On the zero of the fermion zero mode

We argue that the fermionic zero mode in non-trivial gauge field backgrounds must have a zero. We demonstrate this explicitly for calorons where its location is related to a constituent monopole. Furthermore a topological reasoning for the existence of the zero is given which therefore will be present for any non-trivial configuration. We propose the use of this property in particular for lattice simulations in order to uncover the topological content of a configuration.Comment: 6 pages, 3 figures in 5 part

Probing for Instanton Quarks with epsilon-Cooling

We use epsilon-cooling, adjusting at will the order a^2 corrections to the lattice action, to study the parameter space of instantons in the background of non-trivial holonomy and to determine the presence and nature of constituents with fractional topological charge at finite and zero temperature for SU(2). As an additional tool, zero temperature configurations were generated from those at finite temperature with well-separated constituents. This is achieved by "adiabatically" adjusting the anisotropic coupling used to implement finite temperature on a symmetric lattice. The action and topological charge density, as well as the Polyakov loop and chiral zero-modes are used to analyse these configurations. We also show how cooling histories themselves can reveal the presence of constituents with fractional topological charge. We comment on the interpretation of recent fermion zero-mode studies for thermalized ensembles at small temperatures.Comment: 26 pages, 14 figures in 33 part

Gluino zero-modes for non-trivial holonomy calorons

We couple fermion fields in the adjoint representation (gluinos) to the SU(2) gauge field of unit charge calorons defined on R^3 x S_1. We compute corresponding zero-modes of the Dirac equation. These are relevant in semiclassical studies of N=1 Super-symmetric Yang-Mills theory. Our formulas, show that, up to a term proportional to the vector potential, the modes can be constructed by different linear combinations of two contributions adding up to the total caloron field strength.Comment: 17 pages, 3 Postscript figures, late

Writhe of center vortices and topological charge -- an explicit example

The manner in which continuum center vortices generate topological charge density is elucidated using an explicit example. The example vortex world-surface contains one lone self-intersection point, which contributes a quantum 1/2 to the topological charge. On the other hand, the surface in question is orientable and thus must carry global topological charge zero due to general arguments. Therefore, there must be another contribution, coming from vortex writhe. The latter is known for the lattice analogue of the example vortex considered, where it is quite intuitive. For the vortex in the continuum, including the limit of an infinitely thin vortex, a careful analysis is performed and it is shown how the contribution to the topological charge induced by writhe is distributed over the vortex surface.Comment: 33 latex pages, 10 figures incorporating 14 ps files. Furthermore, the time evolution of the vortex line discussed in this work can be viewed as a gif movie, available for download by following the PostScript link below -- watch for the cute feature at the self-intersection poin

Decomposition of meron configuration of SU(2) gauge field

For the meron configuration of the SU(2) gauge field in the four dimensional Minkowskii spacetime, the decomposition into an isovector field \bn, isoscalar fields $\rho$ and $\sigma$, and a U(1) gauge field $C_{\mu}$ is attained by solving the consistency condition for \bn. The resulting \bn turns out to possess two singular points, behave like a monopole-antimonopole pair and reduce to the conventional hedgehog in a special case. The $C_{\mu}$ field also possesses singular points, while $\rho$ and $\sigma$ are regular everywhere.Comment: 18 pages, 5 figures, Sec.4 rewritten. 5 refs. adde

2+1 Dimensional Georgi-Glashow Instantons in Weyl Gauge

Semiclassical instanton solutions in the 3D SU(2) Georgi-Glashow model are transformed into the Weyl gauge. This illustrates the tunneling interpretation of these instantons and provides a smooth regularization of the singular unitary gauge. The 3D Georgi-Glashow model has both instanton and sphaleron solutions, in contrast to 3D Yang-Mills theory which has neither, and 4D Yang-Mills theory which has instantons but no sphaleron, and 4D electroweak theory which has a sphaleron but no instantons. We also discuss the spectral flow picture of fundamental fermions in a Georgi-Glashow instanton background.Comment: 22 pages, 8 figures, revtex4; v2 - references and comments adde

