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We construct a symbol and coaction for $l$-loop sunrise integrals, both forthe equal-mass and generic-mass cases. These constitute the first concreteexamples of symbols and coactions for integrals involving Calabi-Yau threefoldsand higher. In order to achieve a symbol of finite length, we recast thedifferential equations satisfied by the master integrals of this topology inthe form of a unipotent differential equation. We augment the basis of masterintegrals in a natural way by including ratios of maximal cuts $\tau_i$. Wediscuss the relationship of this construction to constructions of symbols andcoactions for multiple polylogarithms and elliptic multiple polylogarithms, inparticular its connection to notions of transcendental weight.

A Symbol and Coaction for Higher-Loop Sunrise Integrals