non-Abelian Confinement Research Articles

Adiabatic continuity and confinement in supersymmetric Yang-Mills theory on the lattice

This work is a step towards merging the ideas that arise from semi-classical methods in continuum QFT with analytic/numerical lattice field theory. In this context, we consider Yang-Mills theories coupled to fermions transforming in the adjoint representation of the gauge group. These theories have the remarkable property that confinement and discrete chiral symmetry breaking can persist at weak coupling on ℝ3 × S1 up to small (non-thermal) compactification radii. This work presents a lattice investigation of a gauge theory coupled to a single adjoint Majorana fermion, the mathcal{N}=1 Supersymmetric Yang-Mills theory (SYM), and opens the prospect to understand analytically a number of non-perturbative phenomena, such as confinement, mass gap, chiral and center symmetry realizations, both on the lattice and in the continuum. We study the compactification of mathcal{N}=1 SYM on the lattice with periodic and thermal boundary conditions applied to the fermion field. We provide numerical evidences for the conjectured absence of phase transitions with periodic boundary conditions for sufficiently light lattice fermions (stability of center-symmetry), for the suppression of the chiral transition, and we provide also a diagnostic for Abelian vs. non-Abelian confinement, based on per-site Polyakov loop eigenvalue distribution functions. We identify the role of the lattice artefacts that become relevant in the very small radius regime, and we resolve some puzzles in the naive comparison between continuum and lattice.

Physics of non-Abelian confinement and the dual gauge symmetry: Many faces of flavor symmetry

We review the physics of confinement based on non-Abelian dual superconductor picture, relying on exact solutions in N=2 supersymmetric QCD and based on the recent developments in our understanding of non-Abelian vortices and monopoles. The non-Abelian monopoles, though they are basically just the ʼt Hooft-Polyakov SU(2) monopoles embedded in various corners of the larger gauge group, require flavor symmetry in an essential way for their very existence. The phenomenon of flavor-color-flavor separation characterizes the multiple roles flavor symmetry plays in producing quantum-mechanical non-Abelian monopoles.

Strong versus weak coupling confinement in [formula omitted] supersymmetric QCD

We consider N = 2 supersymmetric QCD with the gauge group S U ( N c ) = SU ( N + 1 ) and N f number of quark matter multiplets, being perturbed by a small mass term for the adjoint matter, so that its Coulomb branch shrinks to a number of isolated vacua. We discuss the vacuum where r = N quarks develop VEV's for N f ⩾ 2 N = 2 N c − 2 (in particular, we focus on the N f = 2 N and N f = 2 N + 1 cases). In the equal quark mass limit at large masses this vacuum stays at weak coupling, the low-energy theory has U ( N ) gauge symmetry and one observes the non-Abelian confinement of monopoles. As we reduce the average quark mass and enter the strong coupling regime the quark condensate transforms into the condensate of dyons. We show that the low energy description in the strongly-coupled domain for the original theory is given by U ( N ) dual gauge theory of N f ⩾ 2 N light non-Abelian dyons, where the condensed dyons still cause the confinement of monopoles, and not of the quarks, as can be thought by naive duality.

Multiflavor QCD∗ on [formula omitted]: Studying transition from Abelian to non-Abelian confinement

The center-stabilized multiflavor QCD∗ theories formulated on R3×S1 exhibit both Abelian and non-Abelian confinement as a function of the S1 radius, similar to the Seiberg–Witten theory as a function of the mass deformation parameter. For sufficiently small number of flavors and small r(S1), we show occurrence of a mass gap in gauge fluctuations, and linear confinement. This is a regime of confinement without continuous chiral symmetry breaking (χSB). Unlike one-flavor theories where there is no phase transition in r(S1), the multiflavor theories possess a single phase transition associated with breaking of the continuous χS. We conjecture that the scale of the χSB is parametrically tied up with the scale of Abelian to non-Abelian confinement transition.

Quantum Phase Transitions and New Scales in QCD-like Theories

It is commonly believed that in confining vectorlike gauge theories the center and chiral symmetry transition scales are parametrically of the same order and take place around the strong scale Lambda -1. We demonstrate that (nonthermal) compactification of such theories on R 3 x S1 exhibit new phase transition scales and unexpected phenomena. There are cases with single chiral symmetry breaking at an exotic scale Lambda-1/Nc in the absence of any change in center symmetry. The scale Lambda -1/N c,invisible in perturbation theory, is also the scale where Abelian versus non-Abelian confinement regimes meet. Large N c volume independence provides new insights and independently confirms the existence of these scales. We also show that certain phases and scales are outside the reach of holographic (supergravity) modeling of QCD.

