L. Bonora

Noncommutative SO(n) and Sp(n) gauge theories

Abstract We study the generalization of noncommutative gauge theories to the case of orthogonal and symplectic groups. We find out that this is possible, since we are allowed to define orthogonal and symplectic subgroups of noncommutative unitary gauge transformations even though the gauge potentials and gauge transformations are not valued in the orthogonal and symplectic subalgebras of the Lie algebra of antihermitean matrices. Our construction relies on an anti-automorphism of the basic noncommutative algebra of functions which generalizes the charge conjugation operator of ordinary field theory. We show that the corresponding noncommutative picture from low energy string theory is obtained via orientifold projection in the presence of a non-trivial NSNS B field.

Conformal affine sl2 toda field theory

Abstract We present a model based on the sl 2 affine algebra, which is integrable and conformally invariant. It reduces to the standard Liouville theory or to the sinh-Gordon model under certain limiting conditions. We find the general classical solution of this model and the exchange algebra.

A note on consistent anomalies in noncommutative YM theories

Abstract Via descent equations we derive formulas for consistent gauge anomalies in noncommutative Yang–Mills theories.

A Global Operator Formalism on Higher Genus Riemann Surfaces: b — c Systems

We explicitly construct bases for meromorphicλ-differentials over genusg Riemann surfaces. With the help of these bases we introduce a new operator formalism over Riemann surfaces which closely resembles the operator formalism on the sphere. As an application we calculate the propagators forb-c systems with arbitrary integer or half-integerλ (in the Ramond and Neveu-Schwarz sectors). We also give explicit expressions for the zero modes and for the Teichmüller deformations for a generic Riemann surface.

String partition functions, Hilbert schemes and affine Lie algebra representations on homology groups

This review paper contains a concise introduction to highest weight representations of infinite dimensional Lie algebras, vertex operator algebras and Hilbert schemes of points, together with their physical applications to elliptic genera of superconformal quantum mechanics and superstring models. The common link of all these concepts and of the many examples considered in the paper is to be found in a very important feature of the theory of infinite dimensional Lie algebras: the modular properties of the characters (generating functions) of certain representations. The characters of the highest weight modules represent the holomorphic parts of the partition functions on the torus for the corresponding conformal field theories. We discuss the role of the unimodular (and modular) groups and the (Selberg-type) Ruelle spectral functions of hyperbolic geometry in the calculation of elliptic genera and associated q-series. For mathematicians, elliptic genera are commonly associated to new mathematical invariants for spaces, while for physicists elliptic genera are one-loop string partition function (therefore they are applicable, for instance, to topological Casimir effect calculations). We show that elliptic genera can be conveniently transformed into product expressions which can then inherit the homology properties of appropriate polygraded Lie algebras.

Relevant deformations in open string field theory: a simple solution for lumps

A bstractWe propose a remarkably simple solution of cubic open string field theory which describes inhomogeneous tachyon condensation. The solution is in one-to-one correspondence with the IR fixed point of the RG-flow generated in the two-dimensional worldsheet theory by integrating a relevant operator with mild enough OPE on the boundary. It is shown how the closed string overlap correctly captures the shift in the closed string one point function between the UV and the IR limits of the flow. Examples of lumps in non-compact and compact transverse directions are given.

Chiral anomalies in higher dimensional supersymmetric theories

Abstract We derive explicit formulas for pure gauge anomalies in a SYM theory in 6D as well as in 10D. Each anomaly consists of two terms: a gauge cocycle and a cocycle of the superdiffeomorphisms. The derivation is based essentially on a remarkable property of supersymmetric theories which we call Weil triviality and is directly connected with the constraints. The analogous problem for Lorentz anomalies is stated in the same way. However, in general, there are difficulties concerning Weil triviality. We prove that for pure SUGRA in 6D as well as in 10D it is possible to prove Weil triviality and, consequently, to obtain explicit expressions for pure Lorentz anomalies. However, as far as SUGRA coupled to SYM a la Chapline-Manton or a la Green-Schwarz is concerned, no self-evident solution is available.

An alternative approach to KP hierarchy in matrix models

Abstract We show that there exists an alternative procedure in order to extract differential hierarchies, such as the KdV hierarchy, from one-matrix models, without taking a continuum limit . To prove this we introduce the Toda lattice and reformulate it in operator form. We then consider the reduction to the systems appropriate for a one-matrix model.We show that there exists an alternative procedure in order to extract differential hierarchies, such as the KdV hierarchy, from one--matrix models, without taking a continuum limit. To prove this we introduce the Toda lattice and reformulate it in operator form. We then consider the reduction to the systems appropriate for one--matrix model.

String interactions from Matrix string theory

Matrix string theory, i.e. the two-dimensional U(N) SYM with N = (8,8) supersymmetry, has classical BPS solutions that interpolate between an initial and a final string configuration via a bordered Riemann surface. The Matrix string theory amplitudes around such a classical BPS background, in the strong Yang-Mills coupling, are therefore candidates to be interpreted in a stringy way as the transition amplitude between given initial and final string configurations. In this paper we calculate these amplitudes and show that the leading contribution is proportional to the factor gs−χ, where χ is the Euler characteristic of the interpolating Riemann surface and gs is the string coupling. This is the factor one expects from perturbative string interaction theory.

The Sugawara construction on genus-g Riemann surfaces

Abstract By using the formalism recently developed by Krichever and Novikov, we carry out the Sugawara construction for a Kac-Moody algebra defined over a generic Riemann surface.