Abstract
We construct a complete heterotic string field theory that includes both the Neveu-Schwarz and Ramond sectors. We give a construction of general string products, which realizes a cyclic L-infinity structure and thus provides with a gauge-invariant action in the homotopy algebraic formulation. Through a map of the string fields, we also give the Wess-Zumino-Witten-like action in the large Hilbert space, and verify its gauge invariance independently.
Highlights
There are three main formulations of superstring field theories: the formulation based on a homotopy algebraic structure in the small Hilbert space [1,2], the Wess-Zumino-Witten(WZW)like formulation in the large Hilbert space [3,4], and Sen’s formulation with an extra free string field [5,6], each of which has both advantages and disadvantages
In this paper we propose a similar but slightly different prescription to construct string products realizing a cyclic L∞ algebra, and construct a complete gauge-invariant action for the heterotic string field theory in the homotopy algebraic formulation
After decomposing the commutator of coderivations into two operations projecting onto the definite cyclic Ramond number, we propose equations for the generating function of string products generalizing the L∞ relation and the closedness condition in the small Hilbert space
Summary
There are three main formulations of superstring field theories: the formulation based on a homotopy algebraic structure in the small Hilbert space [1,2], the Wess-Zumino-Witten(WZW)like formulation in the large Hilbert space [3,4], and Sen’s formulation with an extra free string field [5,6], each of which has both advantages and disadvantages. In this paper we focus on the former two formulations since they are not yet fully established for all the superstring field theories, while Sen’s formulation is In these formulations important progress has recently been made: a complete gauge-invariant action for the open superstring field theory including both the Neveu-Schwarz (NS) and Ramond (R) sectors was constructed first in the WZW-like formulation [7] and soon afterwards in the homotopy algebraic formulation based on the A∞ structure [8]. In this paper we propose a similar but slightly different prescription to construct string products realizing a cyclic L∞ algebra, and construct a complete gauge-invariant action for the heterotic string field theory in the homotopy algebraic formulation.
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