اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAnomalous dimensions of leading twist conformal operators
217
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We extend and develop a method for perturbative calculations of anomalous dimensions and mixing matrices of leading twist conformal primary operators in conformal field theories. Such operators lie on the unitarity bound and hence are conserved (irreducible) in the free theory. The technique relies on the known pattern of breaking of the irreducibility conditions in the interacting theory. We relate the divergence of the conformal operators via the field equations to their descendants involving an extra field and accompanied by an extra power of the coupling constant. The ratio of the two-point functions of descendants and of their primaries determines the anomalous dimension, allowing us to gain an order of perturbation theory. We demonstrate the efficiency of the formalism on the lowest-order analysis of anomalous dimensions and mixing matrices which is required for two-loop calculations of the former. We compare these results to another method based on anomalous conformal Ward identities and constraints from the conformal algebra. It also permits to gain a perturbative order in computations of mixing matrices. We show the complete equivalence of both approaches.
قيم البحث
اقرأ أيضاً
Using some techniques of conformal field theories, we find a closed expression for the contribution of leading twist operators and their descendants, obtained by adding total derivatives, to the operator product expansion (OPE) of two electromagnetic
currents in QCD. Our expression resums contributions of all twists and to all orders in perturbation theory up to corrections proportional to the QCD $beta$-function. At tree level and to twist-four accuracy, our result agrees with the expression derived earlier by a different method. The results are directly applicable to deeply-virtual Compton scattering and, e.g., $gammagamma^ast$ annihilation in two mesons. As a byproduct, we derive a simple representation for the OPE of two scalar currents that is convenient for applications.
We consider folded spinning strings in AdS_5xS^5 (with one spin component S in AdS_5 and J in S^5) corresponding to the Tr(D^S Z^J) operators in the sl(2) sector of the N=4 SYM theory in the special scaling limit in which both the string mass M ~ sqr
t lambda ln S and J are sent to infinity with their ratio fixed. Expanding in the parameter el= J/M we compute the 2-loop string sigma model correction to the string energy and show that it agrees with the expression proposed by Alday and Maldacena in arxiv:0708.0672. We suggest that a resummation of the logarithmic el^2 ln^n el terms is necessary in order to establish an interpolation to the weakly coupled gauge theory results. In the process, we set up a general framework for the calculation of higher loop corrections to the energy of multi-spin string configurations. In particular, we find that in addition to the direct 2-loop term in the string energy there is a contribution from lower loop order due to a finite ``renormalization of the relation between the parameters of the classical solution and the fixed spins, i.e. the charges of the SO(2,4) x SO(6) symmetry.
We present the calculation of the leading instanton contribution to the scaling dimensions of twist-two operators with arbitrary spin and to their structure constants in the OPE of two half-BPS operators in $mathcal N=4$ SYM. For spin-two operators w
e verify that, in agreement with $mathcal N=4$ superconformal Ward identities, the obtained expressions coincide with those for the Konishi operator. For operators with high spin we find that the leading instanton correction vanishes. This arises as the result of a rather involved calculation and requires a better understanding.
In a {cal N}=1 superspace formulation of {cal N}=4 Yang-Mills theory we obtain the anomalous dimensions of chiral operators with large R charge J to infty keeping g^2 N/J^2 finite, to all orders of perturbation theory in the planar limit. Our result
proves the conjecture that the anomalous dimensions are indeed finite in the above limit. This amounts to an exact check of the proposed duality between a sector of {cal N}=4 Yang-Mills theory with large R charge J and string theory in a pp-wave background.
The three-loop four-point function of stress-tensor multiplets in N=4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In this paper we evaluate the unknown integral
s, thus obtaining the three-loop correlation function analytically. The integrals have the generic structure of rational functions multiplied by (multiple) polylogarithms. We use the idea of leading singularities to obtain the rational coefficients, the symbol - with an appropriate ansatz for its structure - as a means of characterising multiple polylogarithms, and the technique of asymptotic expansion of Feynman integrals to obtain the integrals in certain limits. The limiting behaviour uniquely fixes the symbols of the integrals, which we then lift to find the corresponding polylogarithmic functions. The final formulae are numerically confirmed. The techniques we develop can be applied more generally, and we illustrate this by analytically evaluating one of the integrals contributing to the same four-point function at four loops. This example shows a connection between the leading singularities and the entries of the symbol.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
