We study a phenomenological model that mimics the characteristics of QCD theory at finite temperature. The model involves fermions coupled with a modified Abelian gauge field in a tachyon matter. It reproduces some important QCD features such as, confinement, deconfinement, chiral symmetry and quark-gluon-plasma (QGP) phase transitions. The study may shed light on both light and heavy quark potentials and their string tensions. Flux-tube and Cornell potentials are developed depending on the regime under consideration. Other confining properties such as scalar glueball mass, gluon mass, glueball-meson mixing states, gluon and chiral condensates are exploited as well. The study is focused on two possible regimes, the ultraviolet (UV) and the infrared (IR) regimes.
In this paper we consider confinement and screening of the electric field. We study the behavior of a static electric field coupled to a dielectric function with the intent of obtaining an electrical confinement similar to what happens with the field of gluons that bind quarks in hadronic matter. For this we use the phenomenon of `anti-screening' in a medium with exotic dielectric. We show that tachyon matter behaves like an exotic way whose associated dielectric function modifies the Maxwell's equations and affects the fields which results in confining and Coulombian-like potentials in three …
In this paper we present a QCD motivated model that mimics QCD theory. We examine the characteristics of the gauge field coupled with the color dielectric function ($G$) in the presence of temperature ($T$). The aim is to achieve confinement at low temperatures $T<T_{c}$, ($T_{c}$, is the critical temperature), similar to what occurs among quarks and gluons in hadrons at low energies. Also, we investigate scalar glueballs and QCD string tension and effect of temperature on them. To achieve this, we use the phenomenon of color dielectric function in gauge fields in a slowly varying tachyon medi…
In this paper we develop a phenomenological model inspired by QCD that mimics QCD theory. We use gauge theory in color dielectric medium ($G(ϕ)$) coupled with fermion fields to produce scalar and vector confinement in chromoelectric flux tube scenario. Abelian theory will be used to approximate the non-Abelian QCD theory in a consistent manner. We will calculate vector and scalar glueballs and compare the result to the existing simulation and experimental results and projections. The QCD-like vacuum associated with the model will be calculated and its behavior studied relative to changing quar…
In this paper the spectrum of quark-antiquark systems, including light mesons and tachyons, is studied in the true vacuum and in the chiral invariant vacuum. The mass gap equation for the vacua and the Salpeter-RPA equation for the mesons are solved for a simple chiral invariant and confining quark model. At T=0 and in the true vacuum, the scalar and pseudoscalar, or the vector and axial vector are not degenerate, and in the chiral limit, the pseudoscalar groundstates are Goldstone bosons. At T=0 the chiral invariant vacuum is an unstable vacuum, decaying through an infinite number of scalar a…
By dealing with the evaluation of string theory correlators of $<V_C V_T V_{\barΨ} V_Ψ>$, the complete and closed form of the amplitude of two fermion fields, one tachyon and one closed string Ramond-Ramond field in type IIB superstring theory is found. Specifically by comparing infinite tachyon poles in field theory amplitude with infinite tachyon poles of the S-matrix of string amplitude (for $p+1=n$ case), all the infinite higher derivative corrections of two tachyons and two fermions (in type IIB) to all orders of $α'$ have been discovered. Using these new couplings, we are able to produce…
Confinement may be more easily demonstrated at finite temperature using the Polyakov loop than at zero temperature using the Wilson loop. A natural mechanism for confinement can arise via the coupling of the adjoint Polyakov loop to F_{mu nu}^2. We demonstrate this mechanism with a one-loop calculation of the effective potential for SU(2) gluons in a background field consisting of a non-zero color magnetic field and a non-trivial Polyakov loop. The color magnetic field drives the Polyakov loop to non-trivial behavior, and the Polyakov loop can remove the well-known tachyonic mode associated wi…
We present a solution of the five-dimensional gravity-dilaton-tachyon equations of motion with a pure AdS_5 metric and a quadratic dilaton and linear tachyon in conformal coordinates. This leads to an infrared soft wall model where the dilaton profile gives rise to linear Regge trajectories for the four-dimensional mass spectrum of the dual gauge theory. Even though our approach is phenomenological the scalar fields resemble the dilaton and the closed string tachyon of a non-critical string theory. Interestingly, the linear tachyon has the correct profile to imply that chiral symmetry is not r…
The renormalization group equations of the Yang-Mills theory are examined in the non-critical string theory according to the framework of the holography. Under a simple ansatz for the tachyon, we could find several interesting solutions which are classified by the value of the tachyon potential at the vacuum. We show two typical, asymptotic-free solutions which are different in their infrared behaviors. For both types of solutions, we could obtain quark-confinement potential from the Wilson-loop. The stability of the tachyon and the ZigZag symmetry are also discussed for these solutions.
