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Within the framework of string theory, a number of new fields are possiblecorrecting the Einstein-Hilbert action, including a Kalb-Ramond two-form field.In this work we derive explicitly first order relativistic corrections toconservative dynamics with a Kalb-Ramond field, using the effective fieldtheory approach. The resulting additional terms in the Lagrangian governingconservative binary dynamics are presented explicitly.

1PN effective binary Lagrangian for the gravity-Kalb-Ramond sector in the conservative regime