Harmony of spinning conformal blocks

Self Cite

Applications of the bootstrap program to superconformal field theories promise unique new insights into their landscape and could even lead to the discovery of new models. Most existing results of the superconformal bootstrap were obtained form correlation functions of very special fields in short (BPS) representations of the superconformal algebra. Our main goal is to initiate a superconformal bootstrap for long multiplets, one that exploits all constraints from superprimaries and their descendants. To this end, we work out the Casimir equations for four-point correlators of long multiplets of the two-dimensional global N = 2 superconformal algebra. After constructing the full set of conformal blocks we discuss two different applications. The first one concerns two-dimensional (2,0) theories. The numerical bootstrap analysis we perform serves a twofold purpose, as a feasibility study of our long multiplet bootstrap and also as an exploration of (2,0) theories. A second line of applications is directed towards four-dimensional N = 3 SCFTs. In this context, our results imply a new bound c 13 24 for the central charge of such models, which we argue cannot be saturated by an interacting SCFT.

Section: Jhep10(2017)119mentioning

confidence: 56%

Section: Jhep10(2017)119mentioning

confidence: 99%

Long multiplet bootstrap

Cornagliotto

Lemos

Schomerus

2017

Self Cite

“…the vector spaces V i are 1-dimensional, the number M − 1 counts the number of so-called nilpotent conformal invariants. Our derivation of the formula (1.1) in section 2 requires to extend a theorem for the tensor product of principal series representations of the conformal algebra from [45] to superconformal algebra g. The analysis in section 2 is similar to the discussion in [19,20] except that we will adopt an algebraic approach and characterize functions on the group through their infinite sets of Taylor coefficients at the group unit. That has the advantage that we can treat bosonic and fermionic variables on the same footing.…”

Section: Contentsmentioning

confidence: 99%

“…Here H 0 is the Calogero-Sutherland Hamiltonian that gives rise to the Casimir equations of a specific set of spinning conformal blocks for the bosonic group G (0) . These are Calogero-Sutherland Hamiltonians with a matrix valued potential whose form was worked out in [19,20]. The bosonic Hamiltonian H 0 is perturbed by a second term A that may be considered as a nilpotent matrix valued potential.…”

Section: Contentsmentioning

confidence: 99%

Superconformal blocks: general theory

Burić

Schomerus

Sobko

2020

Self Cite

In this work we launch a systematic theory of superconformal blocks for four-point functions of arbitrary supermultiplets. Our results apply to a large class of superconformal field theories including 4-dimensional models with any number N of supersymmetries. The central new ingredient is a universal construction of the relevant Casimir differential equations. In order to find these equations, we model superconformal blocks as functions on the supergroup and pick a distinguished set of coordinates. The latter are chosen so that the superconformal Casimir operator can be written as a perturbation of the Casimir operator for spinning bosonic blocks by a fermionic (nilpotent) term. Solutions to the associated eigenvalue problem can be obtained through a quantum mechanical perturbation theory that truncates at some finite order so that all results are exact. We illustrate the general theory at the example of d = 1 dimensional theories with N = 2 supersymmetry for which we recover known superblocks. The paper concludes with an outlook to 4-dimensional blocks with N = 1 supersymmetry.

“…We cast our discussion in terms of the embedding space formalism [11,16,[45][46][47] throughout. Other recent work on spinning conformal blocks can be found in [31,32,[48][49][50][51][52][53][54][55][56][57][58][59].…”

Section: Jhep11(2017)060mentioning

confidence: 99%

Spinning geodesic Witten diagrams

Dyer¹,

Freedman²,

Sully³

2017

We present an expression for the four-point conformal blocks of symmetric traceless operators of arbitrary spin as an integral over a pair of geodesics in Anti-de Sitter space, generalizing the geodesic Witten diagram formalism of Hijano et al.[1] to arbitrary spin. As an intermediate step in the derivation, we identify a convenient basis of bulk threepoint interaction vertices which give rise to all possible boundary three point structures. We highlight a direct connection between the representation of the conformal block as geodesic Witten diagram and the shadow operator formalism.