What are the topics available for a PhD in Indian English Literature?
In many cases, if you want a PhD regarding literature specific to a particular region or culture, you study the predominate language. For example, if you're interested in literature from the US or Canada or Australia or pretty much any English-speaking country, you go for a PhD in English, then add an emphasis like American Literature, British Literature, Canadian Literature, etc. With regards to literature written in South America, you could study a PhD in Spanish or in Latin-American Studies.
Since you're interested in Indian literature, you could search out PhDs that are specific to India, which may fall under a Humanities umbrella. Some such PhDs could be: Cultural, Literary and Postcolonial Studies (University of London) or English Literature (Central University of Haryana).
If those are too specific or you want a wider range of options, you could search out PhDs in English that emphasize Postcolonial Studies, Comparative Literature, Comparative Literary Studies, Cultural Studies, or English Studies.
Keep in mind that studying literature of a particular country in that country is is sure to unfold more opportunities and experiences than, perhaps studying that literature in a foreign country--trying to find a decent program that focuses on Indian Literature may be difficult, for example, in a country like Bolivia or Uganda or Ukraine opposed to studying in India or the UK.
Anglophone Indian literature is an important area within the study of global literatures in English. It is available as an area of post-graduate specialization at universities in India, Britain, Canada, and the United States, and is sometimes located in Comparative Literature, sometimes in Asian Studies, and sometimes in English departments. Each university has its own approach to the field.
Your choice in how you situate yourself and choose topics on the PhD level depends on the discipline in which you wish to pursue an academic career. If you want to specialize in India as a region, you might want to be in a program that focuses on India, and do work comparing India literature in English with Indian literature in Indian languages. If you are interested in Indian literature as an example of post-colonial studies, an English or comparative literature department might be an appropriate home. Bollywood has received increasing academic attention, and it is also possible to choose a topic that in some way compares Bollywood to literary works or looks at literary influences on Bollywood.
One important subfield in the study of Indian literature is that of dalit literature. Another popular area is the literature of the Indian diaspora, often treated within a theoretical framework of diaspora studies. The study of works by and about Indian hijra or eunuchs is an important area within gender studies.
In the construction of any pursuit of higher studies, I strongly advise working with a professor or instructor who has both a good feel for where you are and where the discipline is. If this is not available, I strongly suggest examining your own preferences in the discipline and sensing where there is the strongest amount of interest or attraction. If not one then both of these avenues should be pursued to fully grasp or understand the choice that lies in front of you because there is going to be a long road to walk within it once your choice is made. With all of this in mind, I think that a very interesting element that comes out of Indian English Literature is the collision between modern globalization and traditional notions of the good. Writers in the genre play with this idea in different ways because India is playing with this dichotomy in different manners. There are plenty of ideas within this paradigm that could make for rich analysis. Such discussion could move into political, historical, and spiritual dimensions. This might be where there is fertile information and ground that sustains much in way of inquiry and analysis.