Mass Spectra of Supersymmetric Yang-Mills Theories in 1+1 Dimensions

TL;DR

By an exact diagonalization of the supercharge matrix between up to several hundred color singlet bound states, this work finds a rapidly increasing density of states as the mass increases.

Abstract

Physical mass spectra of supersymmetric Yang-Mills theories in 1+1 dimensions are evaluated in the light-cone gauge with a compact spatial dimension. The supercharges are constructed and the infrared regularization is unambiguously prescribed for supercharges, instead of the light-cone Hamiltonian. This provides a manifestly supersymmetric infrared regularization for the discretized light-cone approach. By an exact diagonalization of the supercharge matrix between up to several hundred color singlet bound states, we find a rapidly increasing density of states as mass increases.

Figures (7)

• Figure 1: The accumulated number of bound states as a function of mