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1. Chern-Simons invariants and heterotic superpotentials

   https://doi.org/10.1007/JHEP09(2020)141  

   Anderson, Lara B.; Gray, James; Lukas, Andre; Wang, Juntao (September 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract The superpotential in four-dimensional heterotic effective theories contains terms arising from holomorphic Chern-Simons invariants associated to the gauge and tangent bundles of the compactification geometry. These effects are crucial for a number of key features of the theory, including vacuum stability and moduli stabilization. Despite their importance, few tools exist in the literature to compute such effects in a given heterotic vacuum. In this work we present new techniques to explicitly determine holomorphic Chern-Simons invariants in heterotic string compactifications. The key technical ingredient in our computations are real bundle morphisms between the gauge and tangent bundles. We find that there are large classes of examples, beyond the standard embedding, where the Chern-Simons superpotential vanishes. We also provide explicit examples for non-flat bundles where it is non-vanishing and non-integer quantized, generalizing previous results for Wilson lines. 

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2. Dimensional reduction of higher derivative heterotic supergravity

   https://doi.org/10.1007/JHEP03(2022)081  

   Chang, Hao-Yuan; Sezgin, Ergin; Tanii, Yoshiaki (March 2022, Journal of High Energy Physics)

   A bstract Higher derivative couplings of hypermultiplets to 6 D, N = (1 , 0) supergravity are obtained from dimensional reduction of 10D heterotic supergravity that includes order α ′ higher derivative corrections. Reduction on T 4 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. 

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3. A heterotic Kodaira-Spencer theory at one-loop

   https://doi.org/10.1007/JHEP10(2023)130  

   Ashmore, Anthony; Murgas_Ibarra, Javier José; McNutt, David Duncan; Strickland-Constable, Charles; Svanes, Eirik Eik; Tennyson, David; Winje, Sander (October 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> We consider a heterotic version of six-dimensional Kodaira-Spencer gravity derived from the heterotic superpotential. We compute the one-loop partition function and find it can be expressed as a product of holomorphic Ray-Singer torsions. We discuss its topological properties and potential gauge and gravitational anomalies. We show these anomalies can be cancelled using Green-Schwarz-like counter-terms. We also discuss the dependence on the background geometry, and in particular the choice of hermitian metric needed for quantisation. Given suitable topological constraints, this dependence may again be cancelled by the addition of purely background-dependent counter-terms. We also explain how our methods provide the one-loop partition functions of a large class of more general holomorphic field theories in terms of holomorphic Ray-Singer torsions. 

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4. Extending the geometry of heterotic spectral cover constructions

   https://doi.org/10.1016/j.nuclphysb.2020.115003  

   Anderson, Lara B.; Gao, Xin; Karkheiran, Mohsen (July 2020, Nuclear Physics B)
5. Spacetime Supersymmetry in Low‐Dimensional Perturbative Heterotic Compactifications

   https://doi.org/10.1002/prop.201800027  

   Melnikov, Ilarion V.; Minasian, Ruben; Sethi, Savdeep (April 2018, Fortschritte der Physik)

   Abstract We study the constraints of spacetime supersymmetry for perturbative three– and two–dimensional Minkowski vacua of the critical heterotic string. Assuming a standard RNS construction of the spacetime supersymmetry generators and a compact unitary internal superconformal worldsheet theory, we describe the worldsheet structures associated to various spacetime supersymmetries. In three dimensions we show that there are no CFT surprises: each allowed spacetime supersymmetry is realized by a supergravity compactification. As a recent orbifold construction shows, in two dimensions there are more exotic possibilities, and we discuss how these fit into our analysis. 

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