Defect conformal blocks from Appell functions

Burić, Ilija; Schomerus, Volker

doi:10.1007/jhep05(2021)007

Cited by 11 publications

(18 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, the study of higher-point functions is one of the long-term goals of the bootstrap. Progress in this direction was made in [54], where higher-point functions in the presence of defects were studied. Eventually, one should be able to obtain the corresponding Lorentzian inversion formulas, and implement the multi-point bootstrap in order to obtain even more restrictive constraints.…”

Section: Discussionmentioning

confidence: 99%

Bootstrapping Monodromy Defects in the Wess-Zumino Model

Gimenez-Grau,

Liendo

2021

Preprint

View full text Add to dashboard Cite

We use analytical bootstrap techniques to study supersymmetric monodromy defects in the critical Wess-Zumino model. In preparation for our main result we first study two related systems which are interesting on their own: general monodromy defects (no susy), and the ε-expansion bootstrap for the Wess-Zumino model (no defects).For general monodromy defects we discuss some subtleties specific to the codimension two case. In particular, conformal blocks and the Lorentzian inversion formula have to be slightly modified in order to accommodate odd-spin operators that can have a non-zero one-point function. In the Wess-Zumino model we initiate the ε-expansion bootstrap for four-point functions of chiral operators, with the goal of obtaining spectral information about the bulk theory. We then proceed to tackle the harder technical problem of analyzing monodromy defects in the presence of supersymmetry. We use inversion formula technology and spectral data coming from our four-point function analysis, in order to completely bootstrap two-point functions of chiral operators at leading order in ε. Our result can be written in terms of novel special functions which we analyze in detail, and allows us to efficiently extract the CFT data that characterizes the correlator.

show abstract

Section: Discussionmentioning

confidence: 99%

Bootstrapping Monodromy Defects in the Wess-Zumino Model

Gimenez-Grau,

Liendo

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Finally, the study of higher-point functions is one of the long-term goals of the bootstrap. Progress in this direction was made in [56], where higher-point functions in the presence of defects were studied. Eventually, one should be able to obtain the corresponding Lorentzian inversion formulas, and implement the multi-point bootstrap in order to obtain even more restrictive constraints.…”

Section: Jhep05(2022)185mentioning

confidence: 99%

Bootstrapping monodromy defects in the Wess-Zumino model

Liendo¹

2022

J. High Energ. Phys.

View full text Add to dashboard Cite

We use analytical bootstrap techniques to study supersymmetric monodromy defects in the critical Wess-Zumino model. In preparation for this result we first study two related systems which are interesting on their own: general monodromy defects (no susy), and the ε-expansion bootstrap for the Wess-Zumino model (no defects). For general monodromy defects, we extend previous work on codimension-two conformal blocks and the Lorentzian inversion formula in order to accommodate parity-odd structures. In the Wess-Zumino model, we bootstrap four-point functions of chiral operators in the ε-expansion, with the goal of obtaining spectral information about the bulk theory. We then proceed to bootstrap two-point functions of chiral operators in the presence of a monodromy defect, and obtain explicit expressions in terms of novel special functions which we analyze in detail. Several of the results presented in this paper are quite general and should be applicable to other setups.

show abstract

“…The prefactor Ξ is constructed in section 4.1.1 below, using ideas and constructions from [20] and [31], properly extended to spinning bulk fields. The final formula is stated in eq.…”

Section: Jhep03(2023)133mentioning

confidence: 99%

“…The invariant X that appears in the argument of the special function ψ is simply X = A z 2 A . Once again the prefactor Ξ is constructed explicitly, see section 4.2.1, using ideas and constructions from [20] and [31]. The final formula is stated in eq.…”

Section: Guide To Bulk Channel Blocksmentioning

confidence: 99%

Universal spinning Casimir equations and their solutions

Burić

Schomerus

2023

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

Conformal blocks are a central analytic tool for higher dimensional conformal field theory. We employ Harish-Chandra’s radial component map to construct universal Casimir differential equations for spinning conformal blocks in any dimension d of Euclidean space. Furthermore, we also build a set of differential “shifting” operators that allow to construct solutions of the Casimir equations from certain seeds. In the context of spinning four-point blocks of bulk conformal field theory, our formulas provide an elegant and far reaching generalisation of existing expressions to arbitrary tensor fields and arbitrary dimension d. The power of our new universal approach to spinning blocks is further illustrated through applications to defect conformal field theory. In the case of defects of co-dimension q = 2 we are able to construct conformal blocks for two-point functions of symmetric traceless bulk tensor fields in both the defect and the bulk channel. This opens an interesting avenue for applications to the defect bootstrap. Finally, we also derive the Casimir equations for bulk-bulk-defect three-point functions in the bulk channel.

show abstract

Defect conformal blocks from Appell functions

Cited by 11 publications

References 42 publications

Bootstrapping Monodromy Defects in the Wess-Zumino Model

Bootstrapping Monodromy Defects in the Wess-Zumino Model

Bootstrapping monodromy defects in the Wess-Zumino model

Universal spinning Casimir equations and their solutions

Contact Info

Product

Resources

About