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      Compactification of D=11 supergravity on spaces of exceptional holonomy

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          Abstract

          We investigate the compactification of D=11 supergravity to D=5,4,3, on compact manifolds of holonomy \(SU(3)\) (Calabi-Yau), \(G_2\), and \(Spin(7)\), respectively, making use of examples of the latter two cases found recently by Joyce. In each case the lower dimensional theory is a Maxwell/Einstein supergravity theory. We find evidence for an equivalence, in certain cases, with heterotic string compactifications from D=10 to D=5,4,3, on compact manifolds of holonomy \(SU(2)\) (\(K_3\times S^1\)), \(SU(3)\), and \(G_2\), respectively. Calabi-Yau manifolds with Hodge numbers \(h_{1,1}=h_{1,2}=19\) play a significant role in the proposed equivalences.

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          Unity of Superstring Dualities

          The effective action for type II string theory compactified on a six torus is \(N=8\) supergravity, which is known to have an \(E_{7}\) duality symmetry. We show that this is broken by quantum effects to a discrete subgroup, \(E_7(\Z)\), which contains both the T-duality group \(SO(6,6;\Z)\) and the S-duality group \(SL(2;\Z)\). We present evidence for the conjecture that \(E_7(\Z)\) is an exact \lq U-duality' symmetry of type II string theory. This conjecture requires certain extreme black hole states to be identified with massive modes of the fundamental string. The gauge bosons from the Ramond-Ramond sector couple not to string excitations but to solitons. We discuss similar issues in the context of toroidal string compactifications to other dimensions, compactifications of the type II string on \(K_3\times T^2\) and compactifications of eleven-dimensional supermembrane theory.
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            All the Hodge numbers for all Calabi-Yau complete intersections

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              Supergravity in d=9 and its coupling to the non-compact σmodel

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                Author and article information

                Journal
                22 June 1995
                1995-06-30
                Article
                10.1016/0370-2693(95)00929-F
                hep-th/9506150
                0134f46a-8e15-446c-b241-14383c55ad7d
                History
                Custom metadata
                DAMTP, R/95/31
                Phys.Lett.B357:300-306,1995
                Minor amendments plus some new references
                hep-th

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