95,235 research outputs found
Free Field Theory as a String Theory?
An approach to systematically implement open-closed string duality for free
large gauge theories is summarised. We show how the relevant closed string
moduli space emerges from a reorganisation of the Feynman diagrams contributing
to free field correlators. We also indicate why the resulting integrand on
moduli space has the right features to be that of a string theory on .Comment: 10 pages, 1 figure, Contribution to Strings 2004 (Paris) proceeding
Feynman graph polynomials
The integrand of any multi-loop integral is characterised after Feynman
parametrisation by two polynomials. In this review we summarise the properties
of these polynomials. Topics covered in this article include among others:
Spanning trees and spanning forests, the all-minors matrix-tree theorem,
recursion relations due to contraction and deletion of edges, Dodgson's
identity and matroids.Comment: 35 pages, references adde
Properties of Feynman graph polynomials
In this talk I discuss properties of the two Symanzik polynomials which
characterise the integrand of an arbitrary multi-loop integral in its Feynman
parametric form. Based on the construction from spanning forests and Laplacian
matrices, Dodgson's relation is applied to derive factorisation identities
involving both polynomials. An application of Whitney's 2-isomorphism theorem
on matroids is discussed.Comment: Talk given at the International Workshop 'Loops and Legs in Quantum
Field Theory' (April 25-30, 2010, W\"orlitz, Germany
Relating Covariant and Canonical Approaches to Triangulated Models of Quantum Gravity
In this paper explore the relation between covariant and canonical approaches
to quantum gravity and theory. We will focus on the dynamical
triangulation and spin-foam models, which have in common that they can be
defined in terms of sums over space-time triangulations. Our aim is to show how
we can recover these covariant models from a canonical framework by providing
two regularisations of the projector onto the kernel of the Hamiltonian
constraint. This link is important for the understanding of the dynamics of
quantum gravity. In particular, we will see how in the simplest dynamical
triangulations model we can recover the Hamiltonian constraint via our
definition of the projector. Our discussion of spin-foam models will show how
the elementary spin-network moves in loop quantum gravity, which were
originally assumed to describe the Hamiltonian constraint action, are in fact
related to the time-evolution generated by the constraint. We also show that
the Immirzi parameter is important for the understanding of a continuum limit
of the theory.Comment: 28 pages, 10 figure
The One-Loop Five-Graviton Scattering Amplitude and Its Low-Energy Limit
A covariant path integral calculation of the even spin structure contribution
to the one-loop N-graviton scattering amplitude in the type-II superstring
theory is presented. The apparent divergence of the amplitude is resolved
by separating it into twelve independent terms corresponding to different
orders of inserting the graviton vertex operators. Each term is well defined in
an appropriate kinematic region and can be analytically continued to physical
regions where it develops branch cuts required by unitarity. The zero-slope
limit of the amplitude is performed, and the Feynman diagram content of
the low-energy field theory is examined. Both one-particle irreducible (1PI)
and one-particle redicible (1PR) graphs with massless internal states are
generated in this limit. One set of 1PI graphs has the same divergent
dependence on the cut-off as that found in the four-graviton case, and it is
proved that such graphs exist for all~. The 1PR graphs are contributed by
the poles in the world-sheet chiral Green functions.Comment: 23 pages, ITP-SB-92-6
UV/IR Mixing for Noncommutative Complex Scalar Field Theory, II (Interaction with Gauge Fields)
We consider noncommutative analogs of scalar electrodynamics and N=2 D=4 SUSY
Yang-Mills theory. We show that one-loop renormalizability of noncommutative
scalar electrodynamics requires the scalar potential to be an anticommutator
squared. This form of the scalar potential differs from the one expected from
the point of view of noncommutative gauge theories with extended SUSY
containing a square of commutator. We show that fermion contributions restore
the commutator in the scalar potential. This provides one-loop
renormalizability of noncommutative N=2 SUSY gauge theory. We demonstrate a
presence of non-integrable IR singularities in noncommutative scalar
electrodynamics for general coupling constants. We find that for a special
ratio of coupling constants these IR singularities vanish. Also we show that IR
poles are absent in noncommutative N=2 SUSY gauge theory.Comment: 9 pages, 16 EPS figure
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