dark matter scenario with a modest tuning of a temperature ratio. Astrophysical observations constrain the size of the glueball component relative to the axionic component, while electric dipole moments constrain mixing with the QCD axion.
The special case of 4D string-like theory proposed early is investigated. Regge trajectories in the developed model are non-linear for small masses and the values of spin and have the different asymptotical slopes $α_p$. The value $α_p$ just as the form of the trajectory depends from the quantum state of some ''internal'' {relativistic invariant} variables. It is also shown that some trajectories have the asymptotical slope $α_g$=0.21 $Gev^{-2}$.
We study glueballs in the holographic gauge theories living in a curved space-time. The dual bulk is obtained as a solution of the type IIB superstring theory with two parameters, which correspond to four dimensional (4D) cosmological constant $λ$ and the dark radiation $C$ respectively. The theory is in the confining phase for $λ<0$ and small $C$, then we observe stable glueball states in this theory. However, the stability of the glueball states is lost when the density of the dark radiation ($C$) increases and exceeds a critical point. Above this point, the dark radiation works as the heat …
The spectrum of light baryons and mesons has been reproduced recently by Brodsky and Teramond from a holographic dual to QCD inspired in the AdS/CFT correspondence. They associate fluctuations about the AdS geometry with four dimensional angular momenta of the dual QCD states. We use a similar approach to estimate masses of glueball states with different spins and their excitations. We consider Dirichlet and Neumann boundary conditions and find approximate linear Regge trajectories for these glueballs. In particular the Neumann case is consistent with the Pomeron trajectory.
Hidden sector glueball dark matter is well motivated by string theory, compactifications of which often have extra gauge groups uncoupled to the visible sector. We study the dynamics of glueballs in theories with a period of late time primordial matter domination followed by a low final reheating temperature due to a gravitationally coupled modulus. Compared to scenarios with a high reheating temperature, the required relic abundance is possible with higher hidden sector confinement scales, and less extreme differences in the entropy densities of the hidden and visible sectors. Both of these c…
The closed relativistic string carrying two point-like masses is considered as the model of a glueball with two constituent gluons. Here the gluon-gluon interaction is simulated by a pair of strings. For this system exact solutions of classical equations of motions are obtained. They describe rotational states of the string resulting in the set of quasilinear Regge trajectories with different behavior.
We put forward the Axionic String Ansatz (ASA), which provides a unified description for the worldsheet dynamics of confining strings in pure Yang--Mills theory both in $D=3$ and $D=4$ space-time dimensions. The ASA is motivated by the excitation spectrum of long confining strings, as measured on a lattice, and by recently constructed integrable axionic non-critical string models. According to the ASA, pure gluodynamics in 3D is described by a non-critical bosonic string theory without any extra local worldsheet degrees of freedom. We argue that this assumption fixes the set of quantum numbers…
In previous papers we argued that mesons and baryons can be described as rotating open strings in holographic backgrounds. Now we turn to closed strings, which should be the duals of glueballs. We look at the rotating folded closed string in both flat and curved backgrounds. A basic prediction of the closed string model is that the slope of Regge trajectories is half that of open strings. We propose that a simple method to identify glueballs is to look for resonances that belong to trajectories with a slope of approximately 0.45 GeV^-2, half the meson slope. We therefore look at the experiment…
We review lattice QCD results for glueballs (including a discussion of mixing with scalar mesons), hybrid mesons and exotic mesons (such as $B_s B_s$ molecules). We also discuss string breaking as a mixing between colour flux states and $B \bar{B}$ states.
The glueball dark matter, in the pure SU(N) Yang-Mills theory, engenders dark SU(N) stars that comprise self-gravitating compact configurations of scalar glueball fields. Corrections to the highest frequency of gravitational wave radiation emitted by dark SU(N) star mergers on a fluid brane with variable tension, implemented by the minimal geometric deformation, are derived and their consequences analysed. Hence, dark SU(N) stars mergers on a fluid brane-world are shown to be better detectable by the LIGO and the eLISA experiments.
It has been shown by Polchinski and Strassler that the scaling of high energy QCD scattering amplitudes can be obtained from string theory. They considered an AdS slice as an approximation for the dual space of a confining gauge theory. Here we use this approximation to estimate in a very simple way the ratios of scalar glueball masses imposing Dirichlet boundary conditions on the string dilaton field. These ratios are in good agreement with the results in the literature. We also find that they do not depend on the size of the slice.
