Bootstrapping Monodromy Defects in the Wess-Zumino Model

Abstract

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 $\epsilon$--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 $\epsilon$--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.

arXiv comment44+9 pages, v2: fixed some typos, minor changes. v3: some sections slightly rewritten, as per referee suggestion

References in corpus (51)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Conformal Four Point Functions and the Operator Product Expansion
• Conformal Partial Waves and the Operator Product Expansion
• Analyticity in Spin in Conformal Theories
• The Bootstrap Program for Boundary CFT_d
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Bounds on 4D Conformal and Superconformal Field Theories
• Unitarity and the Holographic S-Matrix
• Bootstrapping the 3d Ising twist defect
• A Mellin space approach to the conformal bootstrap
• A spacetime derivation of the Lorentzian OPE inversion formula
• Conformal Partial Waves: Further Mathematical Results
• Conformal Bootstrap in Mellin Space
• Boundary and Interface CFTs from the Conformal Bootstrap
• Defects in conformal field theory
• Bootstrapping the Three-Dimensional Supersymmetric Ising Model
• Bootstrapping SCFTs with Four Supercharges
• Solving CFTs with Weakly Broken Higher Spin Symmetry
• Universality at large transverse spin in defect CFT
• Taming the $\epsilon$-expansion with Large Spin Perturbation Theory
• Covariant Approaches to Superconformal Blocks
• Line and surface defects for the free scalar field
• An Analytic Approach to BCFT${}_d$
• Mellin space bootstrap for global symmetry
• Analytic Bootstrap for Boundary CFT
• Superconformal surfaces in four dimensions
• Bootstrapping boundary-localized interactions
• The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT
• Bootstrapping holographic defect correlators in $\mathcal{N}=4$ super Yang-Mills
• Bootstrapping the Minimal 3D SCFT
• Anomalous Dimensions in the WF O($N$) Model with a Monodromy Line Defect
• Calogero-Sutherland Approach to Defect Blocks
• Analytic and Numerical Bootstrap of CFTs with $O(m)\times O(n)$ Global Symmetry in 3D
• Monodromy Defects from Hyperbolic Space
• Critical O(N) model to order ${\epsilon }^4$ from analytic bootstrap
• Monodromy Defects in Free Field Theories
• Dispersion Relation for CFT Four-Point Functions
• Random Field Ising Model and Parisi-Sourlas Supersymmetry I. Supersymmetric CFT
• On Analytic Bootstrap for Interface and Boundary CFT
• An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order $1/N^2$
• Random Field Ising Model and Parisi-Sourlas Supersymmetry. Part II. Renormalization Group
• Superconformal Blocks for SCFTs with Eight Supercharges
• Towards a Bootstrap approach to higher orders of epsilon expansion
• Perturbative and Nonperturbative Studies of CFTs with MN Global Symmetry
• Classifying Superconformal Defects in Diverse Dimensions Part I: Superconformal Lines
• The $\epsilon$-expansion of the codimension two twist defect from conformal field theory
• Superconformal Boundaries in $4-\epsilon$ dimensions
• Conformal Bootstrap near the edge
• Regge trajectories for the (2,0) theories
• Defect Conformal Blocks from Appell Functions
• Remarks on spherical monodromy defects for free scalar fields

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