3D gauged supergravity from SU(2) reduction of N=1N=1 6D supergravity

We obtain Yang-Mills $SU(2)\times G$ gauged supergravity in three dimensions from $SU(2)$ group manifold reduction of (1,0) six dimensional supergravity coupled to an anti-symmetric tensor multiplet and gauge vector multiplets in the adjoint of $G$. The reduced theory is consistently truncated to $N=4$ 3D supergravity coupled to $4(1+\textrm{dim}\, G)$ bosonic and $4(1+\textrm{dim}\, G)$ fermionic propagating degrees of freedom. This is in contrast to the reduction in which there are also massive vector fields. The scalar manifold is $\mathbf{R}\times \frac{SO(3,\, \textrm{dim}\, G)}{SO(3)\times SO(\textrm{dim}\, G)}$, and there is a $SU(2)\times G$ gauge group. We then construct $N=4$ Chern-Simons $(SO(3)\ltimes \mathbf{R}^3)\times (G\ltimes \mathbf{R}^{\textrm{dim}G})$ three dimensional gauged supergravity with scalar manifold $\frac{SO(4,\,1+\textrm{dim}G)}{SO(4)\times SO(1+\textrm{dim}G)}$ and explicitly show that this theory is on-shell equivalent to the Yang-Mills $SO(3)\times G$ gauged supergravity theory obtained from the $SU(2)$ reduction, after integrating out the scalars and gauge fields corresponding to the translational symmetries $\mathbf{R}^3\times \mathbf{R}^{\textrm{dim}\, G}$.Comment: 24 pages, no figures, references added and typos correcte

On Subleading Contributions to the AdS/CFT Trace Anomaly

In the context of the AdS/CFT correspondence, we perform a direct computation in AdS_5 supergravity of the trace anomaly of a d=4, N=2 SCFT. We find agreement with the field theory result up to next to leading order in the 1/N expansion. In particular, the order N gravitational contribution to the anomaly is obtained from a Riemann tensor squared term in the 7-brane effective action deduced from heterotic - type I duality. We also discuss, in the AdS/CFT context, the order N corrections to the trace anomaly in d=4, N=4 SCFTs involving SO or Sp gauge groups.Comment: 25 pages, LaTeX, v2: references adde

On the perturbative corrections around D-string instantons

We study ${\cal F}^4$-threshold corrections in an eight dimensional S-dual pair of string theories, as a prototype of dual string vacua with sixteen supercharges. We show that the orbifold CFT description of D-string instantons gives rise to a perturbative expansion similar to the one appearing on the fundamental string side. By an explicit calculation, using the Nambu-Goto action in the static gauge, we show that the first subleading term agrees precisely on the two sides. We then give a general argument to show that the agreement extends to all orders.Comment: 12 page

Duality Symmetries in N=2 Heterotic Superstring

We review the derivation and the basic properties of the perturbative prepotential in N=2 compactifications of the heterotic superstring. We discuss the structure of the perturbative monodromy group and the embedding of rigidly supersymmetric monodromies associated with enhanced gauge groups, at both perturbative and non-perturbative level.Comment: Based on talks presented at several conferences. 12 pages, LaTe

Do we need a hybrid law of contract? Why Hugh Collins is wrong and why it matters

In Regulating Contracts Hugh Collins takes up the challenge presented by 40 years of empirical studies which show that business people make little use of contract law in settling disputes, preferring instead to rely on trust and various non-legal sanctions to organise their transactions. Indeed, business parties often actively avoid the use of law because of its expense, inconvenience and tendency to harm business relationships. These findings pose a challenge to traditional doctrinal scholars. If business parties do not make much use of contract law, one has to ask what role it does play and whether the attention that is paid to it by orthodox legal scholars is misplaced. Regulating Contracts takes on this challenge directly and is the most substantial attempt made so far to explain the role of contract law in light of the questions raised as to its usefulness.John Gava and Janey Green

AdS/CFT correspondence and D1/D5 systems in theories with 16 supercharges

We discuss spectra of $AdS_3$ supergravities, arising in the near horizon geometry of D1/D5 systems in orbifolds/orientifolds of type IIB theory with 16 supercharges. These include models studied in a recent paper (hep-th/0012118), where the group action involves also a shift along a transversal circle, as well as IIB/$\Omega I_4$, which is dual to IIB on $K3$. After appropriate assignements of the orbifold group eigenvalues and degrees to the supergravity single particle spectrum, we compute the supergravity elliptic genus and find agreement, in the expected regime of validity, with the elliptic genus obtained using U-duality map from (4,4) CFTs of U-dual backgrounds. Since this U-duality involves the exchange of KK momentum $P$ and D1 charge $N$, it allows us to test the (4,4) CFTs in the $P < N/4$ and $N < P/4$ regimes by two different supergravity duals.Comment: 28 pages, no figure