27 research outputs found

### 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.

### 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

### 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

### 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.

### Dimensionally Reduced Yang-Mills Theories in Noncommutative Geometry

We study a class of noncommutative geometries that give rise to dimensionally
reduced Yang-Mills theories. The emerging geometries describe sets of copies of
an even dimensional manifold. Similarities to the D-branes in string theory are
discussed.Comment: 12 pages, Latex, minor correction