Abstract
Within the framework of the Becchi-Rouet-Stora-Tyutin (BRST) formalism, we discuss the full set of proper BRST and anti-BRST transformations for a 2D diffeomorphism invariant theory which is described by the Lagrangian density of a standard bosonic string. The above (anti-)BRST transformations are off-shell nilpotent and absolutely anticommuting. The latter property is valid on a submanifold of the space of quantum fields where the 2D version of the universal (anti-)BRST invariant Curci-Ferrari (CF) type of restrictions is satisfied. We derive the precise forms of the BRST and anti-BRST invariant Lagrangian densities as well as the exact expressions for the conserved (anti-)BRST and ghost charges. The lucid derivation of the proper anti-BRST symmetry transformations and the emergence of the CF-type restrictions are completely novel results for our present bosonic string which has already been discussed earlier in literature where only the BRST symmetry transformations have been pointed out. We briefly mention the derivation of the CF-type restrictions from the modified version of the Bonora-Tonin superfield approach, too.
Highlights
One of the most exciting and captivating areas of research in theoretical high energy physics (THEP), over the last few decades, has been the subject ofstrings and related extended objects
In Appendix D, we concisely discuss the derivation of the CF-type restrictions by using the modified version of the Bonora-Tonin superfield approach (MBTSA) to BRST formalism
We have been able to derive the proper anti-BRST symmetry transformations corresponding to the BRST transformations
Summary
One of the most exciting and captivating areas of research in theoretical high energy physics (THEP), over the last few decades, has been the subject of (super)strings and related extended objects (see, e.g., [1,2,3,4] for details). The BRST and anti-BRST symmetry transformations are found to be off-shell nilpotent and absolutely anticommuting in nature The latter property has been shown to be true on a submanifold of the quantum Hilbert space of quantum fields where the CF-type restrictions (20) (see below) are satisfied. We observe that these restrictions are BRST as well as anti-BRST invariant thereby implying that these are physical restrictions (which can be imposed from outside on our present theory). The hallmark of a quantum theory, discussed within the framework of BRST formalism, is the existence of the (non)trivial Curci-Ferrari- (CF-) type restrictions We have derived such restrictions in our present endeavor which ensure the absolute anticommutativity of the (anti-)BRST symmetry transformations. In Appendix D, we concisely discuss the derivation of the CF-type restrictions by using the modified version of the Bonora-Tonin superfield approach (MBTSA) to BRST formalism
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