We study theories with the exceptional gauge group G(2). The 14 adjoint "gluons" of a G(2) gauge theory transform as {3}, {3} and {8} under the subgroup SU(3), and hence have the color quantum numbers of ordinary quarks, anti-quarks and gluons in QCD. Since G(2) has a trivial center, a "quark" in the {7} representation of G(2) can be screened by "gluons". As a result, in G(2) Yang-Mills theory the string between a pair of static "quarks" can break. In G(2) QCD there is a hybrid consisting of one "quark" and three "gluons". In supersymmetric G(2) Yang-Mills theory with a {14} Majorana "gluino" the chiral symmetry is Z Z(4) χ . Chiral symmetry breaking gives rise to distinct confined phases separated by confined-confined domain walls. A scalar Higgs field in the {7} representation breaks G(2) to SU(3) and allows us to interpolate between theories with exceptional and ordinary confinement. We also present strong coupling lattice calculations that reveal basic features of G(2) confinement. Just as in QCD, where dynamical quarks break the Z Z(3) symmetry explicitly, G(2) gauge theories confine even without a center. However, there is not necessarily a deconfinement phase transition at finite temperature.

The Z Z(N) center symmetry plays an important role in the deconfinement phase transition of SU(N) Yang-Mills theory at finite temperature. The exceptional group G(2) is the smallest simply connected gauge group with a trivial center. Hence, there is no symmetry reason why the lowand high-temperature regimes in G(2) Yang-Mills theory should be separated by a phase transition. Still, we present numerical evidence for the presence of a first order deconfinement phase transition at finite temperature. Via the Higgs mechanism, G(2) breaks to its SU(3) subgroup when a scalar field in the fundamental {7} representation acquires a vacuum expectation value v. Varying v we investigate how the G(2) deconfinement transition is related to the one in SU(3) Yang-Mills theory. Interestingly, the two transitions seem to be disconnected. We also discuss a potential dynamical mechanism that may explain this behavior.

We study the behavior of the spatial and temporal 't Hooft loop at zero and finite temperature in the 4D SU(2) Yang-Mills theory, using a new numerical method. In the deconfined phase T . T c , the spatial 't Hooft loop exhibits a dual string tension, which vanishes at T c with a 3D Ising-like critical exponent. DOI: 10.1103/PhysRevLett.86.1438 The 4D SU(2) Yang-Mills theory undergoes a transition between a cold confined phase and a hot deconfined phase at a critical temperature T c . An order parameter widely used to characterize this transition is the Polyakov loop. It develops a nonvanishing expectation value in the deconfined phase. However, the corresponding operator creates a single fundamental static color source, which does not belong to the physical Hilbert space of the theory; it cannot be defined at zero temperature; and it is afflicted by ultraviolet divergences in the continuum limit [1,2]. A long time ago it was proposed [3] to consider instead the 't Hooft loop operator as an order parameter to characterize this transition. It is the purpose of this paper to study this order parameter. The 't Hooft loop,W͑C͒, is an operator associated with a given closed contour C and is defined in the continuum SU͑N͒ theory by the following equal-time commutation relations [3]:where W͑C 0 ͒ is the Wilson loop associated with the closed contour C 0 and n CC 0 is the linking number of C and C 0 . Just like the Wilson loop creates an elementary electric flux along C 0 , the 't Hooft loop creates an elementary magnetic flux along the closed path C affecting any Wilson loop "pierced" by C. In that sense, the two types of loop are dual to each other. At zero temperature, it has been shown [3][4][5] that also the 't Hooft loop behavior is dual to that of the Wilson loop: in the absence of massless excitations, an area law behavior for one implies a perimeter law for the other, and vice versa. Hence, at T 0 the 't Hooft loop obeys a perimeter law.Several analytical [2,6] and numerical [7-9] studies have been carried out in order to investigate this issue of duality at finite temperature. At T . 0, the Lorentz symmetry is broken, so spatial and temporal loops can have different behaviors. Because the spatial string tension persists also above T c for the Wilson loop, temporal 't Hooft loops are expected to show a perimeter law in both phases; spatial 't Hooft loops are expected to obey a perimeter law in the confined phase and an area law -defining a dual string tension (strictly speaking it is an action density)-in the deconfined phase.On the lattice the 't Hooft loop is defined as follows. Let us consider the SU͑2͒ lattice gauge theory with the usual Wilson plaquette action,where the sum extends over all the plaquettes P, and U P is the path-ordered product of the links around P. Starting from S͑b͒, one defines the partition functionLet us now switch on "by hand" an elementary magnetic flux along a closed contour C defined on the dual lattice.To create this magnetic flux, we have to multiply U P by a nontrivial element ...

Some time ago, Svetitsky and Yaffe have argued that -if the deconfinement phase transition of a (d + 1)-dimensional Yang-Mills theory with gauge group G is second order -it should be in the universality class of a d-dimensional spin model symmetric under the center of G. For d = 3 these arguments have been confirmed numerically only in the SU(2) case with center Z Z(2), simply because all SU(N) Yang-Mills theories with N ≥ 3 seem to have non-universal first order phase transitions. The symplectic groups Sp(N) also have the center Z Z(2) and provide another extension of SU(2) = Sp(1) to general N. Using lattice simulations, we find that the deconfinement phase transition of Sp(2) Yang-Mills theory is first order in 3 + 1 dimensions, while in 2 + 1 dimensions stronger fluctuations induce a second order transition. In agreement with the Svetitsky-Yaffe conjecture, for (2 + 1)-d Sp(2) Yang-Mills theory we find the universal critical behavior of the 2-d Ising model. For Sp(3) Yang-Mills theory the transition is first order both in * on leave from MIT

We report on a very accurate measurement of the static quark potential in SU (2) Yang-Mills theory in (2+1) dimensions in order to study the corrections to the linear behaviour. We perform numerical simulations at zero and finite temperature comparing our results with the corrections given by the effective string picture in these two regimes. We also check for universal features discussing our results together with those recently published for the (2+1)-d Z Z(2) and SU (3) pure gauge theories.