We clarify the physical origin of the difference between gauge properties of conserved currents in abelian and nonabelian theories. In the latter, but not in the former, such currents can always be written on shell as gauge invariants modulo identically conserved, superpotential, terms. For the “isotopic” vector and the stress tensor currents of spins 1 and 2 respectively, we explain this diffe...

In the previous paper[1], we derived the Abelian projected effective gauge theory as a low energy effective theory of the SU(N) Yang-Mills theory by adopting the maximal Abelian gauge. At that time, we have demonstrated the multiplicative renormalizability of the propagators for the diagonal gluon and the dual Abelian antisymmetric tensor field. In this paper, we show the multiplicative renorma...

We review the relation between 4n-dimensional quaternion-Kähler metrics with n + 1 abelian isometries and superconformal theories of n + 1 tensor supermultiplets. As an application we construct the class of eight-dimensional quaternion-Kähler metrics with three abelian isometries in terms of a single function obeying a set of linear second-order partial differential equations. Talk given by F.S...

We consider maximal abelian subalgebras of O n which are invariant to the standard circle action. It turns out that these are all contained in the zero grade of O n. Then we consider shift invariant maximal abelian subalgebras of the zero grade, which are also invariant to a " second shift " map, and show that these are just infinite tensor products of diagonal matrices in the standard UHF pict...

We show that the introduction of massless fermions in an abelian gauge theory in Z-t1 dimensions does not lead to any parity anomaly despite a noncommutativity of limits in the structure function of the odd part of the vacuum polarisation tensor. However, a parity anomaly does exist in non-abelian theories due to a conflict between gauge invariance under large gauge transformations and the pari...

The ’t Hooft anomaly matching conditions are a standard tool to study and test nonperturbative issues in quantum field theory. We give a new, simple proof of the anomaly matching conditions in 2D Poincarè invariant theories. We consider the case of invariance under a large class of generalized symmetries, which include abelian and non-abelian internal symmetries, space-time symmetries generated...