Intersecting D-brane models and their T-dual magnetic compactifications yield attractive models of particle physics where magnetic flux plays a twofold role, being the source of fermion chirality as well as supersymmetry breaking. A potential problem of these models is the appearance of tachyons which can only be avoided in certain regions of moduli space and in the presence of Wilson lines. We study the effective four-dimensional field theory for an orientifold compactification of type IIA string theory and the corresponding toroidal compactification of type I string theory. After determining…
We consider a general framework to study holographically the dynamics of fundamental quarks in a confining gauge theory. Flavors are introduced by placing a set of (coincident) branes and antibranes on a background dual to a confining color theory. The spectrum contains an open string tachyon and its condensation describes the U(N_f)_L x U(N_f)_R -> U(N_f)_V symmetry breaking. By studying worldvolume gauge transformations of the flavor brane action, we obtain the QCD global anomalies and an IR condition that allows to fix the quark condensate in terms of the quark mass. We find the expected N_…
A natural mechanism for finite temperature quark confinement arises via the coupling of the adjoint Polyakov loop to the chromomagnetic field. Lattice simulations and analytical results both support this hypothesis. Finite temperature SU(3) lattice simulations show that a large external coupling to the chromomagnetic field restores confinement at temperatures above the normal deconfining temperature. A one-loop calculation of the effective potential for SU(2) gluons in a background field shows that a constant chromomagnetic field can drive the Polyakov loop to confining behavior, and the Polya…
The gluon spin coupling to a Gaussian correlated background gauge field induces an effective tachyonic gluon mass. It is momentum dependent and vanishes in the UV only like 1/p^2. In the IR, we obtain stabilization through a positive m^2_{conf}(p^2) related to confinement. Recently a purely phenomenological tachyonic gluon mass was used to explain the linear rise in the q\bar q static potential at small distances and also some long standing discrepancies found in QCD sum rules. We show that the stochastic vacuum model of QCD predicts a gluon mass with the desired properties.
We investigate a recently proposed Higgs-like model (arXiv:0811.4423 [hep-th]), in the framework of a gauge-invariant but path-dependent variables formalism. We compute the static potential between test charges in a condensate of scalars and fermions. In the case of charged massive scalar we recover the screening potential. On the other hand, in the Higgs case, with a "tachyonic" mass term and a quartic potential in the Lagrangian, unexpected features are found. It is observed that the interaction energy is the sum of an effective-Yukawa and a linear potential, leading to the confinement of st…
We show that, in 1+1 dimensional gauge theories, a heavy probe charge is screened by dynamical massless fermions both in the case when the source and the dynamical fermions belong to the same representation of the gauge group and, unexpectedly, in the case when the representation of the probe charge is smaller than the representation of the massless fermions. Thus, a fractionally charged heavy probe is screened by dynamical fermions of integer charge in the massless Schwinger model, and a colored probe in the fundamental representation is screened in $QCD_2$ with adjoint massless Majorana ferm…
We consider a brane generated by a scalar field domain wall configuration in 4+1 dimensions, interpolating, in most cases, between two vacua of the field. We study the cosmology of such a system in the cases where the effective four-dimensional brane metric is de Sitter or anti de Sitter, including a discussion of the bulk coordinate singularities present in the de-Sitter case. We demonstrate that a scalar field kink configuration can support a brane with dS$_4$ cosmology, despite the presence of coordinate singularities in the metric. We examine the trapping of fermion fields on the domain wa…
We analyze the question of screening versus confinement in bosonized massless QCD in two dimensions. We deduce the screening behavior of massless $SU(N_c)$ QCD with flavored fundamental fermions and fermions in the adjoint representation. This is done by computing the potential between external quarks as well as by bosonizing also the external sources and analyzing the states of the combined system. We write down novel "non-abelian Schwinger like" solutions of the equations of motion, compute their masses and argue that an exchange of massive modes of this type is associated with the screening…
We consider possible dynamical models for a light fermion confined by a potential field. With the Dirac equation only Lorentz scalar confinement yields normalizable wavefunctions, while with the ``no pair'' variant of the Dirac equation only Lorentz vector confinement has normal Regge behaviour. A systematic investigation of Regge properties and phenomenological properties is carried out, including calculations of the Isgur-Wise function. We point out that the Isgur-Wise function provides a sensitive test of confinement models. In particular, the slope of the IW function at zero recoil point i…
Dependence of the confinement transition parameters on the fermion content provides information on the mechanism of confinement. Recent progress in lattice gauge theories has allowed to study it for light flavor number $N_f\sim O(10)$ and found this transition to shift toward significantly stronger coupling. We propose an explanation for that: light fermions can occupy the chromo-magnetic monopoles, via zero modes, making them "distinguishable" and unsuitable for Bose-Einstein Condensation. Such dilution of unoccuplied monopoles is compensated by stronger coupling that makes them lighter and m…
We consider a model for the electroweak interactions based on the assumption that physical particles are singlets under the gauge group SU(2). The concept of complementarity explains why the standard model works with such an extraordinary precision although the fermions and bosons of the model can be viewed as composite objects of some more fundamental fermions and bosons. We study the incorporation of QED in the model. Furthermore we consider possible deviations from the standard model at very high energies, e.g. excited states of the weak bosons.
