# What does it mean for an extended operator to possess "local excitations"?

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?

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