By Constantin P. Bachas, Adel Bilal, Michael R. Douglas, Nikita A. Nekrasov, Francois David

ISBN-10: 3540002766

ISBN-13: 9783540002765

In a distilled and pedagogical type, the contributions to this quantity of the recognized summer season institution in Les Houches hide the hot advancements in supersymmetric string thought, the gauge theory/string idea correspondence and string duality. additional chapters care for quantum gravity and D-brane geometry. Black gap mechanics and cosmology are taken care of too, in addition to the AdS-CFT correspondence. The publication is a finished creation to the hot advancements in string/M-theory and quantum gravity. It addresses graduate scholars in physics and astrophysics.

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**Example text**

5 for a discussion of this) in which case it can possess an anti-de Sitter ground state. According to Table 9, a fully supersymmetric ground state leads to a U (4) R-symmetry group. As we will discuss in Section 6, anti-de Sitter space leads to “remarkable representations”. These are the singletons, which do 28 Unity from Duality: Gravity, Gauge Theory and Strings not have a smooth Poincar´e limit because they are associated with possible degrees of freedom living on a 4-dimensional boundary. Because the 5dimensional anti-de Sitter superalgebra coincides with the 4-dimensional superconformal algebra, the 4-dimensional boundary theory must be consistent with superconformal invariance.

Unfortunately, many theories do not possess (ﬁnite-dimensional) oﬀ-shell representations. Notorious examples are gauge theories and supergravity theories with 16 or more supercharges. This fact makes is much more diﬃcult to construct an extended variety of actions for these theories, because the transformation rules are implicitly dependent on the action. There is an oﬀ-shell counting argument. according to which the ﬁeld degrees of freedom should comprise a massive supermultiplet (while the states that are described could be massless).

7) for the spin connection, the aﬃne connection ab (ω) eρ a ebσ coinbecomes equal to the Christoﬀel symbols and Rµνρ σ = Rµν cides with the standard Riemann tensor. The action corresponding to the above Lagrangian is locally supersymmetric up to terms cubic in the gravitino ﬁeld. 9) where the gravitino variation is the extension to curved spacetime of the spinor gauge invariance of a Rarita-Schwinger ﬁeld. Extending this Lagrangian to a fully supersymmetric one is not always possible. Usually it requires additional ﬁelds of lower spin, whose existence can be inferred from the knowledge of the possible underlying (massless) supermultiplets of states.

### Unity from duality: gravity, gauge theory and strings by Constantin P. Bachas, Adel Bilal, Michael R. Douglas, Nikita A. Nekrasov, Francois David

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