Corrigendum to “Supervariable Approach to the Nilpotent Symmetries for a Toy Model of the Hodge Theory”
In the article titled “Supervariable Approach to the Nilpotent Symmetries for a Toy Model of the Hodge Theory” , two equations (i.e., equations and ) have been written incorrectly and there are some typing errors in the mathematical expressions that have been incorporated in the text after equation . Thus, we are sending, herewith, the correct version of the text after equation and the next paragraph till equation . The rest of the paper is correct and there are no errors. The correct text after equation is given below.
By exploiting the (anti-)co-BRST symmetry transformation , it can be checked that the above expressions do match with (which is also equivalent to expressions given in in terms of the auxiliary variable ). From the above equations, it becomes transparent that the nilpotency of (anti-)co-BRST charges is deeply connected with the nilpotency of (anti-)co-BRST symmetry transformations as well as the nilpotency of the translational generators and along the Grassmannian directions of this -dimensional supermanifold. For instance, if we consider , it is clear that because of and the basic definition of a generator of a given transformation. Furthermore, from the suitable expressions from , it is very evident that due to which, in turn, implies that . Such kind of arguments can be given for the nilpotency of as well. Geometrically, the equation implies that the co-BRST charge is already equivalent to the translation of a composite supervariable along the -direction of the supermanifold. Thus, any further translation along -direction produces a zero result because of the fermionic () nature of . Similar explanation for the nilpotency of the suitable expression for can be given in the language of nilpotency of the translational generator along -direction.
Now we dwell a bit on the geometrical meaning of the absolute anticommutativity of the (anti-)co-BRST charges in the language of the translational generators and along the Grassmannian directions of the supermanifold. Let us take the first example as It is self-evident that because of the nilpotency of and because of the nilpotency of the translational generator . However, if we take the definition of the generator for the transformation , then, due to the nilpotency of which in turn implies the absolute anticommutativity of the (anti-)co-BRST charges . If we operate by on , we should get . However, it leads to the following explicit expressions:
D. Shukla, T. Bhanja, and R. P. Malik, “Supervariable approach to the nilpotent symmetries for a toy model of the hodge theory,” Advances in High Energy Physics, vol. 2016, Article ID 2618150, 13 pages, 2016.View at: Publisher Site | Google Scholar