Index of coregularity zero log Calabi-Yau pairs

We study the index of log Calabi-Yau pairs (X, B) of coregularity 0. We show that 2 lambda(KX + B) similar to 0, where lambda is the Weil index of (X, B). This is in contrast to the case of klt Calabi-Yau varieties, where the index can grow doubly exponentially with the dimension. Our sharp bound on the index extends to the context of generalized log Calabi-Yau pairs, semi-log canonical pairs, and isolated log canonical singularities of coregularity 0. As a consequence, we show that the index of a variety appearing in the Gross-Siebert program or in the Kontsevich-Soibelman program is at most 2. Finally, we discuss applications to Calabi-Yau varieties endowed with a finite group action, including holomorphic symplectic varieties endowed with a purely nonsymplectic automorphism.