It has been shown that a first order confinement phase transition can drastically change the relic dark matter abundance in confining dark sectors with only heavy dark quarks. We study the phenomenology of one such model with a Z' portal to Standard Model. We find that dark glueballs are long-lived in this setup and dilute the dark matter abundance after their decay to Standard Model. With this effect, the correct relic abundance is obtained with dark matter masses up to $\mathcal{O}(10^6)$~TeV. We find that while a part of the parameter space is already ruled out by direct detection and colli…
Recently Polchinski and Strassler reproduced the high energy QCD scaling at fixed angles from a gauge string duality inspired in AdS/CFT correspondence. In their approach a confining gauge theory is taken as approximately dual to an AdS space with an IR cut off. Considering such an approximation (AdS slice) we found a one to one holographic mapping between bulk and boundary scalar fields. Associating the bulk fields with dilatons and the boundary fields with glueballs of the confining gauge theory we also found the same high energy QCD scaling. Here, using this holographic mapping we give a si…
Lattice computations with excited SU(3) representations suggest that the confining gluon-gluon interaction complies with the Casimir scaling. The constituent gluon models have also been assuming the Casimir scaling. Inspired in type-II superconductors, we explore a new scenario for the gluon-gluon interaction where the adjoint string is replaced by a pair of fundamental strings, resulting in a factor of 2, smaller than 9/4. To test our proposal we construct a simple constituent gluon model, extrapolated from the funnel potential for quarkonium, and apply it to compute the wave-function of glue…
The closed string carrying $n$ point-like masses is considered as the model of a baryon ($n=3$), a glueball ($n=2$ or 3) or another exotic hadron. For this system the rotational states are obtained and classified. They correspond to exact solutions of dynamical equations, describing an uniform rotation of the string with massive points. These rotational states result in a set of quasilinear Regge trajectories with different behavior. The stability problem for the so called central rotational states (with a mass at the rotational center) is solved with using the analysis of small disturbances. …
Our understanding of the Universe is known to be incomplete and new gauge forces beyond those of the Standard Model might be crucial to describing its observed properties. A minimal and well-motivated possibility is a pure Yang-Mills non-Abelian dark gauge force with no direct connection to the Standard Model. We determine here the relic abundances of the glueball bound states that arise in such theories and investigate their cosmological effects. Glueballs are first formed in a confining phase transition, and their relic densities are set by a network of annihilation and transfer reactions. T…
We revisit the possibility that Dark Matter is composed of stable scalar glueballs of a confining dark ${\rm SU}(3)$ gauge theory coupled only to gravity. The relic abundance of dark glueballs is studied for the first time in a thermal effective theory accounting for strong-coupling dynamics. An important ingredient of our analysis is the use of an effective potential for glueballs that is fitted by lattice simulations. We predict the relic abundance to be in the range $0.12ζ_{T}^{-3}Λ/(137.9 {\rm eV}) \lesssim Ωh^{2}\lesssim 0.12ζ_{T}^{-3}Λ/(82.7 {\rm eV})$, with $Λ$ being the confinement sca…
The presence of Kaluza-Klein particles in the universe is a potential manifestation of string theory cosmology. In general, they can be present in the high temperature bath of the early universe. In particular examples, string theory inflation often ends with brane-antibrane annihilation followed by the energy cascading through massive closed string loops to KK modes which then decay into lighter standard model particles. However, massive KK modes in the early universe may become dangerous cosmological relics if the inner manifold contains warped throat(s) with approximate isometries. In the c…
It is shown that the eigenstates of the quantized simplest closed (elliptic) Nambu -- Goto string, called glueballs, have quantum numbers I^Gj^{PC}=0^+j^{++}. Lightest glueballs have spins j=0,1 and 2 and the same mass 1500 +/- 20 MeV. They correspond to f_0(1500), f_1(1510) and f_2(1565)- mesons. Next glueballs have j=0,1,2,3,4 and the same mass 2610 +/- 20 MeV. The slope of the glueball Regge trajectories is twice as small as for q\bar q-mesons. The intersept of the leading glueball trajectory - the pomeron Regge trajectory - is 1.07 +/- 0.03
Assuming that the Casimir scaling hypothesis is well verified in QCD, masses of glueballs and hybrid gluelumps (gluon with a point-like $c\bar c$ pair) are computed within the rotating string formalism. In our model, two gluons are attached by an adjoint string in a glueball while the gluon and the colour octet $c\bar c$ pair are attached by two fundamental strings in a hybrid gluelump. Masses for such exotic hadrons are computed with very few free parameters. These predictions can serve as a guide for experimental searches. In particular, the ground state glueballs lie on a Regge trajectory a…
An approximate vacuum wave functional $Ψ_0$ is proposed for $2+1$-dimensional Yang-Mills theories. Using $Ψ_0$, one can compute the $0^{++}$ glueball mass $M_G$ in terms of the string tension. By using the idea of dimensional reduction, a prediction for $M_G$ can be made in $3+1$ dimensions. One finds $M_G \approx 1.5$ GeV.
