D. Shukla

R. P. Malik

T. Bhanja

Advances in High Energy Physics

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CorrigendumCorrigendum to (Supervariable Approach to the NilpotentSymmetries for a Toy Model of the Hodge Theory)D. Shukla,1 T. Bhanja ,1 and R. P. Malik 1,21Physics Department, Centre of Advanced Studies, Banaras Hindu University, Varanasi 221 005, India2DST Centre for Interdisciplinary Mathematical Sciences, Faculty of Science, Banaras Hindu University, Varanasi 221 005, IndiaCorrespondence should be addressed to T. Bhanja; tapobroto.bhanja@gmail.comReceived 22 November 2017; Accepted 10 December 2017; Published 21 February 2018Copyright © 2018 D. Shukla et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Thepublication of this article was funded by SCOAP3.In the article titled “Supervariable Approach to the NilpotentSymmetries for a Toy Model of the Hodge Theory” [1],two equations (i.e., equations (51) and (52)) have beenwritten incorrectly and there are some typing errors in themathematical expressions that have been incorporated in thetext after equation (50). Thus, we are sending, herewith, thecorrect version of the text after equation (50) and the nextparagraph till equation (52). The rest of the paper is correctand there are no errors.The correct text after equation (50) isgiven below.By exploiting the (anti-)co-BRST symmetry transforma-tion (4), it can be checked that the above expressions domatchwith (49) (which is also equivalent to expressions givenin (5) in terms of the auxiliary variable 𝑏(𝑡)). From the aboveequations, it becomes transparent that the nilpotency of (anti-)co-BRST charges is deeply connected with the nilpotency(𝑠2(𝑎)𝑑 = 0) of (anti-)co-BRST symmetry transformations aswell as the nilpotency (𝜕𝜃2 = 0, 𝜕𝜃2 = 0) of the translationalgenerators 𝜕𝜃 and 𝜕𝜃 along the Grassmannian directions ofthis (1, 2)-dimensional supermanifold. For instance, if weconsider 𝑄𝑑 = −𝑖𝑠𝑑[?̇?𝐶 + 𝑖?̇??̇?], it is clear that 𝑠𝑑𝑄𝑑 =𝑖{𝑄𝑑, 𝑄𝑑} = 0 because of 𝑠2𝑑 = 0 and the basic definitionof a generator of a given transformation. Furthermore, fromthe suitable expressions from (48), it is very evident that𝜕𝜃𝑄𝑑 = 0 due to 𝜕𝜃2 = 0 which, in turn, impliesthat 𝑄𝑑2 = 0. Such kind of arguments can be given forthe nilpotency of 𝑄𝑎𝑑 as well. Geometrically, the equation𝑄𝑑 = −𝑖(𝜕/𝜕𝜃)[?̇?(𝑑)𝐹(𝑑) + 𝑖Λ̇(𝑑)?̇?(𝑡)]|𝜃=0 implies that the co-BRST charge 𝑄𝑑 is already equivalent to the translation ofa composite supervariable (?̇?(𝑑)𝐹(𝑑) + 𝑖Λ̇(𝑑)?̇?(𝑡)) along the 𝜃-direction of the supermanifold. Thus, any further translationalong 𝜃-direction produces a zero result because of thefermionic (𝜕𝜃2 = 0) nature of 𝜕𝜃. Similar explanation for thenilpotency of the suitable expression for 𝑄𝑎𝑑 can be givenin the language of nilpotency (𝜕𝜃2 = 0) of the translationalgenerator 𝜕𝜃 along 𝜃-direction.Now we dwell a bit on the geometrical meaning of theabsolute anticommutativity of the (anti-)co-BRST charges𝑄𝑎𝑑 in the language of the translational generators (𝜕𝜃 and𝜕𝜃) along the Grassmannian directions of the supermanifold.Let us take the first example as𝑄𝑑 = 𝑖 𝜕𝜕𝜃 [?̇?(𝑑)𝐹(𝑑)]󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨𝜃=0 ≡ 𝑖𝑠𝑎𝑑 [?̇? 𝐶] . (51)It is self-evident that 𝑠𝑎𝑑𝑄𝑑 = 0 because of the nilpotency(𝑠2𝑎𝑑 = 0) of 𝑠𝑎𝑑 and 𝜕𝜃𝑄𝑑 = 0 because of the nilpotency (𝜕𝜃2 =0) of the translational generator 𝜕𝜃. However, if we take thedefinition of the generator for the transformation 𝑠𝑎𝑑, then,𝑠𝑎𝑑𝑄𝑑 = 𝑖{𝑄𝑑, 𝑄𝑎𝑑} = 0 due to the nilpotency (𝑠2𝑎𝑑 = 0) of𝑠𝑎𝑑 which in turn implies the absolute anticommutativity ofthe (anti-)co-BRST charges𝑄(𝑎)𝑑. If we operate by 𝜕𝜃 on (51),HindawiAdvances in High Energy PhysicsVolume 2018, Article ID 5217871, 2 pageshttps://doi.org/10.1155/2018/52178712 Advances in High Energy Physicswe should get 𝜕𝜃𝑄𝑑 = 0. However, it leads to the followingexplicit expressions:𝜕𝜕𝜃𝑄𝑑 = 0 = 𝑖𝜕𝜕𝜃𝜕𝜕𝜃 [?̇?(𝑑)𝐹(𝑑)]≡ 𝑖2 (𝜕𝜃𝜕𝜃 + 𝜕𝜃𝜕𝜃) [?̇?(𝑑)𝐹(𝑑)] .(52)References[1] D. Shukla, T. Bhanja, and R. P. Malik, “Supervariable approachto the nilpotent symmetries for a toymodel of the hodge theory,”Advances in High Energy Physics, vol. 2016, Article ID 2618150,13 pages, 2016.Hindawiwww.hindawi.com Volume 2018 Active and Passive  Electronic ComponentsHindawiwww.hindawi.com Volume 2018Shock and VibrationHindawiwww.hindawi.com Volume 2018High Energy PhysicsAdvances inHindawi Publishing Corporation http://www.hindawi.com Volume 2013www.hindawi.comThe Scientific World Journal8Acoustics and VibrationAdvances inHindawiwww.hindawi.com Volume 2018Hindawiwww.hindawi.com Volume 2018Advances in  Condensed Matter PhysicsOpticsInternational Journal ofHindawiwww.hindawi.com Volume 2018Hindawiwww.hindawi.com Volume 2018AstronomyAdvances in Antennas andPropagationInternational Journal ofHindawiwww.hindawi.com Volume 2018Hindawiwww.hindawi.com Volume 2018 International Journal ofGeophysicsAdvances inOpticalTechnologiesHindawiwww.hindawi.comVolume 2018Applied Bionics  and BiomechanicsHindawiwww.hindawi.com Volume 2018Advances inOptoElectronicsHindawiwww.hindawi.comVolume 2018Hindawiwww.hindawi.com Volume 2018Mathematical PhysicsAdvances inHindawiwww.hindawi.com Volume 2018ChemistryAdvances inHindawiwww.hindawi.com Volume 2018Journal ofChemistryHindawiwww.hindawi.com Volume 2018Advances inPhysical ChemistryInternational Journal ofRotatingMachineryHindawiwww.hindawi.com Volume 2018Hindawiwww.hindawi.com Journal ofEngineeringVolume 2018Submit your manuscripts atwww.hindawi.com

Corrigendum to “Supervariable Approach to the Nilpotent Symmetries for a Toy Model of the Hodge Theory”

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