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Theta functions were defined for varieties with effective anticanonicaldivisor and are related to certain punctured Gromov-Witten invariants. In thispaper we show that in the case of a log Calabi-Yau surface (X,D) with smoothvery ample anticanonical divisor we can circumvent the notion of puncturedGromov-Witten invariants and relate theta functions and their multiplicativestructure to certain 2-marked log Gromov-Witten invariants. This is a naturalextension of the correspondence between wall functions and 1-marked logGromov-Witten invariants.

Theta functions, broken lines and 2-marked log Gromov-Witten invariants