We point out a unique mechanism to produce the relic abundance for glueball dark matter from a gauged $SU(N)_d$ hidden sector which is bridged to the standard model sector through heavy vectorlike quarks colored under gauge interactions from both sides. A necessary ingredient of our assumption is that the vectorlike quarks, produced either thermally or non-thermally, are abundant enough to dominate the universe for some time in the early universe. They later undergo dark color confinement and form unstable vectorlike-quarkonium states which annihilate decay and reheat the visible and dark sect…
An intuitive approach to the glueball using the flux-tube ring solution in the dual Ginzburg-Landau theory is presented. The description of the flux-tube ring as the relativistic closed string with the effective string tension enables us to write the hamiltonian of the flux-tube ring using the Nambu-Goto action. Analyzing the Schrödinger equation, we discuss the mass spectrum and the wave function of the glueball. The lowest glueball state is found to have the mass $M_G \sim 1.6 GeV$ and the size $R_G \sim 0.5 fm$.
We calculate the low-lying glueball spectrum, some string tensions and some properties of topology and the running coupling for SU(N) lattice gauge theories in 3+1 dimensions. We do so for N = 2,3,...12, using lattice simulations with the Wilson plaquette action, and for glueball states in all the representations of the cubic rotation group, for both values of parity and charge conjugation. We extrapolate these results to the continuum limit of each theory and then to N=infinity. For a number of these states we are able to identify their continuum spins with very little ambiguity. We calculate…
A hidden sector with pure non-abelian gauge symmetry is an elegant and just about the simplest model of dark matter. In this model the dark matter candidate is the lightest bound state made of the confined gauge fields, the dark glueball. In spite of its simplicity, the model has been shown to have several interesting non-standard implications in cosmology. In this work, we explore the gravitational waves from binary boson stars made of self-gravitating dark glueball fields as a natural and important consequence. We derive the dark SU($N$) star mass and radius as functions of the only two fund…
We investigate the possibility that the dark matter candidate is from a pure non-abelian gauge theory of the hidden sector, motivated in large part by its elegance and simplicity. The dark matter is the lightest bound state made of the confined gauge fields, the hidden glueball. We point out this simple setup is capable of providing rich and novel phenomena in the dark sector, especially in the parameter space of large N. They include self-interacting and warm dark matter scenarios, Bose-Einstein condensation leading to massive dark stars possibly millions of times heavier than our sun giving …
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…
Non-Abelian dark gauge forces that do not couple directly to ordinary matter may be realized in nature. The minimal form of such a dark force is a pure Yang-Mills theory. If the dark sector is reheated in the early universe, it will be realized as a set of dark gluons at high temperatures and as a collection of dark glueballs at lower temperatures, with a cosmological phase transition from one form to the other. Despite being dark, the gauge fields of the new force can connect indirectly to the Standard Model through non-renormalizable operators. These operators will transfer energy between th…
We compute the one-loop string corrections to the Wilson loop, glueball Regge trajectory and stringy hadron masses in the Witten model of non supersymmetric, large-N Yang-Mills theory. The classical string configurations corresponding to the above field theory objects are respectively: open straight strings, folded closed spinning strings, and strings orbiting in the internal part of the supergravity background. For the rectangular Wilson loop we show that besides the standard Luescher term, string corrections provide a rescaling of the field theory string tension. The one-loop corrections to …
Motivated in part by the pseudo-Nambu Goldstone Boson mechanism of electroweak symmetry breaking in Composite Higgs Models, in part by dark matter scenarios with strongly coupled origin, as well as by general theoretical considerations related to the large-N extrapolation, we perform lattice studies of the Yang-Mills theories with $Sp(2N)$ gauge groups. We measure the string tension and the mass spectrum of glueballs, extracted from appropriate 2-point correlation functions of operators organised as irreducible representations of the octahedral symmetry group. We perform the continuum extrapol…
We summarise what lattice simulations have to say about the physical properties of continuum SU(N) gauge theories in 3+1 dimensions. The quantities covered are: the glueball mass spectrum, the confining string tension, the temperature at which the theory becomes deconfined, the topological susceptibility, the value of the scale Lambda{MS-bar} that governs the rate at which the coupling runs and the r0 parameter that characterises the static quark potential at intermediate distances.
