# Cut-and-join operators and $\mathcal{N} = 4$ super Yang-Mills

@article{Brown2010CutandjoinOA,
title={Cut-and-join operators and \$\mathcal\{N\} = 4 \$ super Yang-Mills},
author={T. W. Brown},
journal={Journal of High Energy Physics},
year={2010},
volume={2010},
pages={1-46}
}
• T. Brown
• Published 10 February 2010
• Mathematics
• Journal of High Energy Physics
We show which multi-trace structures are compatible with the symmetrisation of local operators in $\mathcal{N} = 4$ super Yang-Mills when they are organised into representations of the global symmetry group. Cut-and-join operators give the non-planar expansion of correlation functions of these operators in the free theory. Using these techniques we find the 1/N corrections to the quarter-BPS operators which remain protected at weak coupling. We also present a new way of counting these chiral…
16 Citations
From counting to construction of BPS states in $\mathcal{N} = 4$ SYM
• Mathematics
• 2010
We describe a universal element $\mathbb{P}$ in the group algebra of symmetric groups, whose characters provides the counting of quarter and eighth BPS states at weak coupling in $\mathcal{N} = 4 Surprisingly simple spectra • Mathematics, Physics • 2010 The large N limit of the anomalous dimensions of operators in$ \mathcal{N} = 4 $super Yang-Mills theory described by restricted Schur polynomials, are studied. We focus on operators labeled by Quarter BPS classified by Brauer algebra We analyse the one-loop dilatation operator with the help of the Brauer algebra. We find some BPS operators in$ \mathcal{N} = 4 $SYM, which are labelled by irreducible representations of the Brauer Quarter-BPS states, multi-symmetric functions and set partitions • Mathematics • 2020 We give a construction of general holomorphic quarter BPS operators in$ \mathcal{N}=4$SYM at weak coupling with$U(N)$gauge group at finite$N$. The construction employs the Mobius inversion From Gauss graphs to giants • Physics, Geology • 2017 A bstractWe identify the operators in N = 4 super Yang-Mills theory that correspond to 18$$\frac{1}{8}$$ -BPS giant gravitons in AdS5 × S5. Our evidence for the identification comes from (1) Young diagrams, Brauer algebras, and bubbling geometries • Mathematics • 2011 A bstractWe study the 1/4 BPS geometries corresponding to the 1/4 BPS operators of the dual gauge theory side, in$ \mathcal{N} = {4} $SYM. By analyzing asymptotic structure and flux integration of Higher spins & strings • Mathematics • 2014 A bstractIt is natural to believe that the free symmetric product orbifold CFT is dual to the tensionless limit of string theory on AdS3 × S3 × T4$${\mathbb{T}}^4$$. At this point in moduli space, BPS Operators and Brane Geometries. In this thesis we explore the finite N spectrum of BPS operators in four-dimensional supersymmetric conformal field theories (CFT), which have dual AdS gravitational descriptions. In the first part Correlators in the simplest gauge-string duality • Mathematics • 2013 A bstractIn this note we compare planar correlators such as$ {{\left\langle {\prod\nolimits_i^n {\mathrm{Tr}{M^{{2{k_i}}}}} } \right\rangle}_{\mathrm{conn}}} $in the Gaussian matrix model with Higher genus BMN correlators: factorization and recursion relations We systematically study the factorization and recursion relations in higher genus correlation functions of BMN (Berenstein-Maldacena-Nastase) operators in free N=4 super Yang Mills theory. These ## References SHOWING 1-10 OF 93 REFERENCES Permutations and the loop We consider the one-loop two-point function for multi-trace operators in the U(2) sector of = 4 supersymmetric Yang-Mills at finite N. We derive an expression for it in terms of U(N) and Sn+1 group Strings in flat space and pp waves from${\cal N}=4$Super Yang Mills • Physics • 2002 We explain how the string spectrum in flat space and pp-waves arises from the large$N$limit, at fixed$g^2_{YM}$, of U(N)${\cal N} =4$super Yang Mills. We reproduce the spectrum by summing a Quarter BPS operators in N = 4 SYM Chiral primary operators annihilated by a quarter of the supercharges are constructed in the four dimensional = 4 Super-Yang-Mills theory with gauge group SU(N). These 1/4-BPS operators share many String Interactions in PP Wave from N=4 Superyang-Mills We consider non-planar contributions to the correlation functions of BMN operators in free N = 4 super Yang Mills theory. We recalculate these non-planar contributions from a different kind of Spin-Bits and N=4 SYM We briefly review the spin-bit formalism, describing the non-planar dynamics of the$\mathcal{N}=4,d=4$Super Yang-Mills SU(N) gauge theory. After considering its foundations, we apply such a Counting BPS operators in gauge theories: quivers, syzygies and plethystics • Mathematics • 2007 We develop a systematic and efficient method of counting single-trace and multi-trace BPS operators with two supercharges, for world-volume gauge theories of$N$D-brane probes for both$N \to
Half-BPS SU(N) correlators in = 4 SYM
In this note we study half-BPS operators in = 4 super Yang-Mills for gauge group SU(N) at finite N. In particular we elaborate on the results of hep-th/0410236, providing an exact formula for the