Kähler Uniformization from Holographic Renormalization Group Flows of M5-branes
- Creators
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Fluder, Martin
Abstract
In this paper, we initiate the study of holographic renormalization group flows for the metric of four-manifolds. In particular, we derive a set of equations which govern the evolution of a generic Kähler four-manifold along the renormalization group flow in seven-dimensional gauged supergravity. The physical eleven-dimensional M-theory setup is given by a stack of M5-branes wrapping a calibrated Kähler four-cycle inside a Calabi-Yau threefold. By topologically twisting the theory in the ultraviolet, we may choose an arbitrary Kähler metric on the four-cycle as an asymptotic boundary condition. We find that at the infrared fixed point, we reach a Kähler-Einstein metric, which can be interpreted as an indication of "uniformizing" behavior of the flow.
Additional Information
© 2018 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: January 31, 2018; Revised: July 9, 2018; Accepted: July 30, 2018; Published: August 10, 2018. The author especially thanks Sergei Gukov for collaboration during the early stages of this project and various interesting and helpful discussions along the way. We would also like to thank Ibrahima Bah, Chris Beem, and James Sparks for insightful discussions, as well as Maxime Gabella for work on related ideas, and Nikolay Bobev and Ying-Hsuan Lin for comments on an initial draft. The work of MF is supported by the David and Ellen Lee Postdoctoral Scholarship and the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. MF thanks the Aspen Center for Physics for hospitality during the course of this work.Attached Files
Published - Fluder2018_Article_KählerUniformizationFromHologr.pdf
Submitted - 1710.09479.pdf
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Additional details
- Eprint ID
- 82763
- Resolver ID
- CaltechAUTHORS:20171028-163548005
- David and Ellen Lee Postdoctoral Scholarship
- DE-SC0011632
- Department of Energy (DOE)
- SCOAP3
- Created
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2017-10-29Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics
- Other Numbering System Name
- CALT-TH
- Other Numbering System Identifier
- 2017-039