RUI: Modular Black Hole Entropy

Indiana University, Bloomington IN

Investigators

Abstract

The goal of this project is to apply results on geometric Calabi-Yau modular forms obtained recently by the PI and Co-PI to the problem of black hole entropy in string theory. The project rests on the observation that the Siegel modular forms considered so far in the black hole context can be constructed in terms of ordinary modular forms that have a geometric interpretation because they are derived from the cycle structure of Calabi-Yau manifolds. These geometric modular forms provide a more general reservoir of modular forms than, for example, the elliptic genera considered in the literature. The project addresses one of the open questions in black hole physics: how the results obtained so far for N = 4 supersymmetric models can be extended to systems with fewer supersymmetries. Such theories are given by compactifications on generic Calabi-Yau manifolds instead of special cases that have been the main manifolds considered at this point. The investigators plan to use their previous work on the construction of geometric modular forms for deformation families of Calabi-Yau threefolds as ingredients. Broader impact: This project can be formulated in such a way that it is easy to involve undergraduate students in the work, and hence is ideal for the PI and Co-PI who work as theorists at a Predominantly Undergraduate Institution.The physics department at IUSB has recently introduced a series of upper level classes that teach some of the techniques used in theoretical research, such as quantum field theory and string theory courses. The students are prepared for the research experience through a combination of attending these courses and guided independent work. IUSB is the only public university in the region with a physics major, hence provides the only opportunity for a large section of the student population to be involved in research in this field. To recruit more students to IUSB and into STEM fields, the investigators regularly talk to high school physics classes about their research and participate extensively in outreach activities organized by the physics department and IUSB.