Induced QCD from the Noncommutative Geometry of a Supermanifold

We study the noncommutative geometry of a two-leaf Parisi--Sourlas supermanifold in Connes' formalism using different $K$-cycles over the Grassmann algebra valued functions on the supermanifold. We find that the curvature of the trivial noncommutative vector bundle defines in the simplest case the super Yang--Mills action coupled to a scalar field. By considering a modified Dirac operator and a suitable limit of its parameters we then obtain an action that turns out to be the continuum limit of the induced QCD in Kazakov--Migdal model.Comment: 15 pages, late

Gerbes and Massive Type II Configurations

We find novel bound states of NS5, D6 and D8-branes in massive Type IIA string theory. As the NS gauge transformations can change the Chern class of the RR field these configurations should be thought of as nonlocal objects called gerbes. We develop a global formalism for theories that involve massive tensor fields in general, and apply it in massive Type IIA supergravity. We check the results by investigating the T-dual NS5/D5-brane configurations in Type IIB, and relate them to an F-theory compactification on a CY3. We comment on the implications to consistency conditions for brane-wrapping and the classification of D-brane charges in terms of K-theory classes.Comment: 27 pages, LaTeX. V2: General clarifications, some omissions, sec 6.2 expanded, corrections in sec 4.1 and eq (67), refs added. V3: Further clarified and cast in jhep forma

Signature reversal invariance

We consider the signature reversing transformation of the metric tensor g_ab goes to -g_ab induced by the chiral transformation of the curved space gamma matrices gamma_a goes to gamma gamma_a in spacetimes with signature (S,T), which also induces a (-1)^T spacetime orientation reversal. We conclude: (1) It is a symmetry only for chiral theories with S-T= 4k, with k integer. (2) Yang-Mills theories require dimensions D=4k with T even for which even rank antisymmentric tensor field strengths and mass terms are also allowed. For example, D=10 super Yang-Mills is ruled out. (3) Gravititational theories require dimensions D=4k+2 with T odd, for which the symmetry is preserved by coupling to odd rank field strengths. In D=10, for example, it is a symmetry of N=1 and Type IIB supergravity but not Type IIA. A cosmological term and also mass terms are forbidden but non-minimal R phi^2 coupling is permitted. (4) Spontaneous compactification from D=4k+2 leads to interesting but different symmetries in lower dimensions such as D=4, so Yang-Mills terms, Kaluza-Klein masses and a cosmological constant may then appear. As a well-known example, IIB permits AdS_5 x S^5.Comment: LaTex, 31 pages; v3: Extended discussion of fermions without vielbeins. Version to appear in Nucl. Phys.

Topological Quantum Field Theory on Non-Abelian Gerbes

The infinitesimal symmetries of a fully decomposed non-Abelian gerbe can be generated in terms of a nilpotent BRST operator, which is here constructed. The appearing fields find a natural interpretation in terms of the universal gerbe, a generalisation of the universal bundle. We comment on the construction of observables in the arising Topological Quantum Field Theory. It is also shown how the BRST operator and the trace part of a suitably truncated set of fields on the non-Abelian gerbe reduce directly to the coboundary operator and the pertinent cochains of the underlying Cech-de Rham complex.Comment: 36 pages, LaTeX; v2: version to appear in J.Geom.Phy

Holonomies of Intersecting Branes

We discuss the geometry of string and M-theory gauge fields in Deligne cohomology. In particular, we show how requiring string structure (or loop space Spin-C structure) on the five-brane leads to topological conditions on the flux in the relative Deligne cohomology of the bulk - brain pair.Comment: 8 pages, LaTeX, talk given in the RTN Workshop "The quantum structure of spacetime and the geometric nature of fundamental interactions," (Kolymbari, Greece, September 2004

Large Gauge Transformations in M-theory

We cast M-brane interactions including intersecting membranes and five-branes in manifestly gauge invariant form using an arrangement of higher dimensional Dirac surfaces. We show that the noncommutative gauge symmetry present in the doubled M-theory formalism involving dual 3-form and 6-form gauge fields is preserved in a form quantised over the integers. The proper context for discussing large noncommutative gauge transformations is relative cohomology, in which the 3-form transformation parameters become exact when restricted to the five-brane worldvolume. We show how this structure yields the lattice of M-theory charges and gives rise to the conjectured 7D Hopf-Wess-Zumino term.Comment: 45 pages, 9 figures, LaTe

Non-Geometric Magnetic Flux and Crossed Modules

It is shown that the BRST operator of twisted N=4 Yang-Mills theory in four dimensions is locally the same as the BRST operator of a fully decomposed non-Abelian gerbe. Using locally defined Yang-Mills theories we describe non-perturbative backgrounds that carry a novel magnetic flux. Given by elements of the crossed module G x Aut G, these non-geometric fluxes can be classified in terms of the cohomology class of the underlying non-Abelian gerbe, and generalise the centre ZG valued magnetic flux found by 't Hooft. These results shed light also on the description of non-local dynamics of the chiral five-brane in terms of non-Abelian gerbes.Comment: 26 pages, LaTeX; v2: expanded, typos corrected; v3: typos corrected, version to apper in Nucl. Phys.

Holographic Renormalisation and Anomalies

The Weyl anomaly in the Holographic Renormalisation Group as implemented using Hamilton-Jacobi language is studied in detail. We investigate the breakdown of the descent equations in order to isolate the Weyl anomaly of the dual field theory close to the (UV) fixed point. We use the freedom of adding finite terms to the renormalised effective action in order to bring the anomalies in the expected form. We comment on different ways of describing the bare and renormalised schemes, and on possible interpretations of the descent equations as describing the renormalisation group flow non-perturbatively. We find that under suitable assumptions these relations may lead to a class of c-functions.Comment: 17 page