Finite-matrix formulation of gauge theories on a non-commutative torus with twisted boundary conditions
arXiv:0810.5234 · doi:10.1088/1126-6708/2009/04/055
Abstract
We present a novel finite-matrix formulation of gauge theories on a non-commutative torus. Unlike the previous formulation based on a map from a square matrix to a field on a discretized torus with periodic boundary conditions, our formulation is based on the algebraic characterization of the configuration space. This enables us to describe the twisted boundary conditions in terms of finite matrices and hence to realize the Morita equivalence at a fully regularized level. Matter fields in the fundamental representation turn out to be represented by rectangular matrices for twisted boundary conditions analogously to the matrix spherical harmonics on the fuzzy sphere with the monopole background. The corresponding Ginsparg-Wilson Dirac operator defines an index, which can be used to classify gauge field configurations into topological sectors. We also perform Monte Carlo calculations for the index as a consistency check. Our formulation is expected to be useful for applications of non-commutative geometry to various problems related to topological aspects of field theories and string theories.
arXiv comment25 pages, 2 figures v2: 2 figures added, version published in JHEP
References in corpus (65)
- String Theory and Noncommutative Geometry
- Quantum Field Theory on Noncommutative Spaces
- The quantum structure of spacetime at the Planck scale and quantum fields
- Noncommutative Geometry and Matrix Theory: Compactification on Tori
- Noncommutative Perturbative Dynamics
- Exactly massless quarks on the lattice
- A Large-N Reduced Model as Superstring
- Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
- More about exactly massless quarks on the lattice
- The index theorem in QCD with a finite cut-off
- Instantons on noncommutative R^4, and (2,0) superconformal six dimensional theory
- Noncommutative Solitons
- Noncommutative Yang-Mills in IIB Matrix Model
- Vector like gauge theories with almost massless fermions on the lattice
- Space-Time Structures from IIB Matrix Model
- Lattice Gauge Fields and Discrete Noncommutative Yang-Mills Theory
- Finite N Matrix Models of Noncommutative Gauge Theory
- Nonperturbative Dynamics of Noncommutative Gauge Theory
- Monopoles and Solitons in Fuzzy Physics
- Quantized Gauge Theory on the Fuzzy Sphere as Random Matrix Model
- Topologically nontrivial field configurations in noncommutative geometry
- Emergent Gravity from Noncommutative Gauge Theory
- Renormalization of Quantum Field Theories on Noncommutative R^d, I. Scalars
- Flux tube solutions in noncommutative gauge theories
- Dynamical Generation of Four-Dimensional Space-Time in the IIB Matrix Model
- Dynamics of Strings in Noncommutative Gauge Theory
- Monopoles and Strings in Noncommutative Gauge Theory
- Phase structure of non-commutative scalar field theories
- Spectrum of Schroedinger field in a noncommutative magnetic monopole
- Exact Noncommutative Solitons
- Exact Solutions of Multi-Vortices and False Vacuum Bubbles in Noncommutative Abelian-Higgs Theories
- Stripes from (noncommutative) stars
- Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term
- Emergent Gravity and Noncommutative Branes from Yang-Mills Matrix Models
- N=4 Super Yang-Mills from the Plane Wave Matrix Model
- UV/IR Mixing via Closed Strings and Tachyonic Instabilities
- The Meaning of Infrared Singularities in Noncommutative Gauge Theories
- Unstable Solitons in Noncommutative Gauge Theory
- The Fuzzy Ginsparg-Wilson Algebra: A Solution of the Fermion Doubling Problem
- A Non-Perturbative Study of Gauge Theory on a Non-Commutative Plane
- Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking
- Dimensional Reduction over Fuzzy Coset Spaces
- Phase diagram and dispersion relation of the non-commutative λϕ^{4} model in d=3
- A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability
- Deconfinement phase transition in N=4 super Yang-Mills theory on RxS^3 from supersymmetric matrix quantum mechanics
- Embedding of theories with SU(2|4) symmetry into the plane wave matrix model
- Ginsparg-Wilson Relation, Topological Invariants and Finite Noncommutative Geometry
- Geometry in transition: A model of emergent geometry
- Emergent Gravity, Matrix Models and UV/IR Mixing
- Fermions on spontaneously generated spherical extra dimensions
- Monopole Bundles over Fuzzy Complex Projective Spaces
- Noncommutative Chiral Gauge Theories on the Lattice with Manifest Star-Gauge Invariance
- Projectors for the fuzzy sphere
- Projective Modules of Finite Type and Monopoles over
- Ginsparg-Wilson Relation and 't Hooft-Polyakov Monopole on Fuzzy 2-Sphere
- Dynamical generation of a nontrivial index on the fuzzy 2-sphere
- Fiber Bundles and Matrix Models
- Ginsparg-Wilson Dirac operator in the monopole backgrounds on the fuzzy 2-sphere
- Chiral Anomaly and Ginsparg-Wilson Relation on the Noncommutative Torus
- On Matrix Model Formulations of Noncommutative Yang-Mills Theories
- The index of the overlap Dirac operator on a discretized 2d non-commutative torus
- Quantum Fluctuations versus Topology - a Study in U(1)_2 Lattice Gauge Theory
- Classical Solutions of the TEK Model and Noncommutative Instantons in Two Dimensions
- Probability distribution of the index in gauge theory on 2d non-commutative geometry
- Index theorem in spontaneously symmetry-broken gauge theories on a fuzzy 2-sphere
Cited by in corpus (10)
- Intertwining Operator Realization of Non-Relativistic Holography
- Emergent Geometry from Quantized Spacetime
- The emergence of expanding space-time and intersecting D-branes from classical solutions in the Lorentzian type IIB matrix model
- Probability of the Standard Model Appearance from a Matrix Model
- Construction of a topological charge on fuzzy S^2 x S^2 via Ginsparg-Wilson relation
- Ginsparg-Wilson relation on a fuzzy 2-sphere for adjoint matter
- Dominance of a single topological sector in gauge theory on non-commutative geometry
- Matrix model and Yukawa couplings on the noncommutative torus
- Gauge-Higgs Unification In Spontaneously Created Fuzzy Extra Dimensions
- Phenomenological studies in the matrix models