76,273 research outputs found
Towards Quantum Dielectric Branes: Curvature Corrections in Abelian Beta Function and Nonabelian Born-Infeld Action
We initiate a programme to compute curvature corrections to the nonabelian BI
action. This is based on the calculation of derivative corrections to the
abelian BI action, describing a maximal brane, to all orders in F. An exact
calculation in F allows us to apply the SW map, reducing the maximal abelian
point of view to a minimal nonabelian point of view (replacing 1/F with [X,X]
at large F), resulting in matrix model equations of motion. We first study
derivative corrections to the abelian BI action and compute the 2-loop beta
function for an open string in a WZW (parallelizable) background. This beta
function is the first step in the process of computing string equations of
motion, which can be later obtained by computing the Weyl anomaly coefficients
or the partition function. The beta function is exact in F and computed to
orders O(H,H^2,H^3) (H=dB and curvature is R ~ H^2) and O(DF,D^2F,D^3F). In
order to carry out this calculation we develop a new regularization method for
2-loop graphs. We then relate perturbative results for abelian and nonabelian
BI actions, by showing how abelian derivative corrections yield nonabelian
commutator corrections, at large F. We begin the construction of a matrix model
describing \a' corrections to Myers' dielectric effect. This construction is
carried out by setting up a perturbative classification of the relevant
nonabelian tensor structures, which can be considerably narrowed down by the
constraint of translation invariance in the action and the possibility for
generic field redefinitions. The final matrix action is not uniquely determined
and depends upon two free parameters. These parameters could be computed via
further calculations in the abelian theory.Comment: JHEP3.cls, 64 pages, 3 figures; v2: added references; v3: more
references, final version for NP
A Diagrammatic Equation for Oriented Planar Graphs
In this paper we introduce a diagrammatic equation for the planar sector of
square non hermitian random matrix models strongly reminiscent of Polchinski's
equation in quantum field theory. Our fundamental equation is first obtained by
a graph counting argument and subsequently derived independently by a precise
saddle point analysis of the corresponding random matrix integral. We solve the
equation perturbatively for a generic model and conclude by exhibiting two
duality properties of the perturbative solution.Comment: References [12] and [13] and subsequent discussion adde
On the refined counting of graphs on surfaces
Ribbon graphs embedded on a Riemann surface provide a useful way to describe
the double line Feynman diagrams of large N computations and a variety of other
QFT correlator and scattering amplitude calculations, e.g in MHV rules for
scattering amplitudes, as well as in ordinary QED. Their counting is a special
case of the counting of bi-partite embedded graphs. We review and extend
relevant mathematical literature and present results on the counting of some
infinite classes of bi-partite graphs. Permutation groups and representations
as well as double cosets and quotients of graphs are useful mathematical tools.
The counting results are refined according to data of physical relevance, such
as the structure of the vertices, faces and genus of the embedded graph. These
counting problems can be expressed in terms of observables in three-dimensional
topological field theory with S_d gauge group which gives them a topological
membrane interpretation.Comment: 57 pages, 12 figures; v2: Typos corrected; references adde
Low momentum expansion of one loop amplitudes in heterotic string theory
We consider the low momentum expansion of the four graviton and the two
graviton--two gluon amplitudes in heterotic string theory at one loop in ten
dimensions, and analyze contributions upto the D^2 R^4 interaction from the
four graviton amplitude, and the D^4 R^2 F^2 interaction from the two
graviton--two gluon amplitude. The calculations are performed by obtaining
equations for the relevant modular graph functions that arise in the modular
invariant integrals, and involve amalgamating techniques used in the type II
theory and the calculation of the elliptic genus in the heterotic theory.Comment: 67 pages, LaTeX, 14 figure
On the Infrared Behavior of Landau Gauge Yang-Mills Theory with a Fundamentally Charged Scalar Field
Recently it has been shown that infrared singularities of Landau gauge QCD
can confine static quarks via a linearly rising potential. We show that the
same mechanism can also provide a confining interaction between charged scalar
fields in the fundamental representation. This confirms that within this
scenario static confinement is a universal property of the gauge sector even
though it is formally represented in the functional equations of the matter
sector. The simplifications compared to the fermionic case make the scalar
system an ideal laboratory for a detailed analysis of the confinement mechanism
in numerical studies of the functional equations as well as in gauge-fixed
lattice simulations.Comment: 8 pages, PDFLaTe
The resultant parameters of effective theory
This is the 4-th paper in the series devoted to a systematic study of the
problem of mathematically correct formulation of the rules needed to manage an
effective field theory. Here we consider the problem of constructing the full
set of essential parameters in the case of the most general effective
scattering theory containing no massless particles with spin J > 1/2. We
perform the detailed classification of combinations of the Hamiltonian coupling
constants and select those which appear in the expressions for renormalized
S-matrix elements at a given loop order.Comment: 21 pages, 4 LaTeX figures, submitted to Phys. Rev.
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