Crossover between Abelian and non-Abelian confinement inN=2supersymmetric QCD

In this paper we investigate the nature of the transition from Abelian to non-Abelian confinement (i.e. crossover vs. phase transition). To this end we consider the basic N=2 model where non-Abelian flux tubes (strings) were first found: supersymmetric QCD with the U(N) gauge group and N_f=N flavors of fundamental matter (quarks). The Fayet-Iliopoulos term \xi triggers the squark condensation and leads to the formation of non-Abelian strings. There are two adjustable parameters in this model: \xi and the quark mass difference \Delta m. We obtain the phase diagram on the (\xi, \Delta m) plane. At large \xi and small \Delta m the world-sheet dynamics of the string orientational moduli is described by N=2 two-dimensional CP(N-1) model. We show that as we reduce \xi the theory exhibits a crossover to the Abelian (Seiberg-Witten) regime. Instead of N^2 degrees of freedom of non-Abelian theory now only N degrees of freedom survive in the low-energy spectrum. Dyons with certain quantum numbers condense leading to the formation of the Abelian Z_N strings whose fluxes are fixed inside the Cartan subalgebra of the gauge group. As we increase N this crossover becomes exceedingly sharper becoming a genuine phase transition at N =\infty.

Non-Abelian confinement near nontrivial conformal vacua

We discuss some aspects of confinement and dynamical symmetry breaking in the so-called non-Abelian Argyres–Douglas vacua, which occur very generally in supersymmetric theories. These systems are characterized by strongly-coupled non-Abelian monopoles and dyons; confinement and dynamical symmetry breaking are caused by the condensation of monopole composites, rather than by condensation of single weakly-coupled monopoles. In general, there are strong constraints on which kind of monopoles can appear as the infrared degrees of freedom, related to the proper realization of the global symmetry of the theory. Drawing analogies to some of the phenomena found here, we make a speculation on the ground state of the standard QCD.

Non-Abelian Meissner effect in Yang-Mills theories at weak coupling

We present a weak-coupling Yang--Mills model supporting non-Abelian magnetic flux tubes and non-Abelian confined magnetic monopoles. In the dual description the magnetic flux tubes are prototypes of the QCD strings. Dualizing the confined magnetic monopoles we get gluelumps which convert a "QCD string" in the excited state to that in the ground state. Introducing a mass parameter m we discover a phase transition between the Abelian and non-Abelian confinement at a critical value m=m_* of order of Lambda. Underlying dynamics are governed by a Z_N symmetry inherent to the model under consideration. At m>m_* the Z_N symmetry is spontaneously broken, resulting in N degenerate Z_N (Abelian) strings. At m<m_* the Z_N symmetry is restored, the degeneracy is lifted, and the strings become non-Abelian. We calculate tensions of the non-Abelian strings, as well as the decay rates of the metastable strings, at N >> 1.

Non-Abelian confinement via Abelian flux tubes in softly broken [formula omitted] SUSY QCD

We study confinement in softly broken N=2 SUSY QCD with gauge group SU( N c ) and N f hypermultiplets of fundamental matter (quarks) when the Coulomb branch is lifted by small mass of adjoint matter. Concentrating mostly on the theory with SU(3) gauge group we discuss the N=1 vacua which arise in the weak coupling at large values of quark masses and study flux tubes and monopole confinement in these vacua. In particular we find the BPS strings in SU(3) gauge theory formed by two interacting U(1) gauge fields and two scalar fields generalizing ordinary Abrikosov–Nielsen–Olesen vortices. Then we focus on the SU(3) gauge theories with N f =4 and N f =5 flavors with equal masses. In these theories there are N=1 vacua with restored SU(2) gauge subgroup in quantum theory since SU(2) subsectors are not asymptotically free. We show that although the confinement in these theories is due to Abelian flux tubes the multiplicity of meson spectrum is the same as expected in a theory with non-Abelian confinement.

Identifying monopoles on a lattice.

The U(1) Villain model is simulated in three and four dimensions. We locate monopoles using both the conventional DeGrand-Toussaint prescription and the exact prescription as provided by the model itself. The two monopole gases thus obtained are compared, in particular with respect to their confining and percolation properties. In this way we investigate to how strong a coupling the conventional definition of lattice monopoles remains reliable. We show that in the interesting range of "intermediate" couplings (${\ensuremath{\beta}}_{v}\ensuremath{\ge}0.3$) the difference between the two monopole gases can be very well reproduced by a random distribution of dipoles (which possesses trivial long-distance properties). This suggests that the DeGrand-Toussaint prescription can indeed be meaningfully used in studies of, for example, the U(1) phase transition and the monopole mechanism for non-Abelian confinement.