The Euler-Heisenberg Lagrangian beyond one loop

We review what is presently known about higher loop corrections to the Euler-Heisenberg Lagrangian and its Scalar QED analogue. The use of those corrections as a tool for the study of the properties of the QED perturbation series is outlined. As a further step in a long-term effort to prove or disprove the convergence of the N photon amplitudes in the quenched approximation, we present a parameter integral representation of the three-loop Euler-Heisenberg Lagrangian in 1+1 dimensional QED, obtained in the worldline formalism.Comment: 11 pages, 2 figures, talk given by Christian Schubert at QFEXT11, Benasque, Spain, Sept. 18-24, 2011, to appear in the conference proceeding

A Gauge-Gravity Relation in the One-loop Effective Action

We identify an unusual new gauge-gravity relation: the one-loop effective action for a massive spinor in 2n dimensional AdS space is expressed in terms of precisely the same function [a certain multiple gamma function] as the one-loop effective action for a massive charged scalar in 4n dimensions in a maximally symmetric background electromagnetic field [one for which the eigenvalues of F_{\mu\nu} are maximally degenerate, corresponding in 4 dimensions to a self-dual field, equivalently to a field of definite helicity], subject to the identification F^2 \Lambda, where \Lambda is the gravitational curvature. Since these effective actions generate the low energy limit of all one-loop multi-leg graviton or gauge amplitudes, this implies a nontrivial gauge-gravity relation at the non-perturbative level and at the amplitude level.Comment: 6 page

On the Yang-Mills two-loop effective action with wordline methods

We derive the two-loop effective action for covariantly constant field strength of pure Yang-Mills theory in the presence of an infrared scale. The computation is done in the framework of the worldline formalism, based on a generalization procedure of constructing multiloop effective actions in terms of the bosonic worldline path integral. The two-loop beta-function is correctly reproduced. This is the first derivation in the worldline formulation, and serves as a nontrivial check on the consistency of the multiloop generalization procedure in the worldline formalism.Comment: 8 pages, 4 figure

Braided Oscillators

The braided Hopf algebra structure of the generalized oscillator is investigated. Using the solutions two types of braided Fibonacci oscillators are introduced. This leads to two types of braided Biedenharn-Macfarlane oscillators.Comment: 12 pages, latex, some references added, published versio

Exact computation of one-loop correction to energy of spinning folded string in AdS_5 x S^5

We consider the 1-loop correction to the energy of folded spinning string solution in the AdS_3 part of AdS_5 x S^5. The classical string solution is expressed in terms of elliptic functions so an explicit computation of the corresponding fluctuation determinants for generic values of the spin appears to be a non-trivial problem. We show how it can be solved exactly by using the static gauge expression for the string partition function (which we demonstrate to be equivalent to the conformal gauge one) and observing that all the corresponding second order fluctuation operators can be put into the standard (single-gap) Lam\'e form. We systematically derive the small spin and large spin expansions of the resulting expression for the string energy and comment on some of their applications.Comment: 52 pp, 12 figures; v3: footnote 9 adde