From counting to construction of BPS states in N=4 SYM
arXiv:1010.1683 · doi:10.1007/JHEP02(2011)078
Abstract
We describe a universal element in the group algebra of symmetric groups, whose characters provides the counting of quarter and eighth BPS states at weak coupling in N=4 SYM, refined according to representations of the global symmetry group. A related projector acting on the Hilbert space of the free theory is used to construct the matrix of two-point functions of the states annihilated by the one-loop dilatation operator, at finite N or in the large N limit. The matrix is given simply in terms of Clebsch-Gordan coefficients of symmetric groups and dimensions of U(N) representations. It is expected, by non-renormalization theorems, to contain observables at strong coupling. Using the stringy exclusion principle, we interpret a class of its eigenvalues and eigenvectors in terms of giant gravitons. We also give a formula for the action of the one-loop dilatation operator on the orthogonal basis of the free theory, which is manifestly covariant under the global symmetry.
arXiv comment41 pages + Appendices, 4 figures; v2 - refs and acknowledgments added
References in corpus (50)
- Gauge Theory Correlators from Non-Critical String Theory
- Strings in flat space and pp waves from Super Yang Mills
- The Bethe-Ansatz for N=4 Super Yang-Mills
- An Index for 4 dimensional Super Conformal Theories
- Correlation functions in the CFT(d)/AdS(d+1) correpondence
- AdS3 Black Holes and a Stringy Exclusion Principle
- Bubbling AdS space and 1/2 BPS geometries
- Invasion of the Giant Gravitons from Anti-de Sitter Space
- The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
- Giant Gravitons in Conformal Field Theory
- Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories
- PP-wave string interactions from perturbative Yang-Mills theory
- BMN Correlators and Operator Mixing in N=4 Super Yang-Mills Theory
- Giant Gravitons from Holomorphic Surfaces
- Diagonal multi-matrix correlators and BPS operators in N=4 SYM
- Exact Multi-Matrix Correlators
- Branes, Anti-Branes and Brauer Algebras in Gauge-Gravity duality
- Large N BPS states and emergent quantum gravity
- The SU(3) spin chain sigma model and string theory
- Supersymmetric states of N=4 Yang-Mills from giant gravitons
- Diagonal free field matrix correlators, global symmetries and giant gravitons
- Anatomy of bubbling solutions
- Giant Gravitons - with Strings Attached (III)
- Counting BPS operators in N=4 SYM
- Exact Multi-Restricted Schur Polynomial Correlators
- Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity
- Finite Factorization equations and Sum Rules for BPS correlators in N=4 SYM theory
- A study of open strings ending on giant gravitons, spin chains and integrability
- A Calculation of the plane wave string Hamiltonian from N=4 super-Yang-Mills theory
- Bit Strings from N=4 Gauge Theory
- BPS Branes From Baryons
- Counting 1/8-BPS Dual-Giants
- OPEs and 3-point correlators of protected operators in N=4 SYM
- Non commutative gravity from the ADS/CFT correspondence
- N=4 Superconformal Characters and Partition Functions
- The String Theory Approach to Generalized 2D Yang-Mills Theory
- Entropy of near-extremal black holes in AdS_5
- Brane webs and 1/4-BPS geometries
- Integrability vs. Information Loss: A Simple Example
- Systematics of Quarter BPS operators in N=4 SYM
- Three-Point Functions of Quarter BPS Operators in N=4 SYM
- Permutations and the Loop
- Spin bit models from non-planar N=4 SYM
- BMN operators and string field theory
- Correlators, Probabilities and Topologies in N=4 SYM
- Cut-and-join operators and N=4 super Yang-Mills
- Quarter BPS classified by Brauer algebra
- Operator mixing and three-point functions in N=4 SYM
- Free particles from Brauer algebras in complex matrix models
- Half-BPS SU(N) Correlators in N=4 SYM
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