56 research outputs found
Quark mass anomalous dimension at O(1/N_f^2) in QCD
We compute the d-dimensional critical exponents corresponding to the wave
function and mass renormalization of the quark in QCD in the Landau gauge at a
new order, O(1/N_f^2), in the large N_f expansion. The computations are
simplified by the establishment in d-dimensions of the critical point
equivalence of QCD and the non-abelian Thirring model beyond leading order. The
form of the O(1/N_f^2) coefficients in the MSbar quark mass anomalous dimension
at five loops is deduced and compared with the numerical asymptotic Pade
approximant prediction.Comment: 13 latex pages, 3 eps figure
Conformal algebra: R-matrix and star-triangle relation
The main purpose of this paper is the construction of the R-operator which
acts in the tensor product of two infinite-dimensional representations of the
conformal algebra and solves Yang-Baxter equation. We build the R-operator as a
product of more elementary operators S_1, S_2 and S_3. Operators S_1 and S_3
are identified with intertwining operators of two irreducible representations
of the conformal algebra and the operator S_2 is obtained from the intertwining
operators S_1 and S_3 by a certain duality transformation. There are
star-triangle relations for the basic building blocks S_1, S_2 and S_3 which
produce all other relations for the general R-operators. In the case of the
conformal algebra of n-dimensional Euclidean space we construct the R-operator
for the scalar (spin part is equal to zero) representations and prove that the
star-triangle relation is a well known star-triangle relation for propagators
of scalar fields. In the special case of the conformal algebra of the
4-dimensional Euclidean space, the R-operator is obtained for more general
class of infinite-dimensional (differential) representations with nontrivial
spin parts. As a result, for the case of the 4-dimensional Euclidean space, we
generalize the scalar star-triangle relation to the most general star-triangle
relation for the propagators of particles with arbitrary spins.Comment: Added references and corrected typo
Large spin systematics in CFT
20 pages; v2: version published in JHEPUsing conformal field theory (CFT) arguments we derive an infinite number of constraints on the large spin expansion of the anomalous dimensions and structure constants of higher spin operators. These arguments rely only on analiticity, unitarity, crossing-symmetry and the structure of the conformal partial wave expansion. We obtain results for both, perturbative CFT to all order in the perturbation parameter, as well as non-perturbatively. For the case of conformal gauge theories this provides a proof of the reciprocity principle to all orders in perturbation theory and provides a new "reciprocity" principle for structure constants. We argue that these results extend also to non-conformal theories.Peer reviewe
Operator product expansion in QCD in off-forward kinematics: Separation of kinematic and dynamical contributions
We develop a general approach to the calculation of target mass and finite
t=(p'-p)^2 corrections in hard processes which can be studied in the framework
of the operator product expansion and involve momentum transfer from the
initial to the final hadron state. Such corrections, which are usually referred
to as kinematic, can be defined as contributions of operators of all twists
that can be reduced to total derivatives of the leading twist operators. As the
principal result, we provide a set of projection operators that pick up the
"kinematic" part of an arbitrary flavor-nonsinglet twist-four operator in QCD.
A complete expression is derived for the time-ordered product of two
electromagnetic currents that includes all kinematic corrections to twist-four
accuracy. The results are immediately applicable to the studies of
deeply-virtual Compton scattering, transition gamma^*-> M gamma form factors
and related processes. As a byproduct of this study, we find a series of
"genuine" twist-four flavor-nonsinglet quark-antiquark-gluon operators which
have the same anomalous dimensions as the leading twist quark-antiquark
operators.Comment: 68 pages, 2 figures. Misprints in Eq.(5.64) and several equations in
Sec.6 are corrected. For readers' convenience all corrections are marked in
re
Renormalisation of heavy-light light ray operators
We calculate the renormalisation of different light ray operators with one
light degree of freedom and a static heavy quark. Both - and
-kernels are considered. A comparison with the light-light case suggests
that the mixing with three-particle operators is solely governed by the light
degrees of freedom. Additionally we show that conformal symmetry is already
broken at the level of the one loop counterterms due to the additional
UV-renormalisation of a cusp in the two contributing Wilson-lines. This general
feature can be used to fix the -renormalisation kernels up to a
constant. Some examples for applications of our results are given.Comment: 23 pages, 5 figures; v2: changed some wording, added a few references
and one appendix concerning some subtleties related to gauge fixing and ghost
terms; v3: clarified calculation in section 3.2., added an explicit
calculation in section 5.2, corrected a few typos and one figure, added a few
comments, results unchanged, except for typesetting matches version to appear
in JHE
Twist operators in N=4 beta-deformed theory
In this paper we derive both the leading order finite size corrections for
twist-2 and twist-3 operators and the next-to-leading order finite-size
correction for twist-2 operators in beta-deformed SYM theory. The obtained
results respect the principle of maximum transcendentality as well as
reciprocity. We also find that both wrapping corrections go to zero in the
large spin limit. Moreover, for twist-2 operators we studied the pole structure
and compared it against leading BFKL predictions.Comment: 17 pages; v2: minor changes, references adde
Quantization of Integrable Systems and a 2d/4d Duality
We present a new duality between the F-terms of supersymmetric field theories
defined in two- and four-dimensions respectively. The duality relates N=2
supersymmetric gauge theories in four dimensions, deformed by an
Omega-background in one plane, to N=(2,2) gauged linear sigma-models in two
dimensions. On the four dimensional side, our main example is N=2 SQCD with
gauge group SU(L) and 2L fundamental flavours. Using ideas of Nekrasov and
Shatashvili, we argue that the Coulomb branch of this theory provides a
quantization of the classical Heisenberg SL(2) spin chain. Agreement with the
standard quantization via the Algebraic Bethe Ansatz implies the existence of
an isomorphism between the chiral ring of the 4d theory and that of a certain
two-dimensional theory. The latter can be understood as the worldvolume theory
on a surface operator/vortex string probing the Higgs branch of the same 4d
theory. We check the proposed duality by explicit calculation at low orders in
the instanton expansion. One striking consequence is that the Seiberg-Witten
solution of the 4d theory is captured by a one-loop computation in two
dimensions. The duality also has interesting connections with the AGT
conjecture, matrix models and topological string theory where it corresponds to
a refined version of the geometric transition.Comment: 51 pages, 7 figures. Additional comments, minor improvements and
references adde
Quantum Spectral Curve at Work: From Small Spin to Strong Coupling in N=4 SYM
We apply the recently proposed quantum spectral curve technique to the study
of twist operators in planar N=4 SYM theory. We focus on the small spin
expansion of anomalous dimensions in the sl(2) sector and compute its first two
orders exactly for any value of the 't Hooft coupling. At leading order in the
spin S we reproduced Basso's slope function. The next term of order S^2
structurally resembles the Beisert-Eden-Staudacher dressing phase and takes
into account wrapping contributions. This expansion contains rich information
about the spectrum of local operators at strong coupling. In particular, we
found a new coefficient in the strong coupling expansion of the Konishi
operator dimension and confirmed several previously known terms. We also
obtained several new orders of the strong coupling expansion of the BFKL
pomeron intercept. As a by-product we formulated a prescription for the correct
analytical continuation in S which opens a way for deriving the BFKL regime of
twist two anomalous dimensions from AdS/CFT integrability.Comment: 53 pages, references added; v3: due to a typo in the coefficients C_2
and D_2 on page 29 we corrected the rational part of the strong coupling
predictions in equations (1.5-6), (6.22-24), (6.27-30) and in Table
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