A mechanism is suggested by which the dynamics of confinement could be responsible for the fermion mass matrix. In this approach the large top quark Yukawa coupling is generated naturally during confinement, while those of the other quarks and leptons stem from non-renormalizable couplings at the Planck scale and are suppressed. Below the confinement scale(s) the effective theory is minimal supersymmetric $SU(5)$ or the supersymmetric standard model. Particles in the $\bar 5$ representations of $SU(5)$ are fundamental while those in the $10$ and $5$ are composite. The standard model gauge grou…
We formulate the description of the dynamic confinement of a single fermion by a flux tube. The range of applicability of this model extends from the relativistic corrections of a slowly moving quark to the ultra-relativistic motion in a heavy-light meson. The reduced Salpeter equation, also known as the no-pair equation, provides the framework for our discussion. The Regge structure is that of a Nambu string with one end fixed. Numerical solutions are found giving very good fits to heavy-light meson masses. An Isgur-Wise function with a zero recoil slope of $ξ'(1)\simeq -1.26 $ is obtained.
We revisit Nambu's model of quark confinement by a tube of magnetic flux, with two additional features. The quarks are taken to be magnetic monopoles external to the tube, which seal the ends, and are also taken to be fermions. This ensures that the model is inconsistent unless there are at least two species of fermions being confined.
We analyze the properties of a two and three dimensional quantum walk that are inspired by the idea of a brane-world model put forward by Rubakov and Shaposhnikov [1]. In that model, particles are dynamically confined on the brane due to the interaction with a scalar field. We translated this model into an alternate quantum walk with a coin that depends on the external field, with a dependence which mimics a domain wall solution. As in the original model, fermions (in our case, the walker), become localized in one of the dimensions, not from the action of a random noise on the lattice (as in t…
We analytically study the relation between quark confinement and spontaneous chiral-symmetry breaking in QCD. In terms of the Dirac eigenmodes, we derive some formulae for the Polyakov loop, its fluctuations, and the string tension from the Wilson loop. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clover and the domain wall fermion kernels, respectively. For the confinement quantities, the low-lying Dirac/fermion eigenmodes are found to give negligible contribution, while they are essential for chiral symmetry breaking. These relations indicate no direct …
Recently there has been an interest in studying the role that geometry may play in the problem of confining fermions to our four-dimensional spacetime. In general, the focus is on non-Riemannian geometries which possess fields like torsion and non-metricity. In this paper, the degrees of freedom present in the spin connection in a Riemannian manifold are used to confine fermions. It turns out that one can use this connection to trap these particles inside a brane.
Confinement without symmetry breaking in chiral gauge theories
School of Physics, Sun Yat-Sen University（中山大学物理学院）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所跨学科理论与数学科学中心（iTHEMS））；Centre for Cosmology, Particle Physics and Phenomenology (CP3), Université catholique de Louvain（天主教鲁汶大学宇宙学、粒子物理与现象学中心（CP3））
Two-dimensional QED with $N$ flavor fermions is solved at zero and finite temperature with arbitrary fermion masses to explore QCD physics such as chiral condensate and string tension. The problem is reduced to solving a Schrödinger equation for $N$ degrees of freedom with a specific potential determined by the ground state of the Schrödinger problem itself.
