193 research outputs found
Noncommutative Riemann Surfaces
We compactify M(atrix) theory on Riemann surfaces Sigma with genus g>1.
Following [1], we construct a projective unitary representation of pi_1(Sigma)
realized on L^2(H), with H the upper half-plane. As a first step we introduce a
suitably gauged sl_2(R) algebra. Then a uniquely determined gauge connection
provides the central extension which is a 2-cocycle of the 2nd Hochschild
cohomology group. Our construction is the double-scaling limit N\to\infty,
k\to-\infty of the representation considered in the Narasimhan-Seshadri
theorem, which represents the higher-genus analog of 't Hooft's clock and shift
matrices of QCD. The concept of a noncommutative Riemann surface Sigma_\theta
is introduced as a certain C^\star-algebra. Finally we investigate the Morita
equivalence.Comment: LaTeX, 1+14 pages. Contribution to the TMR meeting ``Quantum aspects
of gauge theories, supersymmetry and unification'', Paris 1-7 September 199
An action for the (2,0) self-dual tensor multiplet in a conformal supergravity background
We present the action for a self-dual tensor in six dimensions, coupled to a
(2,0) conformal supergravity background. This action gives rise to the expected
equations of motion. An alternative look upon one of the gauge symmetries
clarifies its role in the supersymmetry transformation rules and the
realisation of the algebra.Comment: 14 pages, accepted by Class. Quant. Gra
Symplectic structure free Chern-Simons Theory
The second class constraints algebra of the abelian Chern-Simons theory is
rigorously studied in terms of the Hamiltonian embedding in order to obtain the
first class constraint system. The symplectic structure of fields due to the
second class constraints disappears in the resulting system. Then we obtain a
new type of Chern-Simons action which has an infinite set of the irreducible
first class constraints and exhibits new extended local gauge symmetries
implemented by these first class constraints.Comment: 12 pages, LaTex, no figure
Black Holes in Supergravity and String Theory
We give an elementary introduction to black holes in supergravity and string
theory. The focus is on BPS solutions in four- and higher-dimensional
supergravity and string theory. Basic ideas and techniques are explained in
detail, including exercises with solutions.Comment: 64 pages, based on lectures given at the school of the TMR network
'Quantum aspects of gauge theories, supersymmetry and unification' in Torino,
January 26 - February 2, 2000. To be published in Class. Quant. Grav. (Some
typos corrected, two references added.
Twenty Years of the Weyl Anomaly
In 1973 two Salam prot\'{e}g\'{e}s (Derek Capper and the author) discovered
that the conformal invariance under Weyl rescalings of the metric tensor
displayed by classical
massless field systems in interaction with gravity no longer survives in the
quantum theory. Since then these Weyl anomalies have found a variety of
applications in black hole physics, cosmology, string theory and statistical
mechanics. We give a nostalgic review. (Talk given at the {\it Salamfest},
ICTP, Trieste, March 1993.)Comment: 43 page
Manifest Duality in Born-Infeld Theory
Born-Infeld theory is formulated using an infinite set of gauge fields, along
the lines of McClain, Wu and Yu. In this formulation electromagnetic duality is
generated by a fully local functional. The resulting consistency problems are
analyzed and the formulation is shown to be consistent.Comment: 15 pages, Late
Symmetries and degrees of freedom in 2-dimensional dual models
The 2-dimensional version of the Schwarz and Sen duality model (Tseytlin
model) is analyzed at the classical and quantum levels. The solutions are
obtained after removing the gauge dependent sector using the Dirac method. The
Poincar\`e invariance is verified at both levels. An extension with global
supersymmetry is also proposed.Comment: 3 pages, revtex, minor correction
Batalin-Vilkovisky gauge-fixing of a chiral two-form in six dimensions
We perform the gauge-fixing of the theory of a chiral two-form boson in six
dimensions starting from the action given by Pasti, Sorokin and Tonin. We use
the Batalin-Vilkovisky formalism, introducing antifields and writing down an
extended action satisfying the classical master equation. Then we gauge-fix the
three local symmetries of the extended action in two different ways.Comment: 15 pages, latex, no figures, version accepted by Class. Quant. Gra
- …