On this page:
1 The BV action
2 Relation to standard notations for antifields
3 BV Hamiltonian vector in flat point

BV formalism

1 The BV action

(16)

field or

antifield

section of

case of flat worldsheet

comment

constraint:

is antifield of

super-diffeomorphism ghost

It would seem to be natural to use , instead of , to denote the antifield of . But in practice such a notation turns out to be absolutely disastrous.

The previously discussed local rescaling symmetries of are extended to the BV action:

(17)

(18)

2 Relation to standard notations for antifields

is an auxiliary field, and we will integrate it out. In other words, the only dynamical component of is . When we insert some operator, we should take care to only insert via the combination .

We are left with and . In PerturbativeSuperstringTheoryRevisited, is called and is called ; we agree with their Equation (3.20).

3 BV Hamiltonian vector in flat point

BV Hamiltonian   

generates