I will discuss attempts to construct eternal traversable wormholes connecting two asymptotically AdS regions by introducing a static coupling between the two dual CFTs. I will focus on asymptotically AdS_D spacetimes (D>2) and assume Poincare invariance in the transverse directions. In this setting, the effect of the non-local coupling can be computed analytically and is shown to violate the null energy condition. However, this violation is too small to support a semiclassical geometry. I will explain some ideas to try to enhance this effect such as adding conventional bulk matter or coupling a large number of fields but I will show that they do not change the conclusion. Given these symmetries, then, I will be able to prove a no-go theorem for semiclassical wormholes. I'll discuss possible ways around this theorem by relaxing some of the assumptions.