Explicit construction of BRST charge of noncommutative D-brane system

TL;DR

This paper explicitly constructs the BRST charge for noncommutative D-brane systems with a constant NS B-field, emphasizing the role of auxiliary variables in achieving BRST invariance.

Contribution

It provides a detailed construction of the BRST charge and invariant Lagrangian for noncommutative D-branes, incorporating ghost fields and auxiliary variables.

Findings

Successfully constructed gauge-fixed Hamiltonian and BRST-invariant Lagrangian.

Highlighted the importance of auxiliary variables in the formalism.

Demonstrated nilpotency of the BRST charge in this context.

Abstract

In the BRST-BFV scheme for noncommutative D-branes with constant NS $B$-field, introducing ghost degrees of freedom we construct the gauge fixed Hamiltonian and corresponding effective Lagrangian invariant under nilpotent BRST charge. It is also shown that the presence of auxiliary variables introduced via the improved Dirac formalism plays a crucial role in the construction of the BRST invariant Lagrangian.