Confinement, Chiral Symmetry Breaking, and Axial Anomaly from Domain Formation at Intermediate Resolution

Based on general renormalization group arguments, Polyakov's loop-space formalism, and recent analytical lattice arguments, suggesting, after Abelian gauge fixing, a description of pure gluodynamics by means of a Georgi-Glashow like model, the corresponding vacuum fields are defined in a non-local way. Using lattice information on the gauge invariant field strength correlator in full QCD, the resolution scale \La_b, at which these fields become relevant in the vacuum, is determined. For SU(3) gauge theory it is found that \La_b\sim 2.4 GeV, 3.1 GeV, and 4.2 GeV for ($N_F=4, m_q=18$ MeV), ($N_F=4, m_q=36$ MeV), and pure gluodynamics, repectively. Implications for the operator product expansion of physical correlators are discussed. It is argued that the emergence of magnetic (anti)monopoles in the vacuum at resolution \La_b is a direct consequence of the randomness in the formation of a low entropy Higgs condensate. This implies a breaking of chiral symmetry and a proliferation of the axial U(1) anomaly at this scale already. Justifying Abelian projection, a decoupling of non-Abelian gauge field fluctuations from the dynamics occurs. The condensation of (anti)monopoles at \La_c<\La_b follows from the demand that vacuum fields ought to have vanishing action at any resolution. As monopoles condense they are reduced to their cores, and hence they become massless. Apparently broken gauge symmetries at resolutions \La_c<\La\le\La_b are restored in this process.Comment: 11 pages, 3 figure

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are "magnetic bions" which carry net magnetic charge and induce a mass gap for gauge fluctuations. Another type are "neutral bions" which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics - which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription - to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion--anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Ecalle's resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.Comment: 112 pages, 7 figures; v2: typos corrected, discussion of supersymmetric models added at the end of section 8.1, reference adde

Ghost Condensates and Dynamical Breaking of SL(2,R) in Yang-Mills in the Maximal Abelian Gauge

Ghost condensates of dimension two in SU(N) Yang-Mills theory quantized in the Maximal Abelian Gauge are discussed. These condensates turn out to be related to the dynamical breaking of the SL(2,R) symmetry present in this gaugeComment: 16 pages, LaTeX2e, final version to appear in J. Phys.

Continuity, Deconfinement, and (Super) Yang-Mills Theory

We study the phase diagram of SU(2) Yang-Mills theory with one adjoint Weyl fermion on R^3xS^1 as a function of the fermion mass m and the compactification scale L. This theory reduces to thermal pure gauge theory as m->infinity and to circle-compactified (non-thermal) supersymmetric gluodynamics in the limit m->0. In the m-L plane, there is a line of center symmetry changing phase transitions. In the limit m->infinity, this transition takes place at L_c=1/T_c, where T_c is the critical temperature of the deconfinement transition in pure Yang-Mills theory. We show that near m=0, the critical compactification scale L_c can be computed using semi-classical methods and that the transition is of second order. This suggests that the deconfining phase transition in pure Yang-Mills theory is continuously connected to a transition that can be studied at weak coupling. The center symmetry changing phase transition arises from the competition of perturbative contributions and monopole-instantons that destabilize the center, and topological molecules (neutral bions) that stabilize the center. The contribution of molecules can be computed using supersymmetry in the limit m=0, and via the Bogomolnyi--Zinn-Justin (BZJ) prescription in the non-supersymmetric gauge theory. Finally, we also give a detailed discussion of an issue that has not received proper attention in the context of N=1 theories---the non-cancellation of nonzero-mode determinants around supersymmetric BPS and KK monopole-instanton backgrounds on R^3xS^1. We explain why the non-cancellation is required for consistency with holomorphy and supersymmetry and perform an explicit calculation of the one-loop determinant ratio.Comment: A discussion of the non-cancellation of the nonzero mode determinants around supersymmetric monopole-instantons in N=1 SYM on R^3xS^1 is added, including an explicit calculation. The non-cancellation is, in fact, required by supersymmetry and holomorphy in order for the affine-Toda superpotential to be reproduced. References have also been adde