Real-Time String Dynamics in a $2+1$D Non-Abelian Lattice Gauge Theory: String Breaking, Glueball Formation, Baryon Blockade, and Tension Reduction
Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Dipartimento di Fisica, Università di Torino（都灵大学物理系）；Ludwig Maximilian University of Munich（慕尼黑大学）；Arnold Sommerfeld Center for Theoretical Physics (ASC)（阿诺德·索末菲理论物理中心）；College of Science, Kyung Hee University（庆熙大学理学院）
The nuclear configurational entropy (NCE) is employed to derive two parameters encoding the Pomeron Regge trajectory and the spectrum of closed strings, which are also related to the glueball mass, precisely matching data of the TOTEM collaboration at the LHC. In the Regge regime of holographic QCD, the (Reggeized) glueball propagator and the gravitational form factor of the proton occupy a relevant spot in AdS/QCD. They are used for deriving the cross-sections for the TeV scale proton-proton scattering process, which are the main ingredient for computing the NCE. The nuclear configurational s…
We consider a simple supersymmetric hidden sector: pure SU(N) gauge theory. Dark matter is made up of hidden glueballinos with mass $m_X$ and hidden glueballs with mass near the confinement scale $Λ$. For $m_X \sim 1\,\text{TeV}$ and $Λ\sim 100\,\text{MeV}$, the glueballinos freeze out with the correct relic density and self-interact through glueball exchange to resolve small-scale structure puzzles. An immediate consequence is that the glueballino spectrum has a hyperfine splitting of order $Λ^2 / m_X \sim 10\,\text{keV}$. We show that the radiative decays of the excited state can explain the…
There is strong evidence in favor of the idea that dark matter is self interacting, with the cross section-to-mass ratio $σ/ m \sim 1\,\mathrm{cm^2/g} \sim 1\,\mathrm{barn/GeV}$. We show that viable models of dark matter with this large cross section are straightforwardly realized with non-Abelian hidden sectors. In the simplest of such models, the hidden sector is a pure gauge theory, and the dark matter is composed of hidden glueballs with a mass around $100\,\mathrm{MeV}$. Alternatively, the hidden sector may be a supersymmetric pure gauge theory with a $\sim 10\,\mathrm{TeV}$ gluino therma…
In an $SU(N_c)$ gauge theory with zero light quark flavours $N_f = 0$, the only hadronic states that form below the confinement scale are composite gluon states called glueballs. These minimal confining sectors arise in many Hidden Valley extensions of the Standard Model, including scenarios that could hold the solution to the dark matter question and the hierarchy problem. Quantitative study of dark glueball phenomenology requires an understanding of pure glue hadronization, which to date is severely lacking. In this work we show that significant progress can be made by combining a perturbati…
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.…
Solving by a canonical string theory, of closed strings for the glueballs and open strings for the mesons, the 't Hooft large-$N$ expansion of QCD is a long-standing problem that resisted all the attempts despite the advent of the celebrated gauge/gravity duality in the framework of string theory. We demonstrate that in the canonical string framework such a solution does not actually exist because an inconsistency arises between the renormalization properties of the QCD S matrix at large $N$ -- a consequence of the asymptotic freedom (AF) -- and the open/closed duality of the would-be string s…
The spectrum of glueballs in 2+1 dimensions is calculated within an extended class of Isgur-Paton flux tube models and is compared to lattice calculations of the low-lying SU(N) glueball mass spectra. Our modifications of the model include a string curvature term and different ways of dealing with the flux tube width. We find that the generic model is remarkably successful at reproducing the positive charge conjugation, C=+, sector of the spectrum. The only large (and robust) discrepancy involves the 0-+ state. This raises the interesting possibility that the lattice spin identification is mis…
We study the decay of a pseudovector glueball with quantum numbers $J^{PC}=1^{+-}$, the lightest glueball with spin different from zero or two, in the top-down holographic Witten-Sakai-Sugimoto model. This glueball is dual to the string-theoretic Kalb-Ramond tensor field, which completely fixes all its couplings by gauge invariance and $D$-brane anomaly inflow. The dominant decay channels are determined by a Chern-Simons-like action for the flavor branes; couplings from the Dirac-Born-Infeld action turn out to be subdominant. While the resulting width is parametrically of order $N_c^{-2}λ^{-1}…
Holography inspired stringy hadrons (HISH) is a set of models that describe hadrons: mesons, baryons and glueballs as strings in four dimensional space time. The models are based on a "map" from stringy hadrons of holographic confining backgrounds. In this note we review the "derivation" of the models. We start with a brief reminder of the passage from the AdS5xS5 string theory to certain flavored confining holographic models. We then describe the string configurations in holographic backgrounds that correspond to a Wilson line,a meson,a baryon and a glueball. The key ingredients of the four d…
The 3d gluodynamics which governs the large T quark gluon plasma is studied in the framework of the field correlator method. Field correlators and spacial string tension are derived through the gluelump Green's functions. The glueball spectrum is calculated both in C=-1 as well as in C=+1 sectors, and multigluon bound states in the form of "gluon rings" and "gluon stars" are computed explicitly. Good overall agreement with available lattice data is observed.
