On the spectral problem of N=4 SYM with orthogonal or symplectic gauge group

We study the spectral problem of N=4 SYM with gauge group SO(N) and Sp(N). At the planar level, the difference to the case of gauge group SU(N) is only due to certain states being projected out, however at the non-planar level novel effects appear: While 1/N-corrections in the SU(N) case are always associated with splitting and joining of spin chains, this is not so for SO(N) and Sp(N). Here the leading 1/N-corrections, which are due to non-orientable Feynman diagrams in the field theory, originate from a term in the dilatation operator which acts inside a single spin chain. This makes it possible to test for integrability of the leading 1/N-corrections by standard (Bethe ansatz) means and we carry out various such tests. For orthogonal and symplectic gauge group the dual string theory lives on the orientifold AdS5xRP5. We discuss various issues related to semi-classical strings on this background.Comment: 25 pages, 3 figures. v2: Minor clarifications, section 5 expande

Wilson Expansion of QCD Propagators at Three Loops: Operators of Dimension Two and Three

In this paper we construct the Wilson short distance operator product expansion for the gluon, quark and ghost propagators in QCD, including operators of dimension two and three, namely, A^2, m^2, m A^2, \ovl{\psi} \psi and m^3. We compute analytically the coefficient functions of these operators at three loops for all three propagators in the general covariant gauge. Our results, taken in the Landau gauge, should help to improve the accuracy of extracting the vacuum expectation values of these operators from lattice simulation of the QCD propagators.Comment: 20 pages, no figure

Feynman Rules for the Rational Part of the Standard Model One-loop Amplitudes in the 't Hooft-Veltman γ5\gamma_5 Scheme

We study Feynman rules for the rational part $R$ of the Standard Model amplitudes at one-loop level in the 't Hooft-Veltman $\gamma_5$ scheme. Comparing our results for quantum chromodynamics and electroweak 1-loop amplitudes with that obtained based on the Kreimer-Korner-Schilcher (KKS) $\gamma_5$ scheme, we find the latter result can be recovered when our $\gamma_5$ scheme becomes identical (by setting $g5s=1$ in our expressions) with the KKS scheme. As an independent check, we also calculate Feynman rules obtained in the KKS scheme, finding our results in complete agreement with formulae presented in the literature. Our results, which are studied in two different $\gamma_5$ schemes, may be useful for clarifying the $\gamma_5$ problem in dimensional regularization. They are helpful to eliminate or find ambiguities arising from different dimensional regularization schemes.Comment: Version published in JHEP, presentation improved, 41 pages, 10 figure

Orbifold equivalence for finite density QCD and effective field theory

In the large N_c limit, some apparently different gauge theories turn out to be equivalent due to large N_c orbifold equivalence. We use effective field theory techniques to explore orbifold equivalence, focusing on the specific case of a recently discovered relation between an SO(2N_c) gauge theory and QCD. The equivalence to QCD has been argued to hold at finite baryon chemical potential, \mu_B, so long as one deforms the SO(2N_c) theory by certain "double-trace" terms. The deformed SO(2N_c) theory can be studied without a sign problem in the chiral limit, in contrast to SU(N_c) QCD at finite \mu_B. The purpose of the double-trace deformation in the SO(2N_c) theory is to prevent baryon number symmetry from breaking spontaneously at finite density, which is necessary for the equivalence to large N_c QCD to be valid. The effective field theory analysis presented here clarifies the physical significance of double-trace deformations, and strongly supports the proposed equivalence between the deformed SO(2N_c) theory and large N_c QCD at finite density.Comment: 39 pages, 5 figures, 2 tables. v2: Minor typo fixes and clarification

Resummation of small-x double logarithms in QCD: semi-inclusive electron-positron annihilation

We have derived the coefficients of the highest three 1/x-enhanced small-x logarithms of all timelike splitting functions and the coefficient functions for the transverse fragmentation function in one-particle inclusive e^+e^- annihilation at (in principle) all orders in massless perturbative QCD. For the longitudinal fragmentation function we present the respective two highest contributions. These results have been obtained from KLN-related decompositions of the unfactorized fragmentation functions in dimensional regularization and their structure imposed by the mass-factorization theorem. The resummation is found to completely remove the huge small-x spikes present in the fixed-order results for all quantities above, allowing for stable results down to very small values of the momentum fraction and scaling variable x. Our calculations can be extended to (at least) the corresponding as^n ln^(2n-l) x contributions to the above quantities and their counterparts in deep-inelastic scattering.Comment: 27 pages, LaTeX, 6 eps-figure