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Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics
Exactly Solvable Floquet Dynamics for Conformal Field Theories in Dimensions Greater than Two
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Paper Summary
Paperzilla title
Quaternion Conformal Gymnastics: Taming Driven CFTs in 3+1 Dimensions!
The paper investigates the dynamics of conformal field theories (CFTs) in 3+1 dimensions under periodic driving protocols involving different deformations of the CFT Hamiltonian. By employing conformal transformations and a quaternion formalism, the authors calculate quantities like fidelity, unequal-time correlators, and energy density, demonstrating the existence of heating and non-heating phases depending on the drive parameters. For protocols with a single SU(1,1) subalgebra of the conformal group involved, the Floquet Hamiltonian is derived, enabling the study of dynamical phase transitions.
Possible Conflicts of Interest
None identified
Identified Weaknesses
Limited applicability beyond CFTs
The focus on CFTs restricts the broader applicability of the findings to other quantum field theories, limiting the generalizability of the proposed methods.
Lack of analysis of multiple cycle behavior
While single cycles are studied extensively, the exploration of multiple cycle behavior and long-time dynamics is deferred to future work, leaving a gap in the understanding of the system's full temporal evolution.
Restriction to d ≤ 3 dimensions for quaternion formalism
The reliance on the quaternion formalism for d ≤ 3 restricts the direct application of the method to higher dimensions, demanding further investigation for more general scenarios.
Incomplete analysis of generic drive protocols
Although the Floquet Hamiltonian is derived for specific cases, the analysis for generic drive protocols with multiple SU(1,1) subgroups is left for future study, limiting the current scope of the work.
Rating Explanation
This paper presents a novel approach to studying driven conformal field theories (CFTs) in higher dimensions, leading to exact solutions for certain Floquet dynamics. The use of quaternion formalism is a significant technical achievement. Although limited to CFTs and d ≤ 3 for now, the methods show promise for broader applications, warranting a rating of 4.
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File Information
Original Title:
Exactly Solvable Floquet Dynamics for Conformal Field Theories in Dimensions Greater than Two
File Name:
2311.13468v3.pdf
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File Size:
7.46 MB
Uploaded:
July 16, 2025 at 12:19 PM
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