String Bits and the Spin Vertex

TL;DR

This paper introduces the spin vertex formalism for computing correlation functions in planar N=4 SYM, revealing an infinite symmetry related to Yangian invariance at weak coupling.

Contribution

It constructs the spin vertex explicitly for all sectors at leading order and proves its Yangian invariance, suggesting a potential all-loop symmetry extension.

Findings

Spin vertex constructed explicitly for all sectors.

Proved the vertex has trivial monodromy and is Yangian invariant.

Suggests infinite symmetry extends to all loop orders.

Abstract

We initiate a novel formalism for computing correlation functions of trace operators in the planar N=4 SYM theory. The central object in our formalism is the spin vertex, which is the weak coupling analogy of the string vertex in string field theory. We construct the spin vertex explicitly for all sectors at the leading order using a set of bosonic and fermionic oscillators. We prove that the vertex has trivial monodromy, or put in other words, it is a Yangian invariant. Since the monodromy of the vertex is the product of the monodromies of the three states, the Yangian invariance of the vertex implies an infinite exact symmetry for the three-point function. We conjecture that this infinite symmetry can be lifted to any loop order.