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Monodromy Pinning Defects in the Critical $\mathrm{O}(2N)$ Model

Petr Kravchuk, Alex Radcliffe

TL;DR

This work constructs and analyzes a spinning defect in the critical $O(2N)$ model, the monodromy pinning DCFT, by perturbing a monodromy defect with a relevant operator of nonzero transverse spin. It employs both large-$N$ and $4-\varepsilon$ expansions to compute leading defect-operator dimensions and bulk one-point functions, and it connects to known monodromy and pinning-field defects in various limits. The authors develop a Weyl-transformed AdS$_{d-1}\times S^1$ framework and a spectral representation of the bulk-to-bulk propagator to extract the defect spectrum, while conformal perturbation theory near $v^*$ provides cross-checks with the large-$N$ results. The results reinforce the consistency between approaches and offer a foundation for exploring richer spinning DCFTs and higher-order analyses in the future.

Abstract

We investigate a novel class of defects in the critical $\mathrm{O}(2N)$ model that preserve conformal symmetry along the defect, but not the symmetry under rotations transverse to the defect. Instead, they only preserve a combination of transverse rotations and a global symmetry. These defects are constructed as IR fixed points of RG flows originating at monodromy defects, triggered by a relevant operator with non-zero transverse spin. Using large-$N$ and $4-\varepsilon$ expansions, we compute leading-order scaling dimensions of defect operators and the one-point functions of the bulk fields. In various limits this theory coincides with the monodromy defect or the pinning field defect, and we compare our results to existing results for these defects.

Monodromy Pinning Defects in the Critical $\mathrm{O}(2N)$ Model

TL;DR

This work constructs and analyzes a spinning defect in the critical model, the monodromy pinning DCFT, by perturbing a monodromy defect with a relevant operator of nonzero transverse spin. It employs both large- and expansions to compute leading defect-operator dimensions and bulk one-point functions, and it connects to known monodromy and pinning-field defects in various limits. The authors develop a Weyl-transformed AdS framework and a spectral representation of the bulk-to-bulk propagator to extract the defect spectrum, while conformal perturbation theory near provides cross-checks with the large- results. The results reinforce the consistency between approaches and offer a foundation for exploring richer spinning DCFTs and higher-order analyses in the future.

Abstract

We investigate a novel class of defects in the critical model that preserve conformal symmetry along the defect, but not the symmetry under rotations transverse to the defect. Instead, they only preserve a combination of transverse rotations and a global symmetry. These defects are constructed as IR fixed points of RG flows originating at monodromy defects, triggered by a relevant operator with non-zero transverse spin. Using large- and expansions, we compute leading-order scaling dimensions of defect operators and the one-point functions of the bulk fields. In various limits this theory coincides with the monodromy defect or the pinning field defect, and we compare our results to existing results for these defects.

Paper Structure

This paper contains 14 sections, 106 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Defect RG flows from a monodromy defect in the $\mathrm{O}(2N)$ model
  3. Symmetries of monodromy defects in the $\mathrm{O}(2N)$ model
  4. RG flow triggered by $\mathop{\mathrm{Re}}(\widehat{\Psi}^1_s)$ for $v\not\in\{0, \tfrac{1}{2}\}$
  5. $v=0$ and $v=\tfrac{1}{2}$
  6. Monodromy pinning DCFTs at large $N$
  7. Weyl transformation to $\text{AdS}_{d-1}\times S^1$ description
  8. Spectral representation of $G_{\delta\sigma\delta\sigma}$
  9. Conformal perturbation theory in the limit $v\nearrow v^*$
  10. $4-\varepsilon$ expansion
  11. Conclusions
  12. Bulk-to-defect OPE of a monodromy defect in the $\mathrm{O}(2N)$ model
  13. Regularization of $G_{\mathrm{bb}}(x, x)$
  14. An explicit formula for $\widetilde{C}_{\Delta_1\Delta_2}(\nu)$

Figures (6)

  • Figure 1: Left: a plot of $v^*$ at large-$N$ for $2<d<4$. Right: a plot of $\sigma_0^{\mathrm{UV}}$ in $d=3$ in the monodromy DCFT for $0\leq v\leq 1$.
  • Figure 2: A plot of the scaling dimension of $\widehat{\Psi}_{s}$ in $d=3$ in the monodromy DCFT for $0\leq v\leq 1$ for $v\in\{-2, -1, 0, 1\}$. Vertical dashed lines indicate positions of $v^*\approx 0.617$ and $1-v^*\approx 0.383$, while the horizontal dashed line indicates the marginal dimension $d-2$.
  • Figure 3: The relationship between various limits of the monodromy pinning DCFT in the $\mathrm{O}(2N)$ model. The monodromy pinning DCFT exists at large-$N$ everywhere below the monodromy defect line.
  • Figure 4: A plot of $J^2$ for $0\leq v\leq v^*$ in $d=3$.
  • Figure 5:
  • ...and 1 more figures