Moyal Formulation of Witten's Star Product in the Fermionic Ghost Sector
arXiv:hep-th/0205107
Abstract
In this paper, we recast the fermionic ghost sector of Witten's open bosonic string field theory in the language of noncommutative field theory. In particular, following the methods of hep-th/0202087, we find that in Siegel gauge Witten's star product roughly corresponds to a continuous tensor product of Clifford Algebras, and we formulate important operators of the theory in this language, notably the kinetic operator of vacuum string field theory and the BRST operator describing the vacuum of the unstable D-25 brane. We find that the BRST operator is singular in this formulation. We explore alternative operator/Moyal representations of the star product analogous to the split string description and the discrete Moyal basis developed extensively in recent work by Bars and Matsuo (hep-th/0204260). Finally, we discuss some interesting singularities in the formalism and how they may be regulated.
arXiv comment35 pages, no figures
References in corpus (12)
- Noncommutative Field Theory
- Half-strings, Projectors, and Multiple D-branes in Vacuum String Field Theory
- Split string field theory I
- Star Algebra Spectroscopy
- String Field Theory Around the Tachyon Vacuum
- Computing in String Field Theory Using the Moyal Star Product
- Half-String Approach to Closed String Field Theory
- Siegel Gauge in Vacuum String Field Theory
- Diagonal Representation of Open String Star and Moyal Product
- Associativity Anomaly in String Field Theory
- Open Superstring Star as a Continuous Moyal Product
- D-branes as GMS Solitons in Vacuum String Field Theory
Cited by in corpus (18)
- Experimental String Field Theory
- Analytical Solutions of Open String Field Theory
- Topics in String Field Theory
- Virasoro operators in the continuous basis of string field theory
- On Continuous Moyal Product Structure in String Field Theory
- Continuous Half-String Representation of String Field Theory
- Fermionic Ghosts in Moyal String Field Theory
- Locality, Causality, and an Initial Value Formulation for Open String Field Theory
- String Amplitudes from Moyal String Field Theory
- Superstar in Noncommutative Superspace via Covariant Quantization of the Superparticle
- A fresh look at midpoint singularities in the algebra of string fields
- Witten's Vertex Made Simple
- Open Superstring Star as a Continuous Moyal Product
- Analytic Study of Nonperturbative Solutions in Open String Field Theory
- A Note on kappa-Diagonal Surface States
- Normalization anomalies in level truncation calculations
- Improved Off-Shell Scattering Amplitudes in String Field Theory and New Computational Methods
- Descent Relations in Cubic Superstring Field Theory