Chiral gauge theories and anomalies in the Wilson renormalization group approach

We extend the Wilson renormalization group (RG) formulation to chiral gauge theories and show that local gauge symmetry can be implemented by a suitable choice of the RG flow boundary conditions. Since the space-time dimension is four, there is no ambiguity in handling the matrix \g_5 and left and right fermions are not coupled. As a result the ultraviolet action contains all possible globally chiral invariant interactions. Nevertheless, the correct chiral anomaly is reproduced.Comment: 16 pages, 4 figures, LaTex, uses epsfig, amssym

Monopole Condensation and Antisymmetric Tensor Fields: Compact QED and the Wilsonian RG Flow in Yang-Mills Theories

A field theoretic description of monopole condensation in strongly coupled gauge theories is given by actions involving antisymmetric tensors B_{\mu\nu} of rank 2. We rederive the corresponding action for 4d compact QED, summing explicitly over all possible monopole configurations. Its gauge symmetries and Ward identities are discussed. Then we consider the Wilsonian RGs for Yang-Mills theories in the presence of collective fields (again tensors B_{\mu\nu}) for the field strengths F_{\mu \nu} associated to the U(1) subgroups. We show that a ``vector-like'' Ward identity for the Wilsonian action involving B_{\mu\nu}, whose validity corresponds to monopole condensation, constitutes a fixed point of the Wilsonian RG flow.Comment: 18 pages (LaTeX2e), 1 fi

Confinement, Monopoles and Wilsonian Effective Action

An effective low energy action for Yang-Mills theories is proposed, which invokes an additional auxiliary field $H_{\mu \nu}$ for the field strength $F_{\mu \nu}$. For a particular relation between the parameters of this action a gluon propagator with a $1/p^4$ behaviour for $p^2 \to 0$ in the Landau gauge is obtained. The abelian subsector of this action admits a duality transformation, where the dual action contains a Goldstone boson $\varphi$ as the dual of $H_{\mu \nu}$, and corresponds to an abelian Higgs model in the broken phase describing the condensation of magnetic charges. The Wilsonian renormalization group equations for the parameters of the original action are integrated in some approximation, and we find that the relation among the parameters associated with confinement appears as an infrared attractive fixed point.Comment: 25 pages, LaTex, 2 figure

First week is editorial, second week is algorithmic : platform gatekeepers and the platformization of music curation

This article investigates the logics that underpin music curation, and particularly the work of music curators, working at digital music streaming platforms. Based on ethnographic research that combines participant observation and a set of interviews with key informants, the article questions the relationship between algorithmic and human curation and the specific workings of music curation as a form of platform gatekeeping. We argue that music streaming platforms in combining proprietary algorithms and human curators constitute the \u201cnew gatekeepers\u201d in an industry previously dominated by human intermediaries such as radio programmers, journalists, and other experts. The article suggests understanding this gatekeeping activity as a form of \u201calgo-torial power\u201d that has the ability to set the \u201clistening agendas\u201d of global music consumers. While the power of traditional gatekeepers was mainly of an editorial nature, albeit data had some relevance in orienting their choices, the power of platform gatekepeers is an editorial power \u201caugmented\u201d and enhanced by algorithms and big data. Platform gatekeepers have more data, more tools to manage and to make sense of these data, and thus more power than their predecessors. Platformization of music curation then consists of a data-intense gatekeeping activity, based on different mixes of algo-torial logics, that produces new regimes of visibility. This makes the platform capitalistic model potentially more efficient than industrial capitalism in transforming audience attention into data and data into commodities

Exact Flow Equations and the U(1)-Problem

The effective action of a SU(N)-gauge theory coupled to fermions is evaluated at a large infrared cut-off scale k within the path integral approach. The gauge field measure includes topologically non-trivial configurations (instantons). Due to the explicit infrared regularisation there are no gauge field zero modes. The Dirac operator of instanton configurations shows a zero mode even after the infrared regularisation, which leads to U_A(1)-violating terms in the effective action. These terms are calculated in the limit of large scales k.Comment: 22 pages, latex, no figures, with stylistic changes and some arguments streamlined, typos corrected, References added, to appear in Phys. Rev.

Dimensional renormalization of Yukawa theories wia Wilsonian methods

In the 't Hooft-Veltman dimensional regularization scheme it is necessary to introduce finite counterterms to satisfy chiral Ward identities. It is a non-trivial task to evaluate these counterterms even at two loops. We suggest the use of Wilsonian exact renormalization group techniques to reduce the computation of these counterterms to simple master integrals. We illustrate this method by a detailed study of a generic Yukawa model with massless fermions at two loops.Comment: 32 pages, 9 figures, revised version: minor errors corrected, a reference adde

Effective Average Action in N=1 Super-Yang-Mills Theory

For N=1 Super-Yang-Mills theory we generalize the effective average action Gamma_k in a manifest supersymmetric way using the superspace formalism. The exact evolution equation for Gamma_k is derived and, introducing as an application a simple truncation, the standard one-loop beta-function of N=1 SYM theory is obtained.Comment: 17 pages, LaTeX, some remarks added, misprints corrected, to appear in Phys. Rev.

Classical evolution of fractal measures generated by a scalar field on the lattice

We investigate the classical evolution of a $\phi^4$ scalar field theory, using in the initial state random field configurations possessing a fractal measure expressed by a non-integer mass dimension. These configurations resemble the equilibrium state of a critical scalar condensate. The measures of the initial fractal behavior vary in time following the mean field motion. We show that the remnants of the original fractal geometry survive and leave an imprint in the system time averaged observables, even for large times compared to the approximate oscillation period of the mean field, determined by the model parameters. This behavior becomes more transparent in the evolution of a deterministic Cantor-like scalar field configuration. We extend our study to the case of two interacting scalar fields, and we find qualitatively similar results. Therefore, our analysis indicates that the geometrical properties of a critical system initially at equilibrium could sustain for several periods of the field oscillations in the phase of non-equilibrium evolution.Comment: 13 pages, 13 figures, version published at Int. J. Mod. Phys.

Evolution equations for the effective four-quark interactions in QCD

A nonperturbative renormalization group equation describes how the momentum dependent four-quark vertex depends on an infrared cutoff. We find a quasilocal one-particle irreducible piece generated by (anomaly-free) multi-gluon exchange. It becomes important at a cutoff scale where scalar and pseudoscalar meson-bound states are expected to play a role. This interaction remains subleading as compared to the effective one-gluon exchange contribution. The local instanton induced four-quark interaction becomes dominant at a scale around 800 MeV. In absence of a gluon mass the strong dependence of the one-gluon exchange on the transferred momentum indicates that the pointlike interactions of the Nambu-Jona-Lasinio model cannot give a very accurate description of QCD. A pointlike effective four-quark interaction becomes more realistic in case of spontaneous color symmetry breaking.Comment: 24 pages, LaTeX file, + 6 PS figure

Multivalued Fields on the Complex Plane and Conformal Field Theories

In this paper a class of conformal field theories with nonabelian and discrete group of symmetry is investigated. These theories are realized in terms of free scalar fields starting from the simple $b-c$ systems and scalar fields on algebraic curves. The Knizhnik-Zamolodchikov equations for the conformal blocks can be explicitly solved. Besides of the fact that one obtains in this way an entire class of theories in which the operators obey a nonstandard statistics, these systems are interesting in exploring the connection between statistics and curved space-times, at least in the two dimensional case.Comment: (revised version), 30 pages + one figure (not included), (requires harvmac.tex), LMU-TPW 92-1