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

TL;DR

This paper develops a discretized string bit model for planar N=4 super Yang-Mills theory at zero coupling, establishing a correspondence between gauge-invariant words and string states, and explores one-loop corrections and integrability properties.

Contribution

It introduces a string bit formulation using oscillators for N=4 SYM, connecting gauge theory correlators with string world-sheet overlaps, and constructs a model capturing one- and two-loop anomalous dimensions.

Findings

Planar correlators are represented by delta-function overlaps of string bits.

One-loop corrections are incorporated via nearest neighbor interactions among bits.

The SU(2) sector model reproduces anomalous dimensions up to two loops and obeys BMN scaling.

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.