A note on CFT correlators in three dimensions

By S. Giombi, Shiroman Prakash, Xi Yin. 2011

185 citations recorded by the source corpus.

A bstractIn this note we present a simple method of constructing general conformally invariant three point functions of operators of various spins in three dimensions. Upon further imposing current conservation conditions, we find new parity violating structures for the three point functions involving either the stress-energy tensor, spin one currents, or higher spin currents. We find that all parity preserving structures for conformally invariant three point functions of higher spin conserved currents can be realized by free fields, whereas there is at most one parity violating structure for three point functions for each set of spins, which is not realized by free fields.

Subfields: Condensed Matter Physics, Electrical and Electronic Engineering, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d671b3e85bc5ba5971e5fdc8ea167e273560b7de

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Condensed Matter Physics

1. David Simmons-Duffin
2. David Poland
3. S. Rychkov
4. J. Penedones
5. M. Costa
6. A. Vichi
7. Xi Yin
8. S. Giombi

In Electrical and Electronic Engineering

1. David Poland
2. Xi Yin
3. S. Giombi
4. David Simmons-Duffin
5. S. Rychkov
6. Ran Yacoby
7. Filip Kos
8. Guy Gur-Ari

In Nuclear and High Energy Physics

1. David Simmons-Duffin
2. David Poland
3. S. Rychkov
4. S. Giombi
5. Ran Yacoby
6. O. Aharony
7. A. Vichi
8. Filip Kos

Citations in the corpus

• Non-Gaussianity as a particle detector (2016, unknown): “However, in the conformally symmetric case, 〈φφσ〉 vanishes when σ has odd spin [56].”
• Shape dependence of entanglement entropy in conformal field theories (2015, background): “(9)In three dimensions there is also potentially a parity odd structure [43, 44] that we did not write down.”
• Spinning conformal correlators (2011, methodology): “It should be possible to give an analogous discussion for parity odd structures, where we expect to find one amplitude if the spins {l1, l2, l3} satisfy the triangle inequality and zero otherwise, to match the conjecture of [33] in the parity odd case.”
• Correlation functions of large N Chern-Simons-Matter theories and bosonization in three dimensions (2012, background): “By conformal invariance, this correlator should have one parity-even and one parity-odd structure [35].”
• The higher spin/vector model duality (2012, methodology): “47) This is indeed the generating function for the three point functions 〈Js1(~x1;λ1)O∆=2(~x2)Js3(~x3;λ3)〉 in the free fermion theory (see [15]).”
• Chern–Simons theory with vector fermion matter (2011, background): “In fact, as shown in [36], for conserved higher spin currents all parity preserving structures of 〈J 1J 2J 3〉 can be realized by free scalars and by free fermions, while a parity odd structure of 〈J 1J 2J 3〉 exists when the three spins s1, s2, s3 obey triangular inequality.”
• The conformal bootstrap: Theory, numerical techniques, and applications (2018, background): “Index free notation can be generalized to mixed-symmetry tensors and fermions, see e.g. Giombi et al. (2013), Simmons-Duffin (2014a), Li and Stergiou (2014), Costa and Hansen (2015), and Iliesiu et al. (2016a).”
• Implications of conformal invariance in momentum space (2013, background): “A complete analysis of all such 3-point functions, and in general dimension, was carried out in [3, 4]; for a sample of more recent work on this topic see also [5–11].”
• d = 3 bosonic vector models coupled to Chern-Simons gauge theories (2011, background): “For simplicity, we study here the U(N) case, which has a conserved current J1, since the correlator 〈J2J1J1〉 is the simplest correlator of conserved currents that can exhibit a parity-breaking structure [39].”
• Bootstrapping mixed correlators in the 3D Ising model (2014, methodology): “Similar index-free techniques were used for classifying correlators of operators with spin in [44, 45, 56].”
• Correlators of large N fermionic Chern-Simons vector models (2012, background): “This correlator has one parity-even and one parity-odd structure, which are conformallyinvariant [12].”
• Spinning conformal blocks (2011, background): “In this case, there are three parity odd building blocks which are however not independent [18, 33].”
• On Higher Spin Gauge Theory and the Critical O(N) Model (2011, background): “The tensor structure of 〈J J ((3))J (1)〉 is uniquely fixed by conformal symmetry up to normalization, as explained in [24].”
• Bootstrapping 3D fermions (2015, background): “In particular, the number of conformal invariants grows with the spin of the insertions (see, for instance, [18, 19]).”