It is shown that if there are two distinct phase transition temperatures to the hadronic phase ( as is currently favoured), then QCD demands a condensation to a weakly interacting massive glueball. This glueball then becomes a natural candidate for the cosmological dark matter. Note that this does not involve any exotic extensions beyond the Standard Model of particle physics. In this revised version at the end of the paper I have added a new section called ADDENDUM which gives new arguments as to how this very heavy glueball can be stable and hence be a dark matter candidate.
We conjecture that in Yang-Mills theories the ratio between the ground-state glueball mass squared and the string tension is proportional to the ratio of the eigenvalues of quadratic Casimir operators in the adjoint and the fundamental representations. The proportionality constant depends on the dimension of the space-time only, and is henceforth universal. We argue that this universality, which is supported by available lattice results, is a direct consequence of area-law confinement. In order to explain this universal behaviour, we provide three analytical arguments, based respectively on a …
Descriptions of hadrons and glueballs can be constructed using strings to preserve gauge invariance. We show how this string dependence may be removed to all orders in perturbation theory.
We study the cosmology of the dark sector consisting of (ultra) light scalars. Since the scalar mass is radiatively unstable, a special explanation is required to make the mass much smaller than the UV scale. There are two well-known mechanisms for the origin of scalar mass. The scalar can be identified as a pseudo-Goldstone boson, whose shift symmetry is explicitly broken by non-perturbative corrections, like the axion. Alternatively, it can be identified as a composite particle like the glueball, whose mass is limited by the confinement scale of the theory. In both cases, the scalar can be n…
It has been suggested recently that self-interacting dark matter fits better the observational characteristics of galaxy dynamics. We propose that the self-interacting dark matter is composed from the glueballs of the hidden sector non-Abelian gauge group, while the hidden matter states exist in vector-like representation and decouple from the light spectrum. It is shown that these glueballs are semi-stable with the life-time larger than the present age of the Universe, if their mass is 1 GeV or less. The constraint on their abundance today suggests that the energy was stored in the hidden sec…
In this paper, we develop models applicable to phenomenological particle physics by using the string analogy of particles. These theories can be used to investigate the phenomenology of confinement, deconfinement, chiral condensate, QGP phase transitions, and even the evolution of the early universe. Other confining properties such as scalar glueball mass, gluon mass, glueball-meson mixing states, QCD vacuum, and color superconductivity can also be investigated in these model frameworks. We use one of the models to describe the phenomenon of color confinement among glueballs at the end of the …
Thermal evolution of dark matter and gravitational-wave production in the early universe from a symplectic glueball model
Milano-Bicocca University（米兰比可卡大学）；INFN, Milano-Bicocca unit（意大利国家核物理研究所，米兰比可卡分部）；Swansea University（斯旺西大学）；University of Turin（都灵大学）；INFN, Turin unit（意大利国家核物理研究所，都灵分部）；University of Helsinki（赫尔辛基大学）；INFN, Roma Tre unit（意大利国家核物理研究所，罗马三校分部）
The solution of the large-N 't Hooft limit of QCD is universally believed to be a String Theory of Closed Strings in the Glueball Sector and of Open Strings in the Meson Sector. Yet, we prove a no-go theorem, that the large-N limit of QCD with massless quarks, or more generally, that the large-N limit of a vast class of confining, i.e. with a Mass Gap in the Glueball Sector, asymptotically-free Gauge Theories coupled to matter fields with no mass scale in perturbation theory cannot be a canonically-defined String Theory of Closed and Open Strings, i.e. admitting Open/Closed Duality. The no-go …
