Bootstrapping 3D fermions

By Luca Iliesiu, Filip Kos, David Poland, Silviu S. Pufu, David Simmons-Duffin, Ran Yacoby. 2015

182 citations recorded by the source corpus.

A bstractWe study the conformal bootstrap for a 4-point function of fermions 〈ψψψψ〉 in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in fermion 4-point functions. Using these results, we find general bounds on the dimensions of operators appearing in the ψ × ψ OPE, and also on the central charge CT . We observe features in our bounds that coincide with scaling dimensions in the GrossNeveu models at large N . We also speculate that other features could coincide with a fermionic CFT containing no relevant scalar operators.

Subfields: Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/705eae135000a06f39b1e9efe21ae094fd75cd55

How researchers see this paper

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

In Mathematical Physics

In Nuclear and High Energy Physics

Citations in the corpus

A proof of the conformal collider bounds (2016, background): “However, it was already demonstrated in [27, 36, 69] and this work that the crossing symmetry of 4-point functions involving spinning operators harbors rich information inaccessible from scalar 4-point functions.”
Recursion relations for conformal blocks (2015, methodology): “There is also a general method to increase the spin of the external operators using differential operators [26, 39, 40].”
Carving out OPE space and precise O(2) model critical exponents (2019, methodology): “In practice, this means we would like to study large systems of correlation functions involving multiple scalars [10–15], fermions [16–18], currents [19, 20], stress tensors [21], various global symmetry representations [22–42], etc.”
Weight shifting operators and conformal blocks (2017, unknown): “This is standard, and this particular case was solved in [35], so we do not explain it in detail.”
A semidefinite program solver for the conformal bootstrap (2015, unknown): “owever, SDPB should also enable wider exploration of new correlators and diverse theories. SDPBis already being used in several bootstrap studies that would have previously been diﬃcult or impossible [71, 73]. An exciting direction that may now be accessible is studying a four-point function of stre”
The conformal bootstrap: Theory, numerical techniques, and applications (2018, methodology): “The precise expressions can be found in Costa et al. (2011a) and Iliesiu et al. (2016b) in 3d or Echeverri et al. (2015) in 4d.”