We present a construction of an open analogue of total descendant and total
ancestor potentials via an "open version" of Givental's action. Our
construction gives a genus expansion for an arbitrary solution to the open WDVV
equations satisfying a semisimplicity condition and admitting a unit. We show
that the open total descendant potentials we define satisfy the open
topological recursion relations in genus 0 and 1, the open string and open
dilaton equations. We finish the paper with a computation of the simplest
nontrivial open correlator in genus 1 using our construction.Comment: v3: minor changes before publication in journal have been made, 34
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