Related papers: Notes on gauging noneffective group actions
We analyze perturbative aspects of gauged matrix models, including those where classically the gauge symmetry is partially broken. Ghost fields play a crucial role in the Feynman rules for these vacua. We use this formalism to elucidate the…
The extraordinary success of the Standard Model asks for a more rigorous control beyond the perturbative approach, which is affected by mathematical problems (interaction picture and canonical quantization, non-convergence of the…
This paper generalizes Bass' work on zeta functions for uniform tree lattices. Using the theory of von Neumann algebras, machinery is developed to define the zeta function of a discrete group of automorphisms of a bounded degree tree. The…
A treatment may be appropriate for some group (the ``sick" group) on whom it has a positive effect, but it can also have a detrimental effect on subjects from another group (the ``healthy" group). In a non-targeted trial both sick and…
We survey some results concerning finite group actions on products of spheres.
The aim of this review is to present an overview over available models and approaches to non-commutative gauge theory. Our main focus thereby is on gauge models formulated on flat Groenewold-Moyal spaces and renormalizability, but we will…
Supersymmetric nonlinear sigma models are obtained from linear sigma models by imposing supersymmetric constraints. If we introduce auxiliary chiral and vector superfields, these constraints can be expressed by D-terms and F-terms depending…
One of the central concepts in modern theoretical physics, gauge symmetry, is typically realised by lifting a finite-dimensional global symmetry group of a given functional to an infinite-dimensional local one by extending the functional to…
A series of sigma models with torsion are analysed which generate their mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories -- in fact SU(2) WZW models at level $k$. In contrast to the more familiar…
This is a brief review of some of the uses of nonlinear sigma models. After a short general discussion touching on point particles, strings and condensed matter systems, focus is shifted to sigma models as probes of target space geometries.…
We calculate the beta function of non-linear sigma models with S^{D+1} and AdS_{D+1} target spaces in a 1/D expansion up to order 1/D^2 and to all orders in \alpha'. This beta function encodes partial information about the spacetime…
We provide and study complete sets of one-loop renormalization group equations of several Finkel'stein non-linear $\sigma$-models, the effective field theories describing the diffusive quantum fluctuations in correlated disordered systems.…
We consider gauged WZW models based on a four dimensional non-semi-simple group. We obtain conformal $\s$-models in $D=3$ spacetime dimensions (with exact central charge $c=3$) by axially and vectorially gauging a one-dimensional subgroup.…
We determine all the terms that are gauge-invariant up to a total spacetime derivative ("semi-invariant terms") for gauged non-linear sigma models. Assuming that the isotropy subgroup $H$ of the gauge group is compact or semi-simple, we…
Bose gas in a random external field is considered. The sigma model like effective action both for weak and strong random fields compared with the interaction between particles is derived by averaging over the random field and integration…
The algebraic formulation of the quantum group gauge models in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider gauge groups taking values in the quantum groups and noncommutative gauge fields…
We study gauge theory with finite group $G$ on a graph $X$ using noncommutative differential geometry and Hopf algebra methods with $G$-valued holonomies replaced by gauge fields valued in a `finite group Lie algebra' subset of the group…
We investigate compact quantum group actions on unital $C^*$-algebras by analyzing invariant subsets and invariant states. In particular, we come up with the concept of compact quantum group orbits and use it to show that countable compact…
After a brief introduction to the sigma model in QCD, we discuss how the sigma model can be relevant in the Standard Model. It is shown to be useful in the analysis of weak processes, such as the study of $\Delta {I} = 1/2$ rule, and in the…
We consider a free massless scalar field coupled to an infinite tower of background higher-spin gauge fields via minimal coupling to the traceless conserved currents. The set of Abelian gauge transformations is deformed to the non-Abelian…