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Authors
Charles B. Thorn
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We develop superstring bit models, in which the lightcone transverse coordinates in D spacetime dimensions are replaced with d=D-2 double-valued flavor indices $x^k-> f_k=1,2$; $k=2,...,d+1$. In such models the string bits have no space to move. Letting each string bit be an adjoint of a color group U(N), we then analyze the physics of t Hoofts limit $N->infty$, in which closed chains of many string bits behave like free lightcone IIB superstrings with d compact coordinate bosonic worldsheet fields $x^k$, and s pairs of Grassmann fermionic fields $theta_{L,R}^a$, a=1,..., s. The coordinates $x^k$ emerge because, on the long chains, flavor fluctuations enjoy the dynamics of d anisotropic Heisenberg spin chains. It is well-known that the low energy excitations of a many-spin Heisenberg chain are identical to those of a string worldsheet coordinate compactified on a circle of radius $R_k$, which is related to the anisotropy parameter $-1<Delta_k<1$ of the corresponding Heisenberg system. Furthermore there is a limit of this parameter, $Delta_k->pm 1$, in which $R_k->infty$. As noted in earlier work [Phys.Rev.D{bf 89}(2014)105002], these multi-string-bit chains are strictly stable at $N=infty$ when d<s and only marginally stable when d=s. (Poincare supersymmetry requires d=s=8, which is on the boundary between stability and instability.)
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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.
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