In these lectures we describe the construction of a gauge invariant renormalization group equation for pure non-Abelian gauge theory. In the process, a non-perturbative gauge invariant continuum Wilsonian effective action is precisely defined. The formulation makes sense without gauge fixing and thus manifest gauge invariance may be preserved at all stages. In the large N limit (of SU(N) gauge ...

We analyze the question of U⋆(1) gauge invariance in a flat non-commutative space where the parameter of non-commutativity, θ(x), is a local function satisfying Jacobi identity (and thereby leading to an associative Kontsevich product). We show that in this case, both gauge transformations as well as the definitions of covariant derivatives have to modify so as to have a gauge invariant action....

Abstract We show that an effective Abelian gauge theory can be obtained as a renormalizable theory from QCD in the maximal Abelian gauge. The derivation improves the previous version which was obtained by one of the authors and was called the Abelianprojected effective gauge theory. This result supports a view that we can construct an effective Abelian gauge theory from QCD without losing chara...

The graphical method discussed previously can be used to create new gauges not reachable by the path-integral formalism. By this means a new gauge is designed for more efficient two-loop QCD calculations. It is related to but simpler than the ordinary background-field gauge, in that even the triple-gluon vertices for internal lines contain only four terms, not the usual six. This reduction simp...

A dynamical mass generation of a two-component fermion in QED3 with the Chern-Simons term is investigated by solving the Schwinger-Dyson equation formulated in the lowest ladder approximation. Dependence of the dynamical fermion mass on the gauge-fixing parameter, the gauge coupling constant, and the topological mass is examined by approximated analytical and also numerical methods. The inclusi...

Dynamical nature of the gauge degree of freedom and its effect to fermion spectrum are studied at β = ∞ for two-dimensional nonabelian chiral gauge theory in the vacuum overlap formulation. It is argued that the disordered gauge degree of freedom does not necessarily cause the massless chiral state in the (waveguide) boundary correlation function. An asymptotically free self-coupling for the ga...

Lattice Landau gauge and other related lattice gauge fixing schemes are known to violate spectral positivity. The most direct sign of the violation is the rise of the effective mass as a function of distance. The origin of this phenomenon lies in the quenched character of the auxiliary field g used to implement lattice gauge fixing, and is similar to quenched QCD in this respect. This is best s...

In the context of AdS/CFT with flavor, we consider the type IIB supergravity solution corresponding to a fully localized D3/D7 intersection. We complete the standard metric ansatz by providing an analytic expression for the warp factor, under the assumption of a logarithmically running axion-dilaton. From the gauge dual perspective, this behavior is related to the positive beta function of the ...

The thermal partition function of photons in any covariant gauge and gravitons in the harmonic gauge, propagating in a Rindler wedge, are computed using a local ζ-function regularization approach. The correct Planckian leading order temperature dependence T 4 is obtained in both cases. For the photons, the existence of a surface term giving a negative contribution to the entropy is confirmed, a...