Light States in Chern-Simons Theory Coupled to Fundamental Matter
Abstract
Motivated by developments in vectorlike holography, we study SU(N) Chern-Simons theory coupled to matter fields in the fundamental representation on various spatial manifolds. On the spatial torus T^2, we find light states at small `t Hooft coupling \lambda=N/k, where k is the Chern-Simons level, taken to be large. In the free scalar theory the gaps are of order \sqrt {\lambda}/N and in the critical scalar theory and the free fermion theory they are of order \lambda/N. The entropy of these states grows like N Log(k). We briefly consider spatial surfaces of higher genus. Based on results from pure Chern-Simons theory, it appears that there are light states with entropy that grows even faster, like N^2 Log(k). This is consistent with the log of the partition function on the three sphere S^3, which also behaves like N^2 Log(k). These light states require bulk dynamics beyond standard Vasiliev higher spin gravity to explain them.
Keywords
Cite
@article{arxiv.1207.4195,
title = {Light States in Chern-Simons Theory Coupled to Fundamental Matter},
author = {Shamik Banerjee and Simeon Hellerman and Jonathan Maltz and Stephen H. Shenker},
journal= {arXiv preprint arXiv:1207.4195},
year = {2017}
}
Comments
58 pages, LaTeX, no figures, Minor error corrected, references added, The main results of the paper have not changed