On the supersymmetric solutions of the Heterotic Superstring effective action

Abstract

We consider the effective action of the Heterotic Superstring to first order in alpha prime and derive the necessary and sufficient conditions that a field configuration has to satisfy in order to admit at least one Killing spinor using the spinor bilinear method and making minimal coordinate and frame choices. As a previous step in this derivation, we compute the complete spinor bilinear algebra using the Fierz identities, obtaining as a by-product the algebra satisfied by the Spin(7) structure contained in the bilinears in an arbitrary basis. We find the relations existing between the left-hand-sides of the bosonic equations of motion evaluated on supersymmetric field configurations using the Killing Spinor Identities instead of the (far more complicated) integrability conditions of the Killing Spinor Equations as it is common in the literature. We show how to include the Kalb-Ramond's Bianchi identity in the Killing Spinor Identities.

arXiv commentLaTeX2e file, 49 pages, no figures. An error in the derivation of necessary conditions for unbroken supersymmetry and a few typos have been corrected

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• The first law and Wald entropy formula of heterotic stringy black holes at first order in alpha prime
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• O(n,n) invariance and Wald entropy formula in the Heterotic Superstring effective action at first order in alpha'
• Higher Derivative Supergravities in Diverse Dimensions
• Supersymmetry, T-duality and Heterotic ${\alpha }^{\prime }$-corrections
• The Supersymmetric Neveu-Schwarz Branes of Non-Relativistic String Theory
• On small black holes, KK monopoles and solitonic 5-branes
• On the consistency of a class of R-symmetry gauged 6D N=(1,0) supergravities
• Higher-derivative corrections to small black rings
• Non-supersymmetric black holes with ${\alpha }^{\prime }$ corrections