Abstract
Higher derivative couplings of hypermultiplets to 6D, N = (1, 0) supergravity are obtained from dimensional reduction of 10D heterotic supergravity that includes order α′ higher derivative corrections. Reduction on T4 is followed by a consistent truncation. In the resulting action the hyperscalar fields parametrize the coset SO(4, 4)/(SO(4) × SO(4)). While the SO(4, 4) symmetry is ensured by Sen’s construction based on string field theory, its emergence at the field theory level is a nontrivial phenomenon. A number of field redefinitions in the hypermultiplet sector are required to remove several terms that break the SO(4) × SO(4) down to its SO(4) diagonal subgroup in the action and the supersymmetry transformation rules. Working with the Lorentz Chern-Simons term modified 3-form field strength, where the spin connection has the 3-form field strength as torsion, is shown to simplify considerably the dimensional reduction.
Highlights
R-symmetry gauging and Yang-Mills coupling in this paper but we shall study the higher derivative couplings of the hypermultiplets as a first step
Already at the four-derivative level, even with the assumption that the quaternionic Kahler structure is preserved in the case of N = (1, 0), 6D supergravity, one finds that an appropriate ansatz contains a large number of terms, and their variations under supersymmetry gives even larger set of structures that need to vanish
Motivated by the exploration of higher derivative couplings of quaternionic Kahler sigma models to N = (1, 0) supergravity in 6D, we have started with heterotic supergravity at O(α ) [31], and reduced it on T 4 with a consistent N = (1, 0) supersymmetric truncation
Summary
The heterotic supergravity multiplet consists of the fields ( eμr, ψμ Bμν , χ, φ ) ,. The Bergshoeff-de Roo extended heterotic supergravity Lagrangian, in the absence of Yang-Mills multiplets, and in string frame and up to quartic fermion terms, takes the form [31]. The Lagrangian L0, O(α) can be absorbed to the H-dependent terms in L0 by letting. The covariant derivative Dμ(ω, Ω−)ψrs requires extreme care, due to its unusual form in which the spinor indices are rotated by torsion free connection ω, while the Lorentz vector. Indices are rotated by the torsionful connection Ω− This asymmetric occurrence of the spin connection arises because the construction of Lα (R2) relies on treating Rμνrs(Ω(−sc)) as Lorentz algebra valued Yang-Mills curvature [12, 31]. The α dependent terms in δψμ and δχ can be absorbed into to the definition of H by letting.
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