Dynamical symmetry enhancement near IIA horizons

Abstract

We show that smooth type IIA Killing horizons with compact spatial sections preserve an even number of supersymmetries, and that the symmetry algebra of horizons with non-trivial fluxes includes an sl(2, R) subalgebra. This confirms the conjecture of [1] for type IIA horizons. As an intermediate step in the proof, we also demonstrate new Lichnerowicz type theorems for spin bundle connections whose holonomy is contained in a general linear group.

Supersymmetry of IIA warped flux AdS and flat backgrounds

“…The proof that AdS 2 × w M 8 backgrounds preserve an even number of supersymmetries requires the additional assumption that M 8 and the fields satisfy suitable conditions such that the maximum principle applies, eg M 8 is closed and fields are smooth. The result is a special case of the more general theorem that all near horizon geometries of (massive) IIA supergravity preserve an even number of supersymmetries given in [18,19]. For the counting of supersymmetries for the rest of AdS n × w M 10−n , n > 2, backgrounds no such assumption is necessary.…”

“…A convenient way to do this is to write these backgrounds as near horizon geometries as suggested in [22] and then we use the results of [18,19]. For warped flux AdS 2 × w M 8 backgrounds, the counting of supersymmetries and the rest of the results are a special case of those of [18,19] for IIA horizons.…”

“…A convenient way to do this is to write these backgrounds as near horizon geometries as suggested in [22] and then we use the results of [18,19]. For warped flux AdS 2 × w M 8 backgrounds, the counting of supersymmetries and the rest of the results are a special case of those of [18,19] for IIA horizons. For the rest of the AdS n × w M 10−n backgrounds, we integrate the KSEs along the AdS n directions and demonstrate that the Killing spinors ǫ depend on the coordinates of AdS n and four 16-component spinors σ ± , τ ± which in turn depend only on the coordinates of M 10−n .…”

“…As has already been mentioned, all AdS backgrounds are included in the near horizon geometries. To describe the fields of AdS 2 × w M 8 it suffices to impose the isometries of the AdS 2 space on all the fields of the near horizon geometries of [18,19]. In such a case, the fields 2 can be written as…”

“…The above metric is not in 2 The choice of the fields of AdS2 ×w M 8 backgrounds here is different from that of near horizon geometries in [18,19]. In particular all R-R fields have been multiplied by e Φ .…”