Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userChiral Observables and Modular Invariants
109
0
0.0
(
0
)
Added by
Karl-Henning Rehren
Publication date
1999
fields
Physics
and research's language is
English
Authors
K.-H. Rehren
Ask ChatGPT about the research
No Arabic abstract
Various definitions of chiral observables in a given Moebius covariant two-dimensional theory are shown to be equivalent. Their representation theory in the vacuum Hilbert space of the 2D theory is studied. It shares the general characteristics of modular invariant partition functions, although SL(2,Z) transformation properties are not assumed. First steps towards classification are made.
rate research
Read More
We introduce a new approach to find the Tomita-Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo-Martin-Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann-Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.
We give a pedagogical review of the computation of Gromov-Witten invariants via localization in 2D gauged linear sigma models. We explain the relationship between the two-sphere partition function of the theory and the Kahler potential on the conformal manifold. We show how the Kahler potential can be assembled from classical, perturbative, and non-perturbative contributions, and explain how the non-perturbative contributions are related to the Gromov-Witten invariants of the corresponding Calabi-Yau manifold. We then explain how localization enables efficient calculation of the two-sphere partition function and, ultimately, the Gromov-Witten invariants themselves.
We construct a sheaf of Fock spaces over the moduli space of elliptic curves E_y with Gamma_1(3)-level structure, arising from geometric quantization of H^1(E_y), and a global section of this Fock sheaf. The global section coincides, near appropriate limit points, with the Gromov-Witten potentials of local P^2 and of the orbifold C^3/mu_3. This proves that the Gromov-Witten potentials of local P^2 are quasi-modular functions for the group Gamma_1(3), as predicted by Aganagic-Bouchard-Klemm, and proves the Crepant Resolution Conjecture for [C^3/mu_3] in all genera.
In earlier work we studied features of non-holomorphic modular functions associated with Feynman graphs for a conformal scalar field theory on a two-dimensional torus with zero external momenta at all vertices. Such functions, which we will refer to as modular graph functions, arise, for example, in the low energy expansion of genus-one Type II superstring amplitudes. We here introduce a class of single-valued elliptic multiple polylogarithms, which are defined as elliptic functions associated with Feynman graphs with vanishing external momenta at all but two vertices. These functions depend on a coordinate, $zeta$, on the elliptic curve and reduce to modular graph functions when $zeta$ is set equal to $1$. We demonstrate that these single-valued elliptic multiple polylogarithms are linear combinations of multiple polylogarithms, and that modular graph functions are sums of single-valued elliptic multiple polylogarithms evaluated at the identity of the elliptic curve, in both cases with rational coefficients. This insight suggests the many interrelations between modular graph functions (a few of which were established in earlier papers) may be obtained as a consequence of identities involving multiple polylogarithms, and explains an earlier observation that the coefficients of the Laurent polynomial at the cusp are given by rational numbers times single-valued multiple zeta values.
We revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical observables. Wave equations on noncommutative spaces are derived from a quantum Hodge star operator. This general noncommutative geometry construction is then exemplified in the case of k-Minkowski spacetime. The corresponding quantum Poincare-Weyl Lie algebra of infinitesimal translations, rotations and dilatations is obtained. The dAlembert wave operator coincides with the quadratic Casimir of quantum translations and it is deformed as in Deformed Special Relativity theories. Also momenta (infinitesimal quantum translations) are deformed, and correspondingly the Einstein-Planck relation and the de Broglie one. The energy-momentum relations (dispersion relations) are consequently deduced. These results complement those of the phenomenological literature on the subject.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
