Back to Search
Start Over
The large charge limit of scalar field theories and the Wilson-Fisher fixed point at $\epsilon=0$
- Publication Year :
- 2019
-
Abstract
- We study the sector of large charge operators $\phi^n$ ($\phi$ being the complexified scalar field) in the $O(2)$ Wilson-Fisher fixed point in $4-\epsilon$ dimensions that emerges when the coupling takes the critical value $g\sim \epsilon$. We show that, in the limit $g\to 0$, when the theory naively approaches the gaussian fixed point, the sector of operators with $n\to \infty $ at fixed $g\,n^2\equiv \lambda$ remains non-trivial. Surprisingly, one can compute the exact 2-point function and thereby the non-trivial anomalous dimension of the operator $\phi^n$ by a full resummation of Feynman diagrams. The same result can be reproduced from a saddle point approximation to the path integral, which partly explains the existence of the limit. Finally, we extend these results to the three-dimensional $O(2)$-symmetric theory with $(\bar{\phi}\,\phi)^3$ potential.<br />Comment: 14 pages
- Subjects :
- High Energy Physics - Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1908.11347
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/JHEP10(2019)201