We consider the harmonic superspace formulation of higher-derivative $6D,\mathcal{N}=(1,0)$ supersymmetric gauge theory and its minimal coupling to a hypermultiplet. In components, the kinetic term for the gauge field in such a theory involves four space-time derivatives. The theory is quantized in the framework of the superfield background method ensuring manifest $6D,\mathcal{N}=(1,0)$ supersymmetry and the classical gauge invariance of the quantum effective action. We evaluate the superficial degree of divergence and prove it to be independent of the number of loops. Using the regularization by dimensional reduction, we find possible counterterms and show that they can be removed by the coupling constant renormalization for any number of loops, while the divergences in the hypermultiplet sector are absent at all. Assuming that the deviation of the gauge-fixing term from that in the Feynman gauge is small, we explicitly calculate the divergent part of the one-loop effective action in the lowest order in this deviation. In the approximation considered, the result is independent of the gauge-fixing parameter and agrees with the earlier calculation for the theory without a hypermultiplet.

我们考虑高阶导数的谐波超空间公式 $6d，\mathcal{ñ}=（\mathrm{1个}，0）$超对称规范理论及其与超多重性的最小耦合。在组件中，这种理论中的规范场的动力学项涉及四个时空导数。该理论在超场背景方法的框架内进行了量化，以确保其表现出来。$6d，\mathcal{ñ}=（\mathrm{1个}，0）$超对称性和量子有效作用的经典规范不变性。我们评估了表面差异的程度，并证明它与循环数无关。使用通过降维进行正则化，我们发现了可能的反条件，并表明可以通过耦合常数重整化将其消除，无论多少循环，而超倍数扇区中完全没有散度。假设轨距固定项与费曼轨距的偏差较小，我们以该偏差的最低顺序显式计算单环有效作用的发散部分。在考虑的近似值中，结果与量规固定参数无关，并且与较早的无超倍数理论的计算相符。