We rewrite $\lambda {\phi }^4$ theory as a dual string expansion by performing a combined topological strong-coupling expansion on an $x^{+}$, $P^{+}$ lattice. The resulting expansion is the standard dual loop expansion plus the pointenergy-momentum density graphs of Green. The expansion goes through only for the "wrong" sign of $\lambda$, i.e., when the theory is asymptotically free and infrared unstable. The coupling strength $\lambda$ is fixed by an eigenvalue condition, and the rest tension of the string, $T_0$ replaces it as a free parameter. The continuum limit only exists for the critical dimension $D=26\mathrm{}$. We suggest that this approach might be a suitable starting point for spectrum calculations in quantum chromodynamics.

• Received 23 November 1977

DOI:https://doi.org/10.1103/PhysRevD.17.1073