Bootstrapping the 3d Ising twist defect

Abstract

Recent numerical results point to the existence of a conformally invariant twist defect in the critical 3d Ising model. In this note we show that this fact is supported by both epsilon expansion and conformal bootstrap calculations. We find that our results are in good agreement with the numerical data. We also make new predictions for operator dimensions and OPE coefficients from the bootstrap approach. In the process we derive universal bounds on one-dimensional conformal field theories and conformal line defects.

Figures (8)

• Figure 1: The one-loop contribution to $\langle\phi(x_1)\phi(x_2)\rangle$
• Figure 2: The diagrams contributing to the properties of $\psi_{s_1}\psi_{s_2}$ up to one loop. The double line denotes the one-loop-corrected propagator.
• Figure 3: Anomalous dimensions of the leading operators of spin $s$ at one loop. Dashed blue lines interpolate between the even and odd spins. They both asymptote to the dashed red line $\delta_s=-1/12$.
• Figure 4: One-dimensional bounds derived from \ref{['eq:beq1']}. In red the curves corresponding to the generalized free fermion solution. Left: bound on scalar dimension. Right: OPE coefficient of the leading scalar, in the solution to crossing corresponding to the dots on the top plot.
• Figure 5: Single equation bound in red and two equation bound in black. In the latter, the leading scalar is parity odd, up to about $d=1$, where the parity even and odd scalars have identical spectra.