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Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
Emergent 3-manifolds from four dimensional superconformal indices
Yuji Terashima1, Masahito Yamazaki
1Department of Mathematics, Tokyo Institute for Technology, Tokyo, Japan.
Physical Review Letters
|September 26, 2012
Summary
We demonstrate how hyperbolic 3-manifold geometry arises from a 2D spin system, equivalent to reducing a 4D supersymmetric gauge theory to 3D. This links quantum field theory with classical integrable spin chains and manifold geometry.
Area of Science:
- Theoretical Physics
- Mathematical Physics
- High Energy Physics
Background:
- The relationship between quantum field theories and geometric structures is a key area of research.
- Dimensional reduction and its implications for emergent phenomena are actively studied.
- Supersymmetric gauge theories and integrable systems offer rich frameworks for exploring these connections.
Purpose of the Study:
- To establish a concrete link between a 4D supersymmetric gauge theory and a 2D classical spin system.
- To demonstrate the emergence of hyperbolic 3-manifold geometry from a lower-dimensional system.
- To explore the concept of "dimensional oxidation" as an equivalence to dimensional reduction.
Main Methods:
- Proposing an equality between the 4D superconformal index of a specific quiver gauge theory and the partition function of a classical integrable spin chain.
- Utilizing the Higgs mechanism within the 4D gauge theory framework.
- Analyzing the dimensional reduction process from 4D to 3D.
Main Results:
- The smooth geometry of a hyperbolic 3-manifold is shown to emerge from a classical spin system on a 2D lattice.
- The "dimensional oxidation" process is shown to be equivalent to the dimensional reduction of a supersymmetric gauge theory from 4D to 3D.
- A concrete mathematical equality is proposed between specific quantities in gauge theory and spin systems.
Conclusions:
- The study provides a novel connection between quantum field theory, integrable systems, and differential geometry.
- The proposed framework offers new insights into the emergence of geometric structures from fundamental physical theories.
- This work bridges concepts from high-energy physics and condensed matter physics through a geometric lens.
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