Various commentators have said that US and Iran and/or Israel and Iran are engaged in a "shadow war". Have there been works/proposals in political science/theory literature clearly defining this "shadow war" concept? If so, what are the proposed definitions?
Interestingly, I did find some proposed definitions for a "global shadow war":
By "networked character" they seem to mean:
A networked organization is a hybrid between hierarchical and horizontal structures, meaning that even though directives trickle down the hierarchy the lower echelons enjoy a degree of autonomy.
So it seems to include things like militias and so forth.
Oddly enough, the paper doesn't mention "hybrid warfare" or similar terms. But it does discuss "drone warfare" aplenty.
By "non-public nature" they mean that actions are seldom advertised, and if they are so it is only it the context of a successful strike, e.g.
eliminating Bin Laden, which was not advertised to the public until after its successful execution
I guess that if we drop the "globals scope" characteristic, we may get a bilateral definition of a shadow war. (Of course, it's not clear if journalists have heard of these definitions or actually use them.)
Another article says however that "shadow war" is basically a synonym for "grey-zone conflict".
Gray Zone conflicts or Shadow Wars are not a formal type war. They are not traditional conflicts or full scale wars between nations or states. Gray Zone conflicts are not new, the El Salvador conflict in the 1980s and the Somalia Wars in the 1990s are examples of past Gray Zone or Shadow Wars supported by minimum US SOF Forces. Gray Zone conflicts are prevalent as ever and are now becoming the new normal with the recent examples as the Russia Shadow War in the Crimea, the growth of ISIL in the Levant, and the Boko-Harim incursion into West Africa.
The latter term (i.e. "grey-zone conflict") appears to be more widespread in the academic literature, e.g. another paper discusses its relationship with "hybrid war":
Recent years have seen many military conflicts which are described as residing in a grey zone between peace and war. I am thinking here of the Russian invasion of Crimea, various low-intensive conflicts around the world and asymmetrical conflicts where one of the parties is a state and the other party is not a state, or at any rate does not obviously qualify as a state. [...]
The main purpose of this paper is to attempt to illuminate the grey zone between war and peace – the kind of conflict that in recent years has been called “hybrid war.” Or, more precisely, I am primarily interested in conflicts where it is unclear whether or not the use and threat of force involved meets the threshold for the conflict to qualify as a war. The term “hybrid war” has in recent years been used in a quite wide sense so as to encompass not only conflicts involving the use of force, but also conflicts which does not involve the use of force, but, for example, “only” involves cyberattacks or information operations. I will only in passing attempt to analyse these dimensions of hybrid conflicts.
So yeah, "shadow war" or "hybrid war" are synonymous to some extent as well, but perhaps there is a difference in emphasis, e.g. involvement of cyberattacks doesn't seem to be a main characteristic proposed for shadow/grey-zone wars. This latter article actually devotes quite a bit of space to the conceptual history of "hybrid conflict" and finds a lot of mutations in the definition of this latter notion. (Yet another paper proposes to use "grey-zone conflict" as a strategic descriptor, restricting "hybrid warfare" to the tactical level.)
There has been plenty of talk about hybrid warfare, including definitions and doctrines. Much of it has been in the context of Russian operations in the Ukraine and elsewhere, but the Wikipedia article mentions Iran as well.
A different concept is drone warfare, which describes what the US is doing in parts of the Middle East.
As for "shadow war," I consider that mostly journalists seeking a colorful phrase.
The Shadow War: European Resistance 1939–1945 may be the origin of the term. Originally published in French. Published in English in 1973. This link is to a book review of the English translation.
The Shadow War: European Resistance 1939-1945 by Henri Michel. Book review by Walter Pforzheimer is a previously classified review by the CIA. It has a footnote "La Guerre de L'Ombre (Grasset, Paris, 1970)." (Google Translate: The Shadow War). (There were "20 editions published between 1970 and 1975 in 3 languages...").
Given that the book was the origin of the term, "shadow war" would refer to any covert operations seeking to undermine the current power, political or military, of a country.