V. Kazakov

E. Sobko

K. Zarembo

The first exact solution for the vacuum state of an asymptotically free QFT in a general external field found for the Principal Chiral Model.

_tex: Asymptotically free QFTs exhibit fundamental, non-perturbative properties in external fields but no analytic solutions for them are known for generic field configurations. Here, we solve the 2d $SU(N)$ Principal Chiral Model at large-$N$ for any set of chemical potentials. An emergent third dimension in the solution supports our earlier conjecture of a possible dual string description in a specific double-scaled limit.

_tex: We report the explicit solution for the vacuum state of the two-dimensional SU(N) Principal Chiral Model at large-N for an arbitrary set of chemical potentials and any interaction strength, a unique result of such kind for an asymptotically free QFT. The solution matches one-loop perturbative calculation at weak coupling, and in the opposite strong-coupling regime exhibits an emergent spacial dimension from the continuum limit of the SU(N) Dynkin diagram.

Large-N principal chiral model in arbitrary external fields