What is the BRST-anti-BRST formalism? Is the Sp(2) doublet the ghost, antighost pair? Introductory accounts of this subject seem to be hard to find. I would appreciate a reference for someone who knows BRST well.
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2 Answers
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Jim. I think the following references might be helpful:
Grégoire, Philippe; Henneaux, Marc. Hamiltonian BRST--anti-BRST theory. Communications in Mathematical Physics 157 (1993), no. 2, 279--303. http://projecteuclid.org/euclid.cmp/1104253940.
P Gregoire and M Henneaux, Antifield-antibracket formulation of the anti-BRST transformation, 1993 J. Phys. A: Math. Gen. 26 6073 http://dx.doi.org/10.1088/0305-4470/26/21/045
The idea seems to be to choose a non-minimal (with extra ghosts and anti-fields) solution of the usual BRST (or BV-BRST) master equation with extra structure (invariance with respect to an anti-BRST transformation, which is another cohomological vector field/differential). As far as I can tell, the main difference/advantage seems to be in how the gauge fixing is done. In the usual formalism, one adds a BRST-exact term to the Hamiltonian (or action), which is the image of a gauge fixing fermion under the BRST transformation. In this non-minimal formalism, the gauge fixing fermion is itself chosen to be anti-BRST exact, which means that it is the image of a gauge fixing boson under the anti-BRST transformation.
I'm afraid that I'm not familiar enough with the applications of this formalism to judge why this way of gauge fixing is actually advantageous. I also can't comment intelligently about the $sp(2)$ structure.
answered Nov 15, 2014 at 10:03
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$\begingroup$ Thanks especially for the precise references - see also my next comment $\endgroup$ Commented Nov 16, 2014 at 14:45
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To complete Igor Khavkine's answer: as explained here, in the Sp(2) covariant description the BRST and anti-BRST charges form a doublet with opposite ghost number.
answered Nov 15, 2014 at 11:20
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$\begingroup$ I was aware of those words ` the BRST and anti-BRST charges form a doublet' but had missed where anyone mentioned the ghost numbers - would an example be ghost,antighost in the BV case? will study the refs $\endgroup$ Commented Nov 16, 2014 at 14:47