We study the analytical structure of the fermion propagator in planar quantum electrodynamics coupled to a Chern-Simons term within a four-component spinor formalism. The dynamical generation of parity-preserving and parity-violating fermion mass terms is considered, through the solution of the corresponding Schwinger-Dyson equation for the fermion propagator at leading order of the 1/N approximation in Landau gauge. The theory undergoes a first order phase transition toward chiral symmetry restoration when the Chern-Simons coefficient $θ$ reaches a critical value which depends upon the number…
We study the experimental constraints on strongly interacting vector-fermions compatible with the relaxion mechanism and investigate any possible tuning. The focus is on a minimal model and low confinement scale. More precisely, we study bounds from electroweak precision tests, Higgs decay, Big Bang nucleosynthesis and direct collider searches. The effect of these new fermions on vacuum stability is also investigated. Combining our bounds, we show that the relaxion mechanism becomes increasingly constrained and fine-tuned as the confinement scale decreases. For example, a confinement scale of …
In this Honours Research Project the aim is to build a toy model of an SO(10) Grand Unified Theory with an extra spatial dimension. Utilising the Clash of Symmetries mechanism proposed for brane-world models by Davidson, Toner, Volkas and Wali and using the asymmetric kink solution for the Higgs Field in the 45 of SO(10) discovered by Shin and Volkas, the symmetry on the brane will be broken to SU(4) x SU(2) x U(1), whereas the symmetry in the bulk is G_SM x U(1). However, any fermions localised on the brane would experience slight leakage into the bulk, and hence the symmetry is broken down t…
A non-perturbative construction of the 3-point fermion-boson vertex which obeys its Ward-Takahashi or Slavnov-Taylor identity, ensures the massless fermion and boson propagators transform according to their local gauge covariance relations, reproduces perturbation theory in the weak coupling regime and provides a gauge independent description for dynamical chiral symmetry breaking (DCSB) and confinement has been a long-standing goal in physically relevant gauge theories such as quantum electrodynamics (QED) and quantum chromodynamics (QCD). In this paper, we demonstrate that the same simple an…
We discuss the phase diagnostics used in our finite-temperature study of an SU(4) gauge theory with dynamical fermions in both the fundamental and two-index antisymmetric representations. Beyond the usual Polyakov loop diagnostics of confinement, we employ several Wilson flow phase diagnostics. The first, what we call the "flow anisotropy", is known in the literature: the deconfinement transition introduces anisotropy between the spatial and temporal directions, to which the flow is extremely sensitive. The second, the "long flow time Polyakov loop," is related but novel. While we do not claim…
We study the nontrivial solutions of the QCD fermionic gap equation including the contribution of dynamically massive gluons and the confining propagator proposed by Cornwall. Without the confining propagator, in the case of non-running gluon mass (mg), we found the multivacuum solutions (replicas) reported in the literature and we were able to define limits on mg for dynamical chiral symmetry breaking. On the other side, when considering the running in the gluon mass the vacuum replicas are absent in the limits on mg where the chiral symmetry is broken. In the pure confining sector, the multi…
Analytical properties of the photon propagator in QED3 in the N^1-approximation are considered. It is noticed that in given approximation if the dynamical fermions mass is nonzero this propagator has a single pole at the point k^2=0 and a branch point at k^2=-4m^2 (m is the fermion mass). When m=0, the propagator gets the pole at the spacelike domain of the variable k^2. It witnesses the unstability of the state conforming to the photon and leads to the screening of the source field at r speeds to infinity. The approximation by the rational function of the photon propagator containing the vacu…
Confinement has been introduced into the quark gap equation, as proposed by Cornwall, as a possible solution to the problem of chiral symmetry breaking in QCD with dynamically massive gluons. We argue that the same mechanism can be applied for technicolor with dynamically massive technigluons. Within this approach both theories develop a hard self-energy dynamics, resulting from an effective four-fermion interaction, which does not lead to the known technicolor phenomenological problems. We outline a quite general type of technicolor model within this proposal that may naturally explain the ma…
We give another derivation of quark confinement in QCD from the viewpoint of the low-energy effective Abelian gauge theory of QCD obtained via Abelian projection. It is based on the recently discovered Berezinskii-Kosterlitz-Thouless phase transition in the four-dimensional Abelian gauge theory. Moreover, we show that there exists a critical gauge coupling constant in QCD, above which confinement set in and below which there is no confinement. In a SU(N) gauge theory with $N_f$ flavored fermions, we argue that this leads to a critical value of fermion flavors $N_f^c$ for the confinement as wel…
We establish that QED3 can possess a critical number of flavours, N_f^c, associated with dynamical chiral symmetry breaking if, and only if, the fermion wave function renormalisation and photon vacuum polarisation are homogeneous functions at infrared momenta when the fermion mass function vanishes. The Ward identity entails that the fermion-photon vertex possesses the same property and ensures a simple relationship between the homogeneity degrees of each of these functions. Simple models for the photon vacuum polarisation and fermion-photon vertex are used to illustrate these observations. Th…
We explore the possibility that dark matter is a pair of vector-like fermionic $\mathrm{SU}(2)_{\rm L}$ doublets and propose a novel mechanism of dark matter production that proceeds through the confinement of the weak sector of the Standard Model. This confinement phase causes the Standard Model doublets and dark matter to confine into pions. The dark pions freeze-out before the weak sector deconfines and generate a relic abundance of dark matter. We solve the Boltzmann equations for this scenario to determine the scale of confinement and constituent dark matter mass required to produce the o…
We calculate the energy of a single fermion interacting resonantly with a Fermi sea of different-species fermions in asymmetric traps, and show that finite particle numbers and the trap geometry impact the phase structure and the critical polarization. Our findings contribute to understanding some experimental discrepancies in spin-polarized Fermi gases as finite-size and confinement effects.
