Vortex solution in 2+1 dimensional Yang-Mills theory at high temperatures

At high temperatures the A_0 component of the Yang--Mills field plays the role of the Higgs field, and the 1-loop potential V(A_0) plays the role of the Higgs potential. We find a new stable vortex solution of the Abrikosov-Nielsen-Olesen type, and discuss its properties and possible implications.Comment: 8 p., three .eps figures include

Monopoles, vortices and confinement in SU(3) gauge theory

We compute, in SU(3) pure gauge theory, the vacuum expectation value (vev) of the operator which creates a $Z_3$ vortex wrapping the lattice through periodic boundary conditions (dual Polyakov line). The technique used is the same already tested in the SU(2) case. The dual Polyakov line proves to be a good disorder parameter for confinement, and has a similar behaviour to the monopole condensate. The new features which characterise the construction of the disorder operator in SU(3) are emphasised.Comment: 8 pages, 4 eps figures, typed with elsart.cl

Domain Walls and Metastable Vacua in Hot Orientifold Field Theories

We consider "Orientifold field theories", namely SU(N) gauge theories with Dirac fermions in the two-index representation at high temperature. When N is even these theories exhibit a spontaneously broken Z2 centre symmetry. We study aspects of the domain wall that interpolates between the two vacua of the theory. In particular we calculate its tension to two-loop order. We compare its tension to the corresponding domain wall in a SU(N) gauge theory with adjoint fermions and find an agreement at large-N, as expected from planar equivalence between the two theories. Moreover, we provide a non-perturbative proof for the coincidence of the tensions at large-N. We also discuss the vacuum structure of the theory when the fermion is given a large mass and argue that there exist N-2 metastable vacua. We calculate the lifetime of those vacua in the thin wall approximation.Comment: 29 pages, 4 figures. v2: minor changes in the introduction section. to appear in JHE

Domain walls and perturbation theory in high temperature gauge theory: SU(2) in 2+1 dimensions

We study the detailed properties of Z_2 domain walls in the deconfined high temperature phase of the d=2+1 SU(2) gauge theory. These walls are studied both by computer simulations of the lattice theory and by one-loop perturbative calculations. The latter are carried out both in the continuum and on the lattice. We find that leading order perturbation theory reproduces the detailed properties of these domain walls remarkably accurately even at temperatures where the effective dimensionless expansion parameter, g^2/T, is close to unity. The quantities studied include the surface tension, the action density profiles, roughening and the electric screening mass. It is only for the last quantity that we find an exception to the precocious success of perturbation theory. All this shows that, despite the presence of infrared divergences at higher orders, high-T perturbation theory can be an accurate calculational tool.Comment: 75 pages, LaTeX, 14 figure

Perturbative analysis for Kaplan's lattice chiral fermions

Perturbation theory for lattice fermions with domain wall mass terms is developed and is applied to investigate the chiral Schwinger model formulated on the lattice by Kaplan's method. We calculate the effective action for gauge fields to one loop, and find that it contains a longitudinal component even for anomaly-free cases. From the effective action we obtain gauge anomalies and Chern-Simons current without ambiguity. We also show that the current corresponding to the fermion number has a non-zero divergence and it flows off the wall into the extra dimension. Similar results are obtained for a proposal by Shamir, who used a constant mass term with free boundaries instead of domain walls.Comment: 25 page, 5 PostScript figures, [some changes in the conclusion

Casimir scaling of domain wall tensions in the deconfined phase of D=3+1 SU(N) gauge theories

We perform lattice calculations of the spatial 't Hooft k-string tensions in the deconfined phase of SU(N) gauge theories for N=2,3,4,6. These equal (up to a factor of T) the surface tensions of the domain walls between the corresponding (Euclidean) deconfined phases. For T much larger than Tc our results match on to the known perturbative result, which exhibits Casimir Scaling, being proportional to k(N-k). At lower T the coupling becomes stronger and, not surprisingly, our calculations show large deviations from the perturbative T-dependence. Despite this we find that the behaviour proportional to k(N-k) persists very accurately down to temperatures very close to Tc. Thus the Casimir Scaling of the 't Hooft tension appears to be a `universal' feature that is more general than its appearance in the low order high-T perturbative calculation. We observe the `wetting' of these k-walls at T around Tc and the (almost inevitable) `perfect wetting' of the k=N/2 domain wall. Our calculations show that as T tends to Tc the magnitude of the spatial `t Hooft string tension decreases rapidly. This suggests the existence of a (would-be) 't Hooft string condensation transition at some temperature which is close to but below Tc. We speculate on the `dual' relationship between this and the (would-be) confining string condensation at the Hagedorn temperature that is close to but above Tc.Comment: 40 pages, 14 figure

