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

  title={Cut-and-join operators and \$ \mathcal\{N\} = 4 \$ super Yang-Mills},
  author={T. W. Brown},
  journal={Journal of High Energy Physics},
  • 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… 
From counting to construction of BPS states in $ \mathcal{N} = 4 $ SYM
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
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
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
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
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
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
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


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
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
The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
Counting BPS operators in gauge theories: quivers, syzygies and plethystics
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
Counting BPS operators in N=4 SYM