Emergent Strings from Quantum Field Theory

Abstract

We develop a procedure that reorganizes the perturbative expansion in a class of quantum field theories into a stringy amplitude expressed as a sum over two-dimensional geometries. Using Schwinger parametrization and the one-to-one correspondence between metric ribboned graphs and the moduli space of Riemann surfaces established via Strebel differentials, we map each Feynman diagram to a surface. We then construct a conformal field theory on the worldsheet whose correlation functions encode the full set of QFT Feynman rules directly from the geometry of the associated Riemann surface. Restoring diffeomorphism and Weyl invariance promotes the integral over moduli space to a path integral over worldsheet metrics, yielding a non-critical string theory whose Liouville mode naturally becomes a holographic direction. By construction, the expansion of the string theory amplitudes in the number of boundary state insertions matches the loop expansion in the QFT at fixed genus. Moreover, loop divergences are shown to match standard string-theoretic degeneration limits, indicating that gravitational backreaction is equivalent to QFT renormalization. Our construction provides a microscopic route from generic QFTs to emergent string theories and offers a framework for deriving holographic duals directly from field-theoretic data.