On the quantization of isomonodromic deformations on the torus

The quantization of isomonodromic deformation of a meromorphic connection on the torus is shown to lead directly to the Knizhnik-Zamolodchikov-Bernard equations in the same way as the problem on the sphere leads to the system of Knizhnik-Zamolodchikov equations. The Poisson bracket required for a Hamiltonian formulation of isomonodromic deformations is naturally induced by the Poisson structure of Chern-Simons theory in a holomorphic gauge fixing. This turns out to be the origin of the appearance of twisted quantities on the torus.Comment: 13 pages, LaTex2

Neukodifikation des lnternationalen Privatrechts in Argentinien

Am 1. August 2015 ist in Argentinien ein neues „Zivil- und Handelsgesetzbuch“ in Kraft getreten, das auch das Internationale Privatrecht umfasst. Während in Argentinien lange der Plan verfolgt wurde, das Internationale Privatrecht in einem eigenen Gesetz zu regeln, setzte sich schließlich die Auffassung durch, diese Materie im Rahmen des neuen Zivilgesetzbuchs zu behandeln. Daraus ergeben sich substantielle Beschränkungen; so wurden in das Gesetz keine Vorschriften über die Anerkennung ausländischer Entscheidungen aufgenommen. Anderseits enthält das Gesetz nicht nur Vorschriften über das anwendbare Recht, sondern auch über die internationale Zuständigkeit. Ein eigener Abschnitt umfasst dazu die allgemeinen Grundsätze, während die einzelnen Gerichtsstände für die jeweiligen Materien zusammen mit dem anwendbaren Recht geregelt werden. Das Gesetz zielt darauf ab, die bisher im Zivilgesetzbuch verstreuten kollisionsrechtlichen Vorschriften und die dazu ergangene Rechtsprechung systematisch zu ordnen und zu modernisieren. Dabei wurden auch ausländische Gesetze und die internationalen Verträge auf diesem Gebiet umfassend berücksichtigt.A new “Civil and Commercial Code” containing a codification of private international law is in force in Argentina from 1 August 2015. The ambitious efforts, which persisted for a long time in Argentina, to create a distinct law for private international law have been replaced by the more practical attempt to regulate this area of law within the new Civil Code. This has substantial implications, as for instance the enforcement of foreign judgments is not regulated in the new codification. On the other hand, it contains not only provisions on the applicable law, but also on international jurisdiction. This topic is regulated in a general way in a separate chapter, but also in detail combined with the articles on the applicable law as concerns the individual fora. While the old Civil Code had only scattered provisions on conflict of laws, the new regulation is aimed at systematizing and modernizing this area of law within a cohesive text, considering the doctrine and jurisprudence in Argentina together with comparative law and international conventions

Six-Dimensional (1,0) Superconformal Models and Higher Gauge Theory

We analyze the gauge structure of a recently proposed superconformal field theory in six dimensions. We find that this structure amounts to a weak Courant-Dorfman algebra, which, in turn, can be interpreted as a strong homotopy Lie algebra. This suggests that the superconformal field theory is closely related to higher gauge theory, describing the parallel transport of extended objects. Indeed we find that, under certain restrictions, the field content and gauge transformations reduce to those of higher gauge theory. We also present a number of interesting examples of admissible gauge structures such as the structure Lie 2-algebra of an abelian gerbe, differential crossed modules, the 3-algebras of M2-brane models and string Lie 2-algebras.Comment: 31+1 pages, presentation slightly improved, version published in JM

Massive Representations of N=4 Higher Spin Symmetry

We assemble the spectrum of single-trace operators in free N=4 SU(N) SYM theory into irreducible representations of the Higher Spin symmetry algebra hs(2,2|4). Higher Spin representations or YT-pletons are associated to Young tableaux (YT) corresponding to representations of the symmetric group compatible with the cyclicity of color traces. After turning on interactions, YT-pletons decompose into infinite towers of representations of the superconformal algebra PSU(2,2|4) and anomalous dimensions are generated. We work out the decompositions of tripletons with respect to the N=4 superconformal algebra PSU(2,2|4) and compute their one anomalous dimensions at large N. We then focus on operators/states sitting in semishort superconformal multiplets. By passing them through a semishort-sieve that removes superdescendants, we derive compact expressions for the partition function of semishort primaries

