In the context of defect conformal field theory, we consider in operator product expansions "local excitations" of the defect (see e.g. text between eq. $(1.1)$ and $(1.2)$ in the paper Defects in Conformal Field Theories). But what is a local excitation of an extended operator?

For example consider the Maldacena-Wilson line defect:

$$\mathcal{W}(C) := \frac{1}{N}\ \text{Tr}\ \mathcal{P} \exp \int_{-\infty}^\infty d\tau \left( i \dot{x}_\mu A^\mu(x) + |\dot{x}| \theta_i \phi^i(x) \right), \tag{1}$$

with $\mathcal{P}$ the path-ordering operator, $i$ the index of the $so(6) \sim su(4)_R$ R-symmetry and $\tau$ the parametrization of the line.

What are examples of "local excitations" of this operator? Is it something like e.g. $\frac{1}{N} i \dot{x}_\mu \text{Tr} A_\mu (x)$ with $x$ on the line?

  • $\begingroup$ Possibly relevant: arxiv.org/abs/1304.4110. In section 3.2, some explicit lattice representations of defect local operators are described. $\endgroup$
    – Arkya
    Jul 10 '20 at 21:45

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