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In this paper, we study the spherically symmetric traversable wormholes with a scalar field supported by a phantom field in the anti-de Sitter (AdS) asymptotic spacetime. Despite coupling the scalar matter field, these wormholes remain massless and symmetric for reflection of the radial coordinate . The solution possesses a finite Noether charge , which varies as a function of frequency with changes in the cosmological constant and the throat size . Under specific conditions, an approximate ``event horizon’’ will appear at the throat.

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