T-Duality as a Duality of Loop Group Bundles

Representing the data of a string compactified on a circle in the background of H-flux in terms of the geometric data of a principal loop group bundle, we show that T-duality in type II string theory can be understood as the interchange of the momentum and winding homomorphisms of the principal loop group bundle, thus giving rise to a new interpretation of T-duality.Comment: 8 pages, latex 2e, new reference added, J.Phys.A: Fast Track Publications (to appear

Duality symmetry and the form fields of M-theory

In previous work we derived the topological terms in the M-theory action in terms of certain characters that we defined. In this paper, we propose the extention of these characters to include the dual fields. The unified treatment of the M-theory four-form field strength and its dual leads to several observations. In particular we elaborate on the possibility of a twisted cohomology theory with a twist given by degrees greater than three.Comment: 12 pages, modified material on the differentia

Loop Groups, Kaluza-Klein Reduction and M-Theory

We show that the data of a principal G-bundle over a principal circle bundle is equivalent to that of a \hat{LG} = U(1) |x LG bundle over the base of the circle bundle. We apply this to the Kaluza-Klein reduction of M-theory to IIA and show that certain generalized characteristic classes of the loop group bundle encode the Bianchi identities of the antisymmetric tensor fields of IIA supergravity. We further show that the low dimensional characteristic classes of the central extension of the loop group encode the Bianchi identities of massive IIA, thereby adding support to the conjectures of hep-th/0203218.Comment: 26 pages, LaTeX, utarticle.cls, v2:clarifications and refs adde

Gerbes, M5-Brane Anomalies and E_8 Gauge Theory

Abelian gerbes and twisted bundles describe the topology of the NS-NS 3-form gauge field strength H. We review how they have been usefully applied to study and resolve global anomalies in open string theory. Abelian 2-gerbes and twisted nonabelian gerbes describe the topology of the 4-form field strength G of M-theory. We show that twisted nonabelian gerbes are relevant in the study and resolution of global anomalies of multiple coinciding M5-branes. Global anomalies for one M5-brane have been studied by Witten and by Diaconescu, Freed and Moore. The structure and the differential geometry of twisted nonabelian gerbes (i.e. modules for 2-gerbes) is defined and studied. The nonabelian 2-form gauge potential living on multiple coinciding M5-branes arises as curving (curvature) of twisted nonabelian gerbes. The nonabelian group is in general $\tilde\Omega E_8$, the central extension of the E_8 loop group. The twist is in general necessary to cancel global anomalies due to the nontriviality of the 11-dimensional 4-form G field strength and due to the possible torsion present in the cycles the M5-branes wrap. Our description of M5-branes global anomalies leads to the D4-branes one upon compactification of M-theory to Type IIA theory.Comment: 19 page

Supersymmetric AdS_5 solutions of M-theory

We analyse the most general supersymmetric solutions of D=11 supergravity consisting of a warped product of five-dimensional anti-de-Sitter space with a six-dimensional Riemannian space M_6, with four-form flux on M_6. We show that M_6 is partly specified by a one-parameter family of four-dimensional Kahler metrics. We find a large family of new explicit regular solutions where M_6 is a compact, complex manifold which is topologically a two-sphere bundle over a four-dimensional base, where the latter is either (i) Kahler-Einstein with positive curvature, or (ii) a product of two constant-curvature Riemann surfaces. After dimensional reduction and T-duality, some solutions in the second class are related to a new family of Sasaki-Einstein spaces which includes T^{1,1}/Z_2. Our general analysis also covers warped products of five-dimensional Minkowski space with a six-dimensional Riemannian space.Comment: 40 pages. v2: minor changes, eqs. (2.22) and (D.12) correcte