Four-point functions in large N Chern-Simons fermionic theories
- PDF / 1,067,858 Bytes
- 25 Pages / 595.276 x 841.89 pts (A4) Page_size
- 56 Downloads / 210 Views
Springer
Received: July 30, 2020 Accepted: September 2, 2020 Published: October 5, 2020
Rohit R. Kalloor Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel
E-mail: [email protected] Abstract: We compute all four-point functions involving the operators J0 and J1 in largeN Chern-Simons fermionic theories, in the regime where all external momenta lie along the z-axis. We find that our result for hJ0 J0 J0 J0 i agrees with previous computations, and that the other correlators fall in line with expectations from bootstrap arguments. Keywords: 1/N Expansion, Chern-Simons Theories, Field Theories in Lower Dimensions ArXiv ePrint: 1910.14617
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)028
JHEP10(2020)028
Four-point functions in large N Chern-Simons fermionic theories
Contents 1 Introduction
1 5 5 6 7 8 9 11
3 Results and discussion 3.1 λ dependence via bootstrap arguments 3.2 Results 3.2.1 hJ0 J0 J0 J0 i 3.2.2 hJ1 J1 J0 J0 i 3.2.3 hJ1 J1 J1 J1 i
3 3.2.4 J1 . . . 3.3 Conclusions and future directions
12 12 14 14 15 15 16 17
A The four-fermion vertex
18
B hJ1 J1 J1 J1 i: the full expression
21
1
Introduction
Three dimensional gauge theories exhibit a rich class of behaviours, thanks in no small part to Chern-Simons (CS) interactions. The topological degrees of freedom brought in by the CS sectors, originally used to create massive gauge bosons, also give rise to features such as anyons and non-trivial ground state manifolds (see [1–3]). As was recently found, there is a large network of dualities — IR and otherwise, that relate such theories [4, 5]. One such class of dualities are the 3d bosonisation dualities [6–9] (see figure 1), which are analogous to the bosonisation duality in two dimensions. Roughly speaking, these dualities connect bosons to fermions via particles that have fractional statistics, and hence “interpolate” between the two. The original motivation for the bosonisation dualities came from looking at the bulk gravity duals of these theories, which are the higher-spin gravity theories of Vasiliev on AdS4 (see [10] for a review and references). These theories, being constrained by the powerful, infinite-dimensional higher-spin symmetry, are believed to be the classical limits
–1–
JHEP10(2020)028
2 Computing hJ1 J1 J0 J0 i and other correlators 2.1 Generalities 2.2 Gauge fixing, regulation, computations 2.3 The diagrams 2.4 p3 -type integrals 2.5 ps -type integrals 2.6 Arriving at the result
Figure 1. The bosonisation dualities have two branches that relate two pairs of CS-matter theories: (a) The quasi-bosonic theories: the starting point is the singlet sector of the free U(N ) bosonic ˜ (a monotonic function of the ’t theory (‘U(N ) free bosons’). We can then turn on the coupling λ Hooft coupling λ; see section 3), and on taking it to infinity (the strong coupling limit λ → 1), the correlators of the CS-bosonic theories go over to that of the critical fermionic (Gross-
Data Loading...
