Geometry of spin-field coupling on the worldline

We derive a geometric representation of couplings between spin degrees of freedom and gauge fields within the worldline approach to quantum field theory. We combine the string-inspired methods of the worldline formalism with elements of the loop-space approach to gauge theory. In particular, we employ the loop (or area) derivative operator on the space of all holonomies which can immediately be applied to the worldline representation of the effective action. This results in a spin factor that associates the information about spin with "zigzag" motion of the fluctuating field. Concentrating on the case of quantum electrodynamics in external fields, we obtain a purely geometric representation of the Pauli term. To one-loop order, we confirm our formalism by rederiving the Heisenberg-Euler effective action. Furthermore, we give closed-form worldline representations for the all-loop order effective action to lowest nontrivial order in a small-N_f expansion.Comment: 18 pages, v2: references added, minor changes, matches PRD versio

On the Gluon Regge Trajectory in O(αs2)O(\alpha_s^2)

We recalculate the gluon Regge trajectory in next-to-leading order to clarify a discrepancy between two results in the literature on the constant part. We confirm the result obtained by Fadin et al.~\cite{FFK}. The effects on the anomalous dimension and on the $s^{\omega}$ behavior of inclusive cross sections are also discussed.Comment: 8 pages Latex + 1 style file all compressed by uufile

Hexagon remainder function in the limit of self-crossing up to three loops

We consider Wilson loops in planar N=4 SYM for null polygons in the limit of two crossing edges. The analysis is based on a renormalisation group technique. We show that the previously obtained result for the leading and next-leading divergent term of the two loop hexagon remainder is in full agreement with the appropriate continuation of the exact analytic formula for this quantity. Furthermore, we determine the coefficients of the leading and next-leading singularity for the three loop remainder function for null n-gons with n >= 6.Comment: 19 pages, 4 figures, typos corrected, comment on relation to recent results for the symbol of three-loop remainder added, version to appear in JHE

Implications of multi-Regge limits for the Bern-Dixon-Smirnov conjecture

Planar ${\cal N} =4$ super Yang-Mills SU(N) theory is expected to exhibit stringy behavior, anticipated by the 't Hooft genus expansion and the $AdS/CFT$ correspondence. We examine the Bern-Dixon-Smirnov (BDS) conjecture for $n$-gluon amplitudes in the context of single-Regge and multi-Regge limits and show that these amplitudes have the expected Regge form in the Euclidean region.Comment: 48 pages, 8 figures; Noted added commenting on related work which appeared after the initial posting. References and clarifications added, as well as typos correcte

From correlation functions to scattering amplitudes

We study the correlators of half-BPS protected operators in N=4 super-Yang-Mills theory, in the limit where the positions of the adjacent operators become light-like separated. We compute the loop corrections by means of Lagrangian insertions. The divergences resulting from the light-cone limit are regularized by changing the dimension of the integration measure over the insertion points. Switching from coordinates to dual momenta, we show that the logarithm of the correlator is identical with twice the logarithm of the matching MHV gluon scattering amplitude. We present a number of examples of this new relation, at one and two loops.Comment: typos corrected, references adde

Worldline Approach to Forward and Fixed Angle fermion-fermion Scattering in Yang-Mills Theories at High Energies

Worldline techniques are employed to study the general behaviour of the fermion-fermion collision amplitude at very high energies in a non-abelian gauge field theory for the forward and fixed angle scattering cases. A central objective of this work is to demonstrate the simplicity by which the worldline methodology isolates that sector of the full theory which carries the soft physics, relevant to each process. Anomalous dimensions pertaining to a given soft sector are identified and subseuently used to facilitate the renormalization group running of the respective four point functions. Gluon reggeization is achieved for forward, while Sudakov suppression is established for fixed angle scattering.Comment: 28 pages, 10 figures in three file

Nonperturbative contributions to the quark form factor at high energy

The analysis of nonperturbative effects in high energy asymptotics of the electomagnetic quark form factor is presented. It is shown that the nonperturbative effects determine the initial value for the perturbative evolution of the quark form factor and find their general structure with respect to the high energy asymptotics. Within the Wilson integral formalism which is natural for investigation of the soft, IR sensitive, part of the factorized form factor, the structure of the instanton induced effects in the evolution equation is discussed. It is demonstrated that the instanton contributions result in the finite renormalization of the subleading perturbative result and numerically are characterized by small factor reflecting the diluteness of the QCD vacuum within the instanton liquid model. The relevance of the IR renormalon induced effects in high energy asymptotic behaviour is discussed. The consequences of the various analytization procedures of the strong coupling constant in the IR domain are considered.Comment: REVTeX, 12 pages, 1 figure. Important references and discussions added, misprints corrected, minor changes in tex

Analyticity for Multi-Regge Limits of the Bern-Dixon-Smirnov Amplitudes

As a consequence of the AdS/CFT correspondence, planar ${\cal N} =4$ super Yang-Mills SU(N) theory is expected to exhibit stringy behavior and multi-Regge asymptotic. In this paper we extend our recent investigation to consider issues of analyticity, a central feature of Regge asymptotics. We contrast flat-space open string theory in the planar limit with the ${\cal N}=4$ super Yang-Mills theory, as represented by the Bern, Dixon and Smirnov \cite{Bern:2005iz} (BDS) conjecture for n-gluon scattering, believed to be exact for $n=4,5$ and modified only by a function of cross-ratios for $n\geq 6$. It is emphasized that multi-Regge factorization should be applied to trajectories with definite signature. A variety of analyticity and factorization constraints realized in flat space string theory are not satisfied by the BDS conjecture, at least when the exponential factors are truncate in the infra-red regulator below $O(\epsilon)$.Comment: Published version of the paper, which includes an expanded discussion on Steinmann Relation for 5-point function, (sect. 4.3 and footnotes #9 and #10) as well as additional clarifying comments on how this work compares to other recent related works in the concluding section. 74 pages, 17 figure

Instanton Corrections to Quark Form Factor at Large Momentum Transfer

Within the Wilson integral formalism, we discuss the structure of nonperturbative corrections to the quark form factor at large momentum transfer analyzing the infrared renormalon and instanton effects. We show that the nonperturbative effects determine the initial value for the perturbative evolution of the quark form factor and attribute their general structure to the renormalon ambiguities of the perturbative series. It is demonstrated that the instanton contributions result in the finite renormalization of the next-to-leading perturbative result and numerically are characterized by a small factor reflecting the diluteness of the QCD vacuum within the instanton liquid model.Comment: Version coincident with the journal publication, 9 pages; REVTe