Back to Search
Start Over
Complex Langevin analysis of 2D U(1) gauge theory on a torus with a θ term
- Source :
- Journal of High Energy Physics, Vol 2020, Iss 9, Pp 1-41 (2020), Journal of High Energy Physics
- Publication Year :
- 2020
- Publisher :
- SpringerOpen, 2020.
-
Abstract
- Monte Carlo simulation of gauge theories with a θ term is known to be extremely difficult due to the sign problem. Recently there has been major progress in solving this problem based on the idea of complexifying dynamical variables. Here we consider the complex Langevin method (CLM), which is a promising approach for its low computational cost. The drawback of this method, however, is the existence of a condition that has to be met in order for the results to be correct. As a first step, we apply the method to 2D U(1) gauge theory on a torus with a θ term, which can be solved analytically. We find that a naive implementation of the method fails because of the topological nature of the θ term. In order to circumvent this problem, we simulate the same theory on a punctured torus, which is equivalent to the original model in the infinite volume limit for |θ| < π. Rather surprisingly, we find that the CLM works and reproduces the exact results for a punctured torus even at large θ, where the link variables near the puncture become very far from being unitary.
- Subjects :
- Physics
Nuclear and High Energy Physics
Lattice Quantum Field Theory
010308 nuclear & particles physics
Field Theories in Lower Dimensions
Computer Science::Information Retrieval
Monte Carlo method
Torus
01 natural sciences
Term (time)
0103 physical sciences
lcsh:QC770-798
lcsh:Nuclear and particle physics. Atomic energy. Radioactivity
Limit (mathematics)
Gauge theory
010306 general physics
Link (knot theory)
U-1
Sign (mathematics)
Mathematical physics
Subjects
Details
- Language :
- English
- ISSN :
- 10298479
- Volume :
- 2020
- Issue :
- 9
- Database :
- OpenAIRE
- Journal :
- Journal of High Energy Physics
- Accession number :
- edsair.doi.dedup.....e704a65a142548038db29cc0b86a87c7