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We present the BRST cohomologies of a class of constraint (super) Lie algebras as detour complexes. By giving physical interpretations to the components of detour complexes as gauge invariances, Bianchi identities and equations of motion we obtain a large class of new gauge theories. The pivotal new machinery is a treatment of the ghost Hilbert space designed to manifest the detour structure. Along with general results, we give details for three of these theories which correspond to gauge invariant spinning particle models of totally symmetric, antisymmetric and Kahler antisymmetric forms. In particular, we give details of our recent announcement of a (p,q)-form Kahler electromagnetism. We also discuss how our results generalize to other special geometries.
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We consider a second degree algebraic curve describing a general conic constraint imposed on the motion of a massive spinless particle. The problem is trivial at classical level but becomes involved and interesting in its quantum counterpart with subtleties in its symplectic structure and symmetries. The model is used here to investigate quantization issues related to the Hamiltonian constraint structure, Dirac brackets, gauge symmetry and BRST transformations. We pursue the complete constraint analysis in phase space and perform the Faddeev-Jackiw symplectic quantization following the Barcelos-Wotzasek iteration program to unravel the fine tuned and more relevant aspects of the constraint structure. A comparison with the longer usual Dirac-Bergmann algorithm, still more well established in the literature, is also presented. While in the standard DB approach there are four second class constraints, in the FJBW they reduce to two. By using the symplectic potential obtained in the last step of the FJBW iteration process we construct a gauge invariant model exhibiting explicitly its BRST symmetry. Our results reproduce and neatly generalize the known BRST symmetry of the rigid rotor showing that it constitutes a particular case of a broader class of theories.
We discuss the BRST quantization of General Relativity (GR) with a cosmological constant in the unimodular gauge. We show how to gauge fix the transverse part of the diffeomorphism and then further to fulfill the unimodular gauge. This process requires the introduction of an additional pair of BRST doublets which decouple from the physical sector together with the other three pairs of BRST doublets for the transverse diffeomorphism. We show that the physical spectrum is the same as GR in the usual covariant gauge fixing. We then suggest to define the quantum theory of Unimodular Gravity (UG) by making Fourier transform of GR in the unimodular gauge with respect to the cosmological constant and slightly generalizing it. This suggests that the quantum theory of UG may describe the same theory as GR but the spacetime volume is fixed. We also discuss problems left in this formulation of UG.
A general method of the BRST--anti-BRST symmetric conversion of second-class constraints is presented. It yields a pair of commuting and nilpotent BRST-type charges that can be naturally regarded as BRST and anti-BRST ones. Interchanging the BRST and anti-BRST generators corresponds to a symmetry between the original second-class constraints and the conversion variables, which enter the formalism on equal footing.
In the AdS/CFT correspondence, bulk information appears to be encoded in the CFT in a redundant way. A local bulk field corresponds to many different non-local CFT operators (precursors). We recast this ambiguity in the language of BRST symmetry, and propose that in the large $N$ limit, the difference between two precursors is a BRST exact and ghost-free term. Using the BRST formalism and working in a simple model with global symmetries, we re-derive a precursor ambiguity appearing in earlier work. Finally, we show within this model that this BRST ambiguity has the right number of parameters to explain the freedom to localize precursors within the boundary of an entanglement wedge order by order in the large $N$ expansion.
We study the construction of the classical nilpotent canonical BRST charge for the nonlinear gauge algebras where a commutator (in terms of Poisson brackets) of the constraints is a finite order polynomial of the constraints.
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