Towards a string bit formulation of N=4 super Yang-Mills

Abstract

We show that planar cal N=4 Yang-Mills theory at zero 't Hooft coupling can be efficiently described in terms of 8 bosonic and 8 fermionic oscillators. We show that these oscillators can serve as world-sheet variables, the string bits, of a discretized string. There is a one to one correspondence between the on shell gauge invariant words of the free Y-M theory and the states in the oscillators' Hilbert space, obeying a local gauge and cyclicity constraints. The planar two-point functions and the three-point functions of all gauge invariant words are obtained by the simple delta-function overlap of the corresponding discrete string world sheet. At first order in the 't Hooft coupling, i.e. at one-loop in the Y-M theory, the logarithmic corrections of the planar two-point and the three-point functions can be incorporated by nearest neighbour interactions among the discretized string bits. In the SU(2) sub-sector we show that the one-loop corrections to the structure constants can be uniquely determined by the symmetries of the bit picture. For the SU(2) sub-sector we construct a gauged, linear, discrete world-sheet model for the oscillators, with only nearest neighbour couplings, which reproduces the anomalous dimension Hamiltonian up to two loops. This model also obeys BMN scaling to all loops.

64 pages, 6 figures, typos fixed, references added

References in corpus (11)

• Bethe Ansatz for Quantum Strings
• Spinning strings and integrable spin chains in the AdS/CFT correspondence
• From Free Fields to $AdS$ -- III
• A three-loop test of the dilatation operator in N=4 SYM
• Yang-Mills Correlation Functions from Integrable Spin Chains
• Structure constants of planar N =4 Yang Mills at one loop
• Higher Impurity AdS/CFT Correspondence in the Near-BMN Limit
• New Integrable System of 2dim Fermions from Strings on AdS_5 x S^5
• N-Impurity Superstring Spectra Near the pp-Wave Limit
• String bits in small radius AdS and weakly coupled N=4 Super Yang-Mills Theory: I
• Higher Spins and Stringy AdS5xS5

Cited by in corpus (31)

• Planar N=4 Gauge Theory and the Hubbard Model
• Two and three-point correlators of operators dual to folded string solutions at strong coupling
• HHL correlators, orbit averaging and form factors
• String field theory vertex from integrability
• Quantum AdS_5 x S^5 superstring in the AdS light-cone gauge
• SL(2) sector: weak/strong coupling agreement of three-point correlators
• The String Dual to Free $\mathcal{N}=4$ Super Yang-Mills
• The hexagon in the mirror: the three-point function in the SoV representation
• The Worldsheet Dual of Free Super Yang-Mills in 4D
• Three-point functions in planar N=4 super Yang-Mills Theory for scalar operators up to length five at the one-loop order
• Comments on worldsheet theories dual to free large N gauge theories
• On a worldsheet dual of the Gaussian matrix model
• Novel construction and the monodromy relation for three-point functions at weak coupling
• Cut-and-join operators and N=4 super Yang-Mills
• String Bits and the Spin Vertex
• From Spacetime to Worldsheet: Four point correlators
• Operator mixing and three-point functions in N=4 SYM
• Three-point correlators from string amplitudes: Mixing and Regge spins
• Three-Point Functions of Twist-Two Operators in N=4 SYM at One Loop
• One-Loop Spectroscopy of Scalar Three-Point Functions in planar N=4 super Yang-Mills Theory
• The two-loop dilatation operator of N=4 super Yang-Mills theory in the SO(6) sector
• On the singlet projector and the monodromy relation for psu(2, 2|4) spin chains and reduction to subsectors
• Correlators of massive string states with conserved currents
• A note on three-point functions of unprotected operators
• Evidence for Gauge/Gravity Correspondence for D$p$-branes at Weak 't Hooft Coupling
• Cutting the cylinder into squares: The square form factor
• Grassmannian Integrals as Matrix Models for Non-Compact Yangian Invariants
• Interactions as conformal intertwiners in 4D QFT
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• A cut-off tubular geometry of loop space
• On the Integrable Structure of Super Yang-Mills Scattering Amplitudes