Yang-Mills-Chern-Simons Supergravity

N=(1,0) supergravity in six dimensions admits AdS_3\times S^3 as a vacuum solution. We extend our recent results presented in hep-th/0212323, by obtaining the complete N=4 Yang-Mills-Chern-Simons supergravity in D=3, up to quartic fermion terms, by S^3 group manifold reduction of the six dimensional theory. The SU(2) gauge fields have Yang-Mills kinetic terms as well as topological Chern-Simons mass terms. There is in addition a triplet of matter vectors. After diagonalisation, these fields describe two triplets of topologically-massive vector fields of opposite helicities. The model also contains six scalars, described by a GL(3,R)/SO(3) sigma model. It provides the first example of a three-dimensional gauged supergravity that can obtained by a consistent reduction of string-theory or M-theory and that admits AdS_3 as a vacuum solution. There are unusual features in the reduction from six-dimensional supergravity, owing to the self-duality condition on the 3-form field. The structure of the full equations of motion in N=(1,0) supergravity in D=6 is also elucidated, and the role of the self-dual field strength as torsion is exhibited.Comment: Latex, 22 pages, hep-th number correcte

The Gaugings of Maximal D=6 Supergravity

We construct the most general gaugings of the maximal D=6 supergravity. The theory is (2,2) supersymmetric, and possesses an on-shell SO(5,5) duality symmetry which plays a key role in determining its couplings. The field content includes 16 vector fields that carry a chiral spinor representation of the duality group. We utilize the embedding tensor method which determines the appropriate combinations of these vectors that participate in gauging of a suitable subgroup of SO(5,5). The construction also introduces the magnetic duals of the 5 two-form potentials and 16 vector fields.Comment: 34 pages, latex, reference added, typo's corrected and minor improvements mad

AdS Duals of Matrix Strings

We review recent work on the holographic duals of type II and heterotic matrix string theories described by warped AdS_3 supergravities. In particular, we compute the spectra of Kaluza-Klein primaries for type I, II supergravities on warped AdS_3xS^7 and match them with the primary operators in the dual two-dimensional gauge theories. The presence of non-trivial warp factors and dilaton profiles requires a modification of the familiar dictionary between masses and ``scaling'' dimensions of fields and operators. We present these modifications for the general case of domain wall/QFT correspondences between supergravities on warped AdS_{d+1}xS^q geometries and super Yang-Mills theories with 16 supercharges.Comment: 7 pages, Proceedings of the RTN workshop ``The quantum structure of spacetime and the geometric nature of fundamental interactions'', Leuven, September 200

Vacua of N=10 three dimensional gauged supergravity

We study scalar potentials and the corresponding vacua of N=10 three dimensional gauged supergravity. The theory contains 32 scalar fields parametrizing the exceptional coset space $\frac{E_{6(-14)}}{SO(10)\times U(1)}$. The admissible gauge groups considered in this work involve both compact and non-compact gauge groups which are maximal subgroups of $SO(10)\times U(1)$ and $E_{6(-14)}$, respectively. These gauge groups are given by $SO(p)\times SO(10-p)\times U(1)$ for $p=6,...10$, $SO(5)\times SO(5)$, $SU(4,2)\times SU(2)$, $G_{2(-14)}\times SU(2,1)$ and $F_{4(-20)}$. We find many AdS$_3$ critical points with various unbroken gauge symmetries. The relevant background isometries associated to the maximally supersymmetric critical points at which all scalars vanish are also given. These correspond to the superconformal symmetries of the dual conformal field theories in two dimensions.Comment: 37 pages no figures, typos corrected and a little change in the forma

The general gaugings of maximal d=9 supergravity

We use the embedding tensor method to construct the most general maximal gauged/massive supergravity in d=9 dimensions and to determine its extended field content. Only the 8 independent deformation parameters (embedding tensor components, mass parameters etc.) identified by Bergshoeff \textit{et al.} (an SL(2,R) triplet, two doublets and a singlet can be consistently introduced in the theory, but their simultaneous use is subject to a number of quadratic constraints. These constraints have to be kept and enforced because they cannot be used to solve some deformation parameters in terms of the rest. The deformation parameters are associated to the possible 8-forms of the theory, and the constraints are associated to the 9-forms, all of them transforming in the conjugate representations. We also give the field strengths and the gauge and supersymmetry transformations for the electric fields in the most general case. We compare these results with the predictions of the E11 approach, finding that the latter predicts one additional doublet of 9-forms, analogously to what happens in N=2, d=4,5,6 theories.Comment: Latex file, 43 pages, reference adde