Recursion relations for conformal blocks

By J. Penedones, Emilio Trevisani, Masahito Yamazaki. 2015

144 citations recorded by the source corpus.

A bstractIn the context of conformal field theories in general space-time dimension, we find all the possible singularities of the conformal blocks as functions of the scaling dimension Δ of the exchanged operator. In particular, we argue, using representation theory of parabolic Verma modules, that in odd spacetime dimension the singularities are only simple poles. We discuss how to use this information to write recursion relations that determine the conformal blocks. We first recover the recursion relation introduced in [1] for conformal blocks of external scalar operators. We then generalize this recursion relation for the conformal blocks associated to the four point function of three scalar and one vector operator. Finally we specialize to the case in which the vector operator is a conserved current.

Subfields: Applied Mathematics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/bec3ee23e5c118d33c517410969752d84eb3c057

How researchers see this paper

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

In Applied Mathematics

1. David Simmons-Duffin
2. David Poland
3. S. Rychkov
4. A. Vichi
5. D. Baumann
6. S. Caron-Huot
7. Filip Kos

In Geometry and Topology

1. S. Rychkov
2. David Simmons-Duffin
3. David Poland
4. A. Vichi
5. G. L. Pimentel
6. D. Baumann
7. Hayden Lee
8. A. Joyce

In Nuclear and High Energy Physics

1. David Simmons-Duffin
2. S. Rychkov
3. David Poland
4. A. Vichi
5. A. Fitzpatrick
6. Jared Kaplan
7. M. Paulos
8. Filip Kos

Citations in the corpus

• Weight shifting operators and conformal blocks (2017, unknown): “This data has been determined for general scalar blocks [14, 22] as well as some examples of spinning blocks [66, 72, 105].”
• TASI Lectures on the Conformal Bootstrap (2016, background): “n the math literature, unitarity bounds for higher-dimensional CFTs were essentially computed long ago by Jantzen [30], though the relevance of that work for physics has only been emphasized recently [32,33]. bbThe quadratic Casimir is L2 because our generators are antihermitian and dier from the co”
• The cosmological bootstrap: weight-shifting operators and scalar seeds (2019, background): “e obtained by noting that the representation must shorten at the second level of descendents, with the spin-2 state becoming null. For a discussion of the shortening of conformal representations, see [90]. 32 Weight 0: The rst descendent state transforms as a vector under SO(d) and has weight = 0. T”
• The conformal bootstrap: Theory, numerical techniques, and applications (2018, background): “F.4 has also been generalized to spinning conformal blocks (Costa et al., 2016b; Penedones et al., 2016).”
• EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions (2016, background): “Recently, Penedones, Trevisani and Yamazaki [27] and Yamazaki [28] pointed out the relevance of the old mathematical work of Jantzen [29] to this problem.”