Abstract
We give a new description of classical Yang-Mills theory by coupling a two-dimensional chiral CFT (which gives the tree-level S-matrix of Yang-Mills theory at genus zero) to a background non-abelian gauge field. The resulting model is solvable, and when the gravitational degrees of freedom are decoupled the non-linear Yang-Mills equations are imposed as an exact worldsheet anomaly cancellation condition. When gravitational modes are reinstated, we find gauge anomalies analogous to those appearing in heterotic string theory.
Highlights
The equations of motion for a classical field theory are usually understood as the Euler-Lagrange equations of a corresponding action functional. For certain theories, such as gauge theory and gravity, the equations of motion can famously be derived from a low-energy expansion of string theory [1,2,3]
To the lowest order in this parameter, anomaly cancellation imposes the field equations of gauge theory or gravity on the background fields; the higher-order corrections impose an infinite tower of additional higher-derivative equations
Recent progress in the study of scattering amplitudes has suggested a new description of field theories as certain string theories in their own right
Summary
The equations of motion for a classical field theory are usually understood as the Euler-Lagrange equations of a corresponding action functional. Compact formulas for the full tree-level S matrix of many massless QFTs (including gauge theory and gravity) present scattering amplitudes in terms of localized integrals on the Riemann sphere rather than a sum of Feynman diagrams or the low-energy limit of an ordinary string theory amplitude [4,5] It was shown that the Abelian Maxwell equations could be obtained in a similar fashion [8] This success has not been extended to other field theories due to a variety of subtleties associated with coupling to background fields and nonunitary gravitational modes which do not exist in the case of NS-NS supergravity. We extend the exact worldsheet description of classical field theories to include Yang-Mills theory This is accomplished by coupling a heterotic version of the ambitwistor string to a non-Abelian background gauge field. We show that recoupling the gravitational modes leads to gauge anomalies, analogous to but distinct from the well-known anomaly [10] of the standard heterotic string
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