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Near Conformal Perturbation Theory in SYK Type Models
- Publication Year :
- 2020
-
Abstract
- We present a systematic procedure to extract the dynamics of the low energy soft mode in SYK type models with a single energy scale $J$ and emergent reparametrization symmetry in the IR. This is given in the framework of the perturbation theory scheme of arXiv:1608.07567 based on specific (off-shell) breaking of conformal invariance in the UV, adjusted to yield the exact large-$N$ saddle point. While this breaking formally vanishes on-shell, it has a non-trivial effect on correlation functions and the effective action. In particular, it leads to the Schwarzian action with a specific coupling to bi-local matter. The method is applied to the evaluation of $O(1)$ corrections to the correlation function of bi-locals. As a byproduct we confirm precise agreement with the explicit, symmetry breaking procedure. We provide a verification in the large $q$ limit (Liouville theory), where the correlators can be calculated exactly at all length scales. In this case, our scheme illuminates how the enhanced $O(J)$ and the subleading $O(1)$ contributions originate from the Schwarzian dynamics of the soft mode and its interaction with $h=2$ (bi-local) matter.<br />Comment: 54 pages, 4 figures
- Subjects :
- High Energy Physics - Theory
Condensed Matter - Strongly Correlated Electrons
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2006.13149
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/JHEP12(2020)171