On Batalin-Vilkovisky Formalism of Non-Commutative Field Theories

Abstract

We apply the BV formalism to non-commutative field theories, introduce BRST symmetry, and gauge-fix the models. Interestingly, we find that treating the full gauge symmetry in non-commutative models can lead to reducible gauge algebras. As one example we apply the formalism to the Connes-Lott two-point model. Finally, we offer a derivation of a superversion of the Harish-Chandra-Itzykson-Zuber integral.

20 pages, LaTeX. v2: minor corrections. v3: Added an Appendix about Harish-Chandra-Itzykson-Zuber integrals. v4: Added References

References in corpus (9)

• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Noncommutative Induced Gauge Theory
• The β-function in duality-covariant noncommutative ϕ^4-theory
• Induced Gauge Theory on a Noncommutative Space
• Non-Commutative U(1) Gauge Theory on R**4 with Oscillator Term and BRST Symmetry
• Local BRST cohomology and Seiberg-Witten maps in noncommutative Yang-Mills theory
• On Generalized Gauge-Fixing in the Field-Antifield Formalism
• Improved Localization of a Renormalizable Non-Commutative Translation Invariant U(1) Gauge Model

Cited by in corpus (3)

• Noncommutative geometry and the BV formalism: application to a matrix model
• The BV formalism: theory and application to a matrix model
• Complex (super)-matrix models with external sources and $q$-ensembles of Chern-Simons and ABJ(M) type