4,395 research outputs found
Getting superstring amplitudes by degenerating Riemann surfaces
We explicitly show how the chiral superstring amplitudes can be obtained
through factorisation of the higher genus chiral measure induced by suitable
degenerations of Riemann surfaces. This powerful tool also allows to derive, at
any genera, consistency relations involving the amplitudes and the measure. A
key point concerns the choice of the local coordinate at the node on degenerate
Riemann surfaces that greatly simplifies the computations. As a first
application, starting from recent ansaetze for the chiral measure up to genus
five, we compute the chiral two-point function for massless Neveu-Schwarz
states at genus two, three and four. For genus higher than three, these
computations include some new corrections to the conjectural formulae appeared
so far in the literature. After GSO projection, the two-point function vanishes
at genus two and three, as expected from space-time supersymmetry arguments,
but not at genus four. This suggests that the ansatz for the superstring
measure should be corrected for genus higher than four.Comment: 32 pages; v2: minor corrections, references adde
Quantum geometry of 3-dimensional lattices
We study geometric consistency relations between angles on 3-dimensional (3D)
circular quadrilateral lattices -- lattices whose faces are planar
quadrilaterals inscribable into a circle. We show that these relations generate
canonical transformations of a remarkable ``ultra-local'' Poisson bracket
algebra defined on discrete 2D surfaces consisting of circular quadrilaterals.
Quantization of this structure leads to new solutions of the tetrahedron
equation (the 3D analog of the Yang-Baxter equation). These solutions generate
an infinite number of non-trivial solutions of the Yang-Baxter equation and
also define integrable 3D models of statistical mechanics and quantum field
theory. The latter can be thought of as describing quantum fluctuations of
lattice geometry. The classical geometry of the 3D circular lattices arises as
a stationary configuration giving the leading contribution to the partition
function in the quasi-classical limit.Comment: 27 pages, 10 figures. Minor corrections, references adde
Quantum Geometry of 3-Dimensional Lattices and Tetrahedron Equation
We study geometric consistency relations between angles of 3-dimensional (3D)
circular quadrilateral lattices -- lattices whose faces are planar
quadrilaterals inscribable into a circle. We show that these relations generate
canonical transformations of a remarkable "ultra-local" Poisson bracket algebra
defined on discrete 2D surfaces consisting of circular quadrilaterals.
Quantization of this structure allowed us to obtain new solutions of the
tetrahedron equation (the 3D analog of the Yang-Baxter equation) as well as
reproduce all those that were previously known. These solutions generate an
infinite number of non-trivial solutions of the Yang-Baxter equation and also
define integrable 3D models of statistical mechanics and quantum field theory.
The latter can be thought of as describing quantum fluctuations of lattice
geometry.Comment: Plenary talk at the XVI International Congress on Mathematical
Physics, 3-8 August 2009, Prague, Czech Republi
T-duality Twists and Asymmetric Orbifolds
We study some aspects of asymmetric orbifolds of tori, with the orbifold
group being some subgroup of the T-duality group and, in
particular, provide a concrete understanding of certain phase factors that may
accompany the T-duality operation on the stringy Hilbert space in toroidal
compactification. We discuss how these T-duality twist phase factors are
related to the symmetry and locality properties of the closed string vertex
operator algebra, and clarify the role that they enact in the modular
covariance of the orbifold theory, mainly using asymmetric orbifolds of tori
which are root lattices as working examples.Comment: 67 pages. v2: references added and typos correcte
- …