Over the last year, I conducted research under two professors A and B on two topics A and B. In the last few months, I have come up with an idea that uses concepts from topic A to present a solution to a problem in B, i.e. the idea could be called "Solution to B using A". As far as I can tell, the idea is new, and (if I may say so myself) quite elegant. I intend to write this up and submit to a decent, normal-ish conference. Note that neither of my advisors are aware that I have been working on this, and hence I intend to put my name as the sole author. I have, however, drawn from research I conducted under them.
Question: Am I under any obligation to show the two advisors my work, and inform them that I plan to submit to a certain conference?
I am a little afraid of negative feedback if I show my work, feedback I would rather get anonymously from reviewers rather than from advisors under whom I continue to conduct research. (This is possibly irrational, and I need to deal with it, but for the moment, it is what it is.)
Neither advisor is familiar with the other topic, and hence neither will be able to judge the paper as a whole. I am also a little worried that by the time I obtain feedback from either (or both) of them, the deadline for my preferred conference would've passed. While I do realize that consulting with them will likely improve the quality of the paper, I will mention that:
- I am confident that the mathematical details are correct.
- Both advisors have been very complimentary of my writing style in previous paper(s) I have published with them. The final, published manuscripts do not differ from the drafts I wrote by more than 5%.
- I don't believe that asking both of them to work together on looking over my paper is a viable option, as it's unlikely they could spare the time. Also, they don't really get along with each other.
If I don't consult with them, I am worried that either (or both) of them would be a little offended, since I have drawn from work I conducted under them. I don't wish for them to think that I have an over-confident or arrogant streak in me, and hence did not consult them. Is that logical?
EDIT: I am not a Ph.D. student. I have just completed my undergraduate degree, and will be joining a master's degree in Fall-2021. The research I conducted under both advisors was not to obtain a degree, it was voluntary. Advisor A is at my undergraduate institution, advisor B was at that institution until last year. There were no institutional rules I was bound by while conducting research.