scholarly journals DISCRETE NONCOMMUTATIVE GAUGE THEORY

2001 ◽  
Vol 16 (04n06) ◽  
pp. 367-386 ◽  
Author(s):  
RICHARD J. SZABO
Keyword(s):  
Gauge Theory ◽  
Matrix Models ◽  
Wilson Line ◽  
Morita Equivalence ◽  
Generic Properties ◽  
Gauge Invariant ◽  
Fundamental Matter ◽  
Generic Relation ◽  
Noncommutative Gauge Theory ◽  
Noncommutative Quantum

A review of the relationships between matrix models and noncommutative gauge theory is presented. A lattice version of noncommutative Yang–Mills theory is constructed and used to examine some generic properties of noncommutative quantum field theory, such as uv/ir mixing and the appearance of gauge-invariant open Wilson line operators. Morita equivalence in this class of models is derived and used to establish the generic relation between noncommutative gauge theory and twisted reduced models. Finite-dimensional representations of the quotient conditions for toroidal compactification of matrix models are thereby exhibited. The coupling of noncommutative gauge fields to fundamental matter fields is considered and a large mass expansion is used to study the properties of gauge-invariant observables. Morita equivalence with fundamental matter is also presented and used to prove the equivalence between the planar loop renormalizations in commutative and noncommutative quantum chromodynamics.

scholarly journals Remarks on the eigenvalues distributions of D≤4 Yang–Mills matrix models

2015 ◽  
Vol 30 (01) ◽  
pp. 1450197
Author(s):  
Badis Ydri
Keyword(s):  
Gauge Theory ◽  
Matrix Models ◽  
Yang Mills ◽  
Fuzzy Geometry ◽  
Noncommutative Gauge Theory

The phenomenon of emergent fuzzy geometry and noncommutative gauge theory from Yang–Mills matrix models is briefly reviewed. In particular, the eigenvalue distributions of Yang–Mills matrix models in lower dimensions in the commuting (matrix or Yang–Mills) phase of these models are discussed.

scholarly journals ANOMALIES IN NONCOMMUTATIVE GAUGE THEORIES, SEIBERG–WITTEN TRANSFORMATION AND RAMOND–RAMOND COUPLINGS

2004 ◽  
Vol 19 (04) ◽  
pp. 613-630 ◽  
Author(s):  
RABIN BANERJEE
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Chern Character ◽  
Exact Expression ◽  
Gauge Invariant ◽  
Axial Anomaly ◽  
Noncommutative Gauge Theory ◽  
Noncommutative Gauge Theories

We propose an exact expression for the unintegrated form of the star gauge-invariant axial anomaly in an arbitrary even dimensional noncommutative gauge theory. The proposal is based on our earlier work,7 as well as on the inverse Seiberg–Witten map and identities related to it, obtained previously15,18 by comparing Ramond–Ramond couplings in different descriptions. The integrated anomalies, found from the unintegrated ones, are expressed in terms of a simplified version of the Elliott formula involving the noncommutative Chern character. These anomalies, under the Seiberg–Witten transformation, reduce to the ordinary (integrated) axial anomalies. Compatibility with existing results of anomalies in noncommutative theories is established.

scholarly journals NOTES ON NONCOMMUTATIVE SUPERSYMMETRIC GAUGE THEORY ON THE FUZZY SUPERSPHERE

2007 ◽  
Vol 22 (28) ◽  
pp. 5179-5209 ◽  
Author(s):  
BADIS YDRI
Keyword(s):  
Monte Carlo ◽  
Supersymmetric Gauge Theory ◽  
Gauge Theory ◽  
Gauge Symmetry ◽  
Finite Number ◽  
Matrix Models ◽  
Degrees Of Freedom ◽  
Noncommutative Gauge Theory ◽  
Supersymmetric Gauge ◽  
Scalar Action

In this paper we review Klimčík's construction of noncommutative gauge theory on the fuzzy supersphere. This theory has an exact SUSY gauge symmetry with a finite number of degrees of freedom and thus in principle it is amenable to the methods of matrix models and Monte Carlo numerical simulations. We also write down in this paper a novel fuzzy supersymmetric scalar action on the fuzzy supersphere.

scholarly journals Noncommutative gauge theory and symmetry breaking in matrix models

2010 ◽  
Vol 81 (8) ◽  
Author(s):  
Harald Grosse ◽  
Fedele Lizzi ◽  
Harold Steinacker
Keyword(s):  
Gauge Theory ◽  
Symmetry Breaking ◽  
Matrix Models ◽  
Noncommutative Gauge Theory

scholarly journals Finite N matrix models of noncommutative gauge theory

1999 ◽  
Vol 1999 (11) ◽  
pp. 029-029 ◽  
Author(s):  
Jan Ambjørn ◽  
Yuri M Makeenko ◽  
Jun Nishimura ◽  
Richard J Szabo
Keyword(s):  
Gauge Theory ◽  
Matrix Models ◽  
Noncommutative Gauge Theory

scholarly journals Gauge invariant correlators in noncommutative gauge theory

2001 ◽  
Vol 608 (1-2) ◽  
pp. 103-124 ◽  
Author(s):  
Moshe Rozali ◽  
Mark Van Raamsdonk
Keyword(s):  
Gauge Theory ◽  
Gauge Invariant ◽  
Noncommutative Gauge Theory

The Standard Theory

2017 ◽  
Author(s):  
John Iliopoulos
Keyword(s):  
Gauge Theory ◽  
Invariant Theory ◽  
Standard Theory ◽  
Strong Interactions ◽  
Gauge Invariant ◽  
Electromagnetic Interactions ◽  
Protons And Neutrons ◽  
Free Particles ◽  
Theoretical Predictions ◽  
Theory And Experiment

All ingredients of the previous chapters are combined in order to build a gauge invariant theory of the interactions among the elementary particles. We start with a unified model of the weak and the electromagnetic interactions. The gauge symmetry is spontaneously broken through the BEH mechanism and we identify the resulting BEH boson. Then we describe the theory known as quantum chromodynamics (QCD), a gauge theory of the strong interactions. We present the property of confinement which explains why the quarks and the gluons cannot be extracted out of the protons and neutrons to form free particles. The last section contains a comparison of the theoretical predictions based on this theory with the experimental results. The agreement between theory and experiment is spectacular.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals Boundary electromagnetic duality from homological edge modes

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Philippe Mathieu ◽  
Nicholas Teh
Keyword(s):  
Gauge Theory ◽  
Symplectic Structure ◽  
Central Charge ◽  
Wilson Line ◽  
Boundary Term ◽  
Global Symmetry ◽  
Homotopy Pullback ◽  
Line Singularities ◽  
Topological Boundary

Abstract Recent years have seen a renewed interest in using ‘edge modes’ to extend the pre-symplectic structure of gauge theory on manifolds with boundaries. Here we further the investigation undertaken in [1] by using the formalism of homotopy pullback and Deligne- Beilinson cohomology to describe an electromagnetic (EM) duality on the boundary of M = B3 × ℝ. Upon breaking a generalized global symmetry, the duality is implemented by a BF-like topological boundary term. We then introduce Wilson line singularities on ∂M and show that these induce the existence of dual edge modes, which we identify as connections over a (−1)-gerbe. We derive the pre-symplectic structure that yields the central charge in [1] and show that the central charge is related to a non-trivial class of the (−1)-gerbe.

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