To understand the string theory controversy, it is essential to understand how string theorists interact with each other in the scientific sphere, i.e. through journal articles. Due to the age of the theory, the ISI Web of Science catalogues approximately 13,000 papers in the category of string theory. As it would be impossible to manually read through all those papers, different approach was used to reconstruct the social networks at play in the scientific sphere. We used the software package Resseau-Lu to analyze records of the 13,000 papers on the Web of Science, and generated maps based on the information. Through these maps, we can get a good sense of what string theorists study, where they publish, and who they collaborate with. To help with our interpretation of the maps, the abstracts of papers critical to the map analyses were examined. These are reported below, as well as in the timeline in the history section.
Above is a map detailing the different subject areas in which string theorists publish papers. This map was generated by first compiling records for all articles published by the top 20 most cited string theory authors. This data was fed into Resseau-Lu, which matched these authors with the subject areas in which their papers were published. The same was also done for the cited references. On the map above, authors are shown with blue circles, while subject areas are shown with green squares.
Looking at the map, we immediately see a few distinct clusters. "Particles and Fields" reveals itself immediately to be the largest subject area, which is sensible since it contains most fields that study string theory as a theory of everything. Linked to this we see physicists additionally publishing in Astrophysics, Mathematical Physics, and Multidisciplinary Physics. These clusters allow us to classify authors by their interests prior to and alongside their involvement in the string theory controversy. In the Astrophysics cluster we recognize actors such as Strominger, Gubser, Polchinski, and Susskind, whose interest in string theory stems from its applicability to understanding black holes and the early universe. In the Mathematical Physics cluster we see familiar names such as Witten, Maldacena, and Vafa, who come from a more mathematical background and whose contributions to string theory are more about elucidating the structure of the theory rather than applying it to explain other phenomena. Lastly, in Multidisciplinary physics we see authors such as Gross, Polyakov and Seiberg. Given the broad scope of this category, all that can really be said is that these authors study string theory by virtue of their interest in new physical developments in general, and due to the theory's wide scope of applicability.
Interestingly, we also see a small cluster of authors who publish in the field of Nuclear Physics. Their relationship to string theory can be understood as stemming from two different sources. First, their is the intimate relationship between the origins of string theory and the study of nuclear interactions, which led some of these authors - such as Polyakov, Raman, and Harvey - into studying string theory early on. Second is the fact that recently, there has been a surge of interest in applications of string theory to the understanding of heavy ion collisions. This has led some younger nuclear physicists into the realm of string theory, and has led some string theorists into the realm of nuclear physics.
Now that we have some idea of the background from which string theorists enter the controversy, we can examine venues in which they publish their results. Above is a map of journal co-citation prepared from the records of cited references obtained from ISI. Each node represents a different journal, and links between nodes signify the citation of articles from one journal by another. A green node means that articles from that journal were predominantly cited in other journals, while a blue node signifies a journal that predominantly cites articles from the journals to which it is linked. An orange node signifies that the journal both cites and is cited by articles from other journals. Also, the size each node is proportional to the number of times that journal is cited.
Although this map is less strongly clustered than the subject area map above, some interesting observations can still be made based on the size of the nodes. We see clearly that the most important journals to the field of string theory are (organized by number of times cited, in descending order) Nuclear Physics B, the Journal of High Energy Physics, Physical Review D, and Physics Letters B. This corroborates our findings from the subject area map, as all of these journals focus on the subject area of Particles and Fields. Despite the other areas to which string theory is applicable, we thus see that the core discussion about the theory comes from its status as a proposed theory of everything.
To learn more about the patterns of co-citation, we move now from the journal map to a map of the co-citation of specific top-cited articles. The nodes on the map above represent the top 200 most cited string theory articles in the ISI Web of Science. Links between the nodes indicate that one of these papers has cited the other. The size of each node is proportional to the number of times that that paper has been cited. In this map we can identify the relative impact of some of the events highlighted in the history section of this site, and the importance of various authors to the controversy as a whole.
To begin, we see most clearly a cluster in the middle right-hand side of the map around papers by Maldacena, Gubser, and Klebanov. From the abstract of these papers and the events on the timeline, we see that this cluster is due to the emergence of the AdS/CFT correspondence as a focal point of string theory research. From the sizes of the nodes for the Maldacena and Gubser papers, we see that these are two of the most cited papers in the entire Web of Science database. This demonstrates that in recent times, the AdS/CFT correspondence has become the most significant research area in the field of string theory.
Another prominent cluster can be seen in the upper-left corner of the map, arranged around David Gross's 1985 and 1986 papers. It was in these two papers that Gross first introduced heterotic string theory. This cluster is thus associated with the proliferation of various different string theories during the first superstring revolution. The ages of all the papers in this cluster show that, while they had a large immediate impact, the hype around them has subsided since the end of this period.
Lastly, there is a large, distributed cluster occupying the majority of the bottom of the map. Spread throughout this cluster are a number of papers by Witten from the early 1990's focusing on various dualities between different types of string theory. Towards the right side of this cluster we see the paper by Banks dealing with the explicit formulation of M-theory, As well as papers by Seiberg and Witten outlining the role of non-commutative geometries in string theory. Thus, it is evident that this large cluster shows the boom in string theory research during the second superstring revolution. This cluster is heavily linked to the focal point of AdS/CFT research, showing that the latter field was a direct outgrowth of the research done into string duality in the mid 1990's.
Generalizing the above analysis, we arrive at a curious conclusion. It appears that string theory research passes through periods in which different aspects of the theory are fashionable. After a time, intense research into a given facet dies out, and it is replaced by investigation into a different area. It appears that these shifts are driven by mathematical developments, such as the AdS/CFT correspondence, heterotic string theory, or duality transformations. This sort of ever-shifting focus is a feature of younger fields of study, where communities of researchers have not yet settled down into specialized subfields. It highlights the fact that string theory is still a controversial theory thirty years in, as clearly no specialized research paradigms are yet in place.
Lastly, we look at the map above detailing paper co-authorship in order to get a picture of how the various scientists involve collaborate with one another. The nodes on the map represent the 150 authors in the dataset who published the greatest number of string theory papers. Connections between nodes signify that two authors have published a paper together. Finally, node size is proportional to the number of papers published by each author.
Unlike the previous maps, we see here one distinct cluster in the upper portion of the map surrounded by a large number of sparsely connected nodes. We see that this cluster focues around major actors we are familiar with, such as Witten, Maldacena, Polchinski, Seiberg and others. As these are the same scientists who emerged to make their most significant contributions during and in the wake of the second superstring revolution, we conclude that this period ushered in a wave of intense collaboration. Prior to the revolution, string theory research was conducted by small groups of researchers. Afterwards, however, we see the emergence of many papers with a large number of co-authors. Comparing the names in this cluster to our subject area map above, we see that these researchers come primarily from a background of mathematical physics and astrophysics. Therefore, our analysis suggests that as various developments such as the AdS/CFT correspondence allowed string theory to be applied to many different areas of physics, and as interest in the cosmological problem of the string theory vacuum grew, collaboration between string theorists with various backgrounds became necessary.