Anomalous dimension with wrapping at four loops in N=4 SYM

TL;DR

The paper delivers a complete, detail-rich four-loop calculation of the Konishi-descendant anomalous dimension in planar ${\cal N}=4$ SYM, explicitly incorporating wrapping effects in the SU(2) sector. Employing an ${\cal N}=1$ superspace framework plus Gegenbauer polynomial $x$-space techniques, the authors subtract the asymptotic-range five contributions, perform a rigorous D‑algebra reduction to isolate divergences, and evaluate wrapping diagrams with GPXT. A key outcome is the appearance of a ${\zeta}(5)$ term at four loops, contradicting previous conjectures, and the final result for the four-loop anomalous dimension is $\gamma_4=-2496+576\zeta(3)-1440\zeta(5)$, yielding the full coupling expansion $\gamma=4+12\lambda-48\lambda^2+336\lambda^3+\lambda^4( -2496+576\zeta(3)-1440\zeta(5) )$. This explicit field-theory calculation strengthens the connection between gauge theory spectra and string theory via AdS/CFT, highlighting the importance of finite-size (wrapping) effects in short operators.

Abstract

In this paper we give all the details of the calculation that we presented in our previous paper arXiv:0712.3522, concerning the four-loop anomalous dimension of the Konishi descendant tr(φZφZ-φφZ Z) in the SU(2) sector of the N=4 planar SYM theory. We explicitly consider all the wrapping diagrams that we compute using an N=1 superspace approach and Gegenbauer polynomial x-space techniques.

Figures (15)

• Figure 1: Building block
• Figure 2: Wrapping diagrams with only chiral interactions
• Figure A.1: Four-loop non-maximal diagrams of class A
• Figure A.2: Four-loop non-maximal diagrams of class B
• Figure A.3: Four-loop non-maximal diagrams of class C