On the effective action of confining strings

We study the low-energy effective action on confining strings (in the fundamental representation) in SU(N) gauge theories in D space-time dimensions. We write this action in terms of the physical transverse fluctuations of the string. We show that for any D, the four-derivative terms in the effective action must exactly match the ones in the Nambu-Goto action, generalizing a result of Luscher and Weisz for D=3. We then analyze the six-derivative terms, and we show that some of these terms are constrained. For D=3 this uniquely determines the effective action for closed strings to this order, while for D>3 one term is not uniquely determined by our considerations. This implies that for D=3 the energy levels of a closed string of length L agree with the Nambu-Goto result at least up to order 1/L^5. For any D we find that the partition function of a long string on a torus is unaffected by the free coefficient, so it is always equal to the Nambu-Goto partition function up to six-derivative order. For a closed string of length L, this means that for D>3 its energy can, in principle, deviate from the Nambu-Goto result at order 1/L^5, but such deviations must always cancel in the computation of the partition function. Next, we compute the effective action up to six-derivative order for the special case of confining strings in weakly-curved holographic backgrounds, at one-loop order (leading order in the curvature). Our computation is general, and applies in particular to backgrounds like the Witten background, the Maldacena-Nunez background, and the Klebanov-Strassler background. We show that this effective action obeys all of the constraints we derive, and in fact it precisely agrees with the Nambu-Goto action (the single allowed deviation does not appear).Comment: 71 pages, 7 figures. v2: added reference, minor corrections. v3: removed one term from the effective action since it is trivial. The conclusions on the corrections to energy levels are unchanged, but the claim that the holographic computation shows a deviation from Nambu-Goto was modified. v4: added reference

Domain-wall fermions with U(1)U(1) dynamical gauge fields

We have carried out a numerical simulation of a domain-wall model in $(2+1)$-dimensions, in the presence of a dynamical gauge field only in an extra dimension, corresponding to the weak coupling limit of a ( 2-dimensional ) physical gauge coupling. Using a quenched approximation we have investigated this model at $\beta_{s} ( = 1 / g^{2}_{s} ) =$ 0.5 ( ``symmetric'' phase), 1.0, and 5.0 (``broken'' phase), where $g_s$ is the gauge coupling constant of the extra dimension. We have found that there exists a critical value of a domain-wall mass $m_{0}^{c}$ which separates a region with a fermionic zero mode on the domain-wall from the one without it, in both symmetric and broken phases. This result suggests that the domain-wall method may work for the construction of lattice chiral gauge theories.Comment: 27 pages (11 figures), latex (epsf style-file needed

Core Structure of Global Vortices in Brane World Models

We study analytically and numerically the core structure of global vortices forming on topologically deformed brane-worlds with a single toroidally compact extra dimension. It is shown that for an extra dimension size larger than the scale of symmetry breaking the magnitude of the complex scalar field at the vortex center can dynamically remain non-zero. Singlevaluedness and regularity are not violated. Instead, the winding escapes to the extra dimension at the vortex center. As the extra dimension size decreases the field magnitude at the core dynamically decreases also and in the limit of zero extra dimension size we reobtain the familiar global vortex solution. Extensions to other types of defects and gauged symmetries are also discussed.Comment: 6 two column pages, 3 figure

Magnetic Symmetries and Vortices In Chern-Simons Theories

We study the locality properties of the vortex operators in compact U(1) Maxwell-Chern-Simons and SU(N) Yang-Mills-Chern-Simons theories in 2+1 dimensions. We find that these theories do admit local vortex operators and thus in the UV regularized versions should contain stable magnetic vortices. In the continuum limit however the energy of these vortex excitations generically is logarithmically UV divergent. Nevertheless the classical analysis shows that at small values of CS coefficient $\kappa$ the vortices become light. It is conceivable that they in fact become massless and condense due to quantum effects below some small $\kappa$. If this happens the magnetic symmetry breaks spontaneously and the theory is confining.Comment: 21 pages, laTe