Heterotic string field theory with cyclic L∞ structure

Hiroshi Kunitomo,Tatsuya Sugimoto

doi:10.1093/ptep/ptz148

Heterotic string field theory with cyclic L∞ structure

Hiroshi Kunitomo, Tatsuya Sugimoto

Open Access

https://doi.org/10.1093/ptep/ptz148

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Abstract

A correction has been published:Progress of Theoretical and Experimental Physics, Volume 2020, Issue 1, January 2020, 019201, https://doi.org/10.1093/ptep/ptz148.

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 WZW1 -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
Using the relation in Eq (A.13) we find that ωl φa, bk+1 (φ1 ∧ · · · ∧ φk ∧ φb ) = ωl φa, π1 BF(φ1 ∧ · · · ∧ φk ∧ φb )
We hope that the string field theory constructed in this paper provides a useful basic approach for studying various interesting nonperturbative properties of heterotic strings

Summary

Introduction

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 WZW1 -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. After decomposing the commutator of coderivations into two operations projecting onto the definite cyclic Ramond number, we propose equations for the generating function of (slightly generalized) string products generalizing the L∞ relation and the closedness condition in the small Hilbert space. Π10 (π11 ) is the projection operator onto HNS (HR ) introduced in Appendix A This combination of string products can be cyclic with respect to the symmetric symplectic form ωs. And hereafter we use the convention that a quantity with the Ramond or cyclic Ramond number outside the range given in Appendix B is identically equal to zero These two mutually commutative L∞ algebras D and C are the heterotic string analogs of the dynamical and constraint L∞ algebras in Ref. (4.16b) we find that it agrees with the first-quantized amplitude in Eq (4.8):

Two-NS-two-R amplitude

Summary and discussion