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Register a new userThe geometry of ${cal N}=3$ AdS$_4$ in massive IIA
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The geometry of the ${cal N} = 3$, SO(4)--invariant, AdS$_4$ solution of massive type IIA supergravity that uplifts from the ${cal N} = 3 $ vacuum of $D=4$ ${cal N} = 8$ dyonic ISO(7) supergravity is investigated. Firstly, a $D=4$, SO(4)--invariant restricted duality hierarchy is constructed and used to uplift the entire, dynamical SO(4)--invariant sector to massive type IIA. The resulting consistent uplift formulae are used to obtain a new local expression for the ${cal N} = 3 $ AdS$_4$ solution in massive IIA and analyse its geometry. Locally, the internal $S^6$ geometry corresponds to a warped fibration of $S^2$ and a hemisphere of $S^4$. This can be regarded as a warped generalisation of the usual twistor fibration geometry. Finally, the triplet of Killing spinors corresponding to the ${cal N}=3$ solution are constructed and shown to obey the massive type IIA Killing spinor equations.
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We revisit various aspects of AdS$_4$ flux vacua with scale separation in type II supergravity and M-theory. We show that massless IIA allows both weakly and strongly coupled solutions for which the classical orientifold backreaction can be tuned small. This is explicitly verified by computing the backreaction at leading order in perturbation theory. We give evidence that the strongly coupled solutions can be lifted to scale-separated and sourceless (but classically singular) geometries in 11D supergravity.
We study, using ADHM construction, instanton effects in an ${CN}=2$ superconformal $Sp(N)$ gauge theory, arising as effective field theory on a system of $N$ D-3-branes near an orientifold 7-plane and 8 D-7-branes in type I string theory. We work out the measure for the collective coordinates of multi-instantons in the gauge theory and compare with the measure for the collective coordinates of $(-1)$-branes in the presence of 3- and 7-branes in type I theory. We analyse the large-N limit of the measure and find that it admits two classes of saddle points: In the first class the space of collective coordinates has the geometry of $AdS_5times S^3$ which on the string theory side has the interpretation of the D-instantons being stuck on the 7-branes and therefore the resulting moduli space being $AdS_5times S^3$, In the second class the geometry is $AdS_5times S^5/Z_2$ and on the string theory side it means that the D-instantons are free to move in the 10-dimensional bulk. We discuss in detail a correlator of four O(8) flavour currents on the Yang-Mills side, which receives contributions from the first type of saddle points only, and show that it matches with the correlator obtained from $F^4$ coupling on the string theory side, which receives contribution from D-instantons, in perfect accord with the AdS/CFT correspondence. In particular we observe that the sectors with odd number of instantons give contribution to an O(8)-odd invariant coupling, thereby breaking O(8) down to SO(8) in type I string theory. We finally discuss correlators related to $R^4$, which receive contributions from both saddle points.
We derive necessary and sufficient conditions for N=1 compactifications of (massive) IIA supergravity to AdS(4) in the language of SU(3) structures. We find new solutions characterized by constant dilaton and nonzero fluxes for all form fields. All fluxes are given in terms of the geometrical data of the internal compact space. The latter is constrained to belong to a special class of half-flat manifolds.
The framework of exceptional field theory is extended by introducing consistent deformations of its generalised Lie derivative. For the first time, massive type IIA supergravity is reproduced geometrically as a solution of the section constraint. This provides a unified description of all ten- and eleven-dimensional maximal supergravities. The action of the E7 deformed theory is constructed, and reduces to those of exceptional field theory and gauged maximal supergravity in respective limits. The relation of this new framework to other approaches for generating the Romans mass non-geometrically is discussed.
We identify the fractions of supersymmetry preserved by the most general warped flux AdS and flat backgrounds in both massive and standard IIA supergravities. We find that $AdS_ntimes_w M^{10-n}$ preserve $2^{[{nover2}]} k$ for $nleq 4$ and $2^{[{nover2}]+1} k$ for $4<nleq 7$ supersymmetries, $kin bN_{>0}$. In addition we show that, for suitably restricted fields and $M^{10-n}$, the killing spinors of AdS backgrounds are given in terms of the zero modes of Dirac like operators on $M^{10-n}$. This generalizes the Lichnerowicz theorem for connections whose holonomy is included in a general linear group. We also adapt our results to $bR^{1,n-1}times_w M^{10-n}$ backgrounds which underpin flux compactifications to $bR^{1,n-1}$ and show that these preserve $2^{[{nover2}]} k$ for $2<nleq 4$, $2^{[{n+1over2}]} k$ for $4<nleq 8$, and $2^{[{nover2}]} k$ for $n=9, 10$ supersymmetries.
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