9 research outputs found
g-Functions and gluon scattering amplitudes at strong coupling
We study gluon scattering amplitudes/Wilson loops in N=4 super Yang-Mills
theory at strong coupling by calculating the area of the minimal surfaces in
AdS_3 based on the associated thermodynamic Bethe ansatz system. The remainder
function of the amplitudes is computed by evaluating the free energy, the T-
and Y-functions of the homogeneous sine-Gordon model. Using conformal field
theory (CFT) perturbation, we examine the mass corrections to the free energy
around the CFT point corresponding to the regular polygonal Wilson loop. Based
on the equivalence between the T-functions and the g-functions, which measure
the boundary entropy, we calculate corrections to the T- and Y-functions as
well as express them at the CFT point by the modular S-matrix. We evaluate the
remainder function around the CFT point for 8 and 10-point amplitudes
explicitly and compare these analytic expressions with the 2-loop formulas. The
two rescaled remainder functions show very similar power series structures.Comment: 51 pages, 4 figures, v2: some comments and references added, based on
the published version, v3: minor change
On O(1) contributions to the free energy in Bethe Ansatz systems: the exact g-function
We investigate the sub-leading contributions to the free energy of Bethe
Ansatz solvable (continuum) models with different boundary conditions. We show
that the Thermodynamic Bethe Ansatz approach is capable of providing the O(1)
pieces if both the density of states in rapidity space and the quadratic
fluctuations around the saddle point solution to the TBA are properly taken
into account. In relativistic boundary QFT the O(1) contributions are directly
related to the exact g-function. In this paper we provide an all-orders proof
of the previous results of P. Dorey et al. on the g-function in both massive
and massless models. In addition, we derive a new result for the g-function
which applies to massless theories with arbitrary diagonal scattering in the
bulk.Comment: 28 pages, 2 figures, v2: minor corrections, v3: minor corrections and
references adde
The Form Factors and Quantum Equation of Motion in the sine-Gordon Model
Using the methods of the 'form factor program' exact expressions of all
matrix elements are obtained for several operators of the quantum sine-Gordon
model alias the massive Thirring model. A general formula is presented which
provides form factors in terms of an integral representation. In particular
charge-less operators as for example the current of the topological charge, the
energy momentum tensor and all higher currents are considered. In the breather
sector it is found the quantum sine-Gordon field equation holds with an exact
relation between the 'bare' mass and the normalized mass. Also a relation for
the trace of the energy momentum is obtained. All results are compared with
Feynman graph expansion and full agreement is found.Comment: TCI-LaTeX, 21 pages with 2 figur
Dynamical Properties of one dimensional Mott Insulators
At low energies the charge sector of one dimensional Mott insulators can be
described in terms of a quantum Sine-Gordon model. Using exact results derived
from integrability it is possible to determine dynamical properties like the
frequency dependent optical conductivity. We compare the exact results to
perturbation theory and renormalisation group calculations. We also discuss the
application of our results to experiments on quasi-1D organic conductors.Comment: 17 pages, 5 figures, to appear in the proceedings of the NATO ASI/EC
summer school "New Theoretical Approaches to Strongly Correlated Systems"
Newton Institute for Mathematical Sciences, Cambridge UK, April 200
THE SPECTRUM OF BOUNDARY SINE- GORDON THEORY ∗
We review our recent results on the on-shell description of sine-Gordon model with integrable boundary conditions. We determined the spectrum of boundary states by closing the boundary bootstrap and gave a derivation of Al.B. Zamolodchikov’s (unpublished) formulae for the boundary energy and the relation between the Lagrangian (ultraviolet) and bootstrap (infrared) parameters. These results have been checked against numerical finite volume spectra coming from the truncated conformal space approach. We find an entirely consistent picture and strong evidence for the validity of the conjectured spectrum and scattering amplitudes, which together give a complete description of the boundary sine-Gordon theory on mass shell