Using Complex Geometry to Rederive the BPS Spectrum of Seiberg-Witten Theory

<a href="https://embed.stanford.edu/iframe/?url=https%3A%2F%2Fpurl.stanford.edu%2Fqv366ft1025" class="su-underline">Show Content</a>

Abstract/Contents

Abstract: This thesis reports on a novel procedure to derive the BPS spectrum of supersymmetric quantum field theories using the geometric properties of their vacuum moduli spaces. This procedure is demonstrated with a 4D, N=2 supersymmetric field theory, Seiberg-Witten theory. We examine the Coulomb branch of the vacuum moduli space of Seiberg-Witten theory compactified from 4D to 3D. It is known that the compactified metric is hyper-Kähler and therefore Ricci flat (Seiberg and Witten, 1996). Through using the wall-crossing formulae outlined by Gaiotto, Moore and Neitzke (Gaiotto, Moore, and A. Neitzke, 2010) and by imposing Ricci flatness on the compactified metric, it should be possible to extract the counts of BPS particles. This thesis reports on a method a validating this hypothesis using Seiberg-Witten theory, where the exact counts of BPS particles are known. In particular, I look at the strong coupling region of Seiberg-Witten theory and find that the integer count of the magnetic monopole can be derived through this approach. Through investigating the Ricci scalar at certain points in the Coulomb branch, the integer count of the monopole minimises the Ricci scalar numerically. This project was undertaken with Lark Wang, another undergraduate student

Type of resource	text
Date created	May 2020

Author	Roy, Sandip
Primary advisor	Kachru, Shamit
Advisor	Zimet, Max
Advisor	Kallosh, Renata
Degree granting institution	Stanford University, Department of Physics

Location	https://purl.stanford.edu/qv366ft1025

Use and reproduction: User agrees that, where applicable, content will not be used to identify or to otherwise infringe the privacy or confidentiality rights of individuals. Content distributed via the Stanford Digital Repository may be subject to additional license and use restrictions applied by the depositor.
License: This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

Preferred Citation: Sandip Roy. (2020). Using Complex Geometry to Rederive the BPS Spectrum of Seiberg-Witten Theory. Stanford Digital Repository. Available at: https://purl.stanford.edu/qv366ft1025

Undergraduate Theses, Department of Physics

Loading usage metrics...