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We propose a nonperturbative approach to nonabelian two-form gauge theory. Weformulate the theory on a lattice in terms of plaquette as fundamentaldynamical variable, and assign U(N) Chan-Paton colors at each boundary link. Weshow that, on hypercubic lattices, such colored plaquette variables constituteYang-Baxter maps, where holonomy is characterized by certain dynamicaldeformation of quantum Yang-Baxter equations. Consistent dimensional reductionto Wilson's lattice gauge theory singles out unique compactness condition. Westudy a class of theories where the compactness condition is solved by Lax pairansatz. We find that, in naive classical continuum limit, these theoriesrecover Lorentz invariance but have degrees of freedom that scales as N^2 atlarge N. This implies that nontrivial quantum continuum limit must be soughtfor. We demonstrate that, after dimensional reduction, these theories arereduced to Wilson's lattice gauge theory. We also show that Wilson surfaces arewell-defined physical observables without ordering ambiguity. Utilizing latticestrong coupling expansion, we compute partition function and correlationfunctions of the Wilson surfaces. We discover that, at large $N$ limit, thecharacter expansion coefficients exhibit large-order behavior growing fasterthan exponential, in striking contrast to Wilson's lattice gauge theory. Thishints a hidden, weakly coupled theory dual to the proposed tensor gauge theory.We finally discuss relevance of our study to topological quantum order instrongly correlated systems.

A Nonperturbative Proposal for Nonabelian Tensor Gauge Theory and Dynamical Quantum Yang-Baxter Maps