I am transferring to a new university. And I found a new supervisor at another university. I have told this to my current advisor. But I am still staying at the current lab as the transfer procedure would take like two or three months. During the two months, I have been collaborating with my new supervisor on the paper and using his experimental facilities remotely. The paper is now almost finished and then we are going to publish. I will consult with my current and future supervisor. But before that, I want to ask if there is a regulation about this.
There don't seem to be regulations, as such, about authorship. There are, however, conventions that vary by field. There is also scientific honesty to consider. If your current supervisor contributed then s/he is likely someone eligible for authorship, otherwise it would be only by "courtesy" which is, itself, a problematic and possibly unethical practice.
However, the conventions in some fields are so strong that a student better not dare to break them.
Note that in some other fields, only the student would be an author and neither supervisor. But in those fields the supervisor probably doesn't provide a physical laboratory and all that goes with it. But acknowledgements are given for contributions in any case.
Consult someone in your own field that you can trust to let you know about the conventions and the strength with which they are "enforced."
However, also note, that if it is in accord with the conventions of your field, then including your current advisor, even with minimal contribution might be a valid political act if it advances your career in some way. Many would, of course, think this a terrible thing to do, but their fields likely have different conventions.
I assume that in the fields in which "authorship" is given away for little work, that readers of papers understand the situation pretty well and are less likely to be misled about who does the work than you might suppose. Thus, in a certain sense, you can also consider such things to be moot.
Everyone who makes a sufficient contribution to your paper for authorship should be an author on your paper (and no one else).
It doesn't matter what institution they are at nor does anything else: everyone that contributes at a level appropriate for authorship is an author.
Standards for what contribution constitutes a sufficient contribution for authorship vary by field, and your plan to consult both your new and old advisor is a good one because part of their mentorship is in helping you make decisions about what governs authorship in your field.
During the two months, I have been collaborating with my new supervisor on the paper and using his experimental facilities remotely. The paper is now almost finished and then we are going to publish.
Assuming (as the above statement implies) that your current supervisor had no involvement commensurate with authorship, then this sounds like a clear-cut case that you should not add your current supervisor as an author. Adding him/her as an author would be unethical, because:
- he/she did not do the work;
- naming him/her as an author would imply his/her endorsement of the paper, which he/she may not have even read (and with which he/she may, in reality, disagree strongly or consider unsound); and
- he she would be expected to be able to answer detailed questions about the paper, its methodology, and any underlying data (although a paper specifies a "corresponding author", a reader is entitled to expect any of the "authors" to be able to comment/present/lecture on it, and an author unable to do so would, quite rightly, suffer serious professional humiliation).