Hermitian matrix-valued nonlocal deformation of the SU($N$) Thirring model at large $N$
We investigate a Hermitian matrix-valued nonlocal deformation of the two-dimensional $SU(N)$ Thirring model at leading order in $1/N$. We impose $f(\slashed{\partial})^\ddagger=f(\slashed{\partial})$ directly on the original action; for real nonlocality scale the admissible exponential choice is $f(\slashed{\partial})=\exp[-i\slashed{\partial}/Λ]$. We construct and analyze the even-in-mass (paired) large-$N$ effective potential and derive its radial kernel, weak-coupling dimensional-transmutation scale, and formal Lambert-$W$ zeros. Its radial gap integral possesses a conditionally convergent infinite-cutoff limit. The pairing prescription, however, differs from the unpaired determinant of the original Hermitian action, so the reported gap and spectral zeros must be understood as properties of this explicitly defined mean-field functional. We identify the further derivation needed to obtain physical mass gaps and fermion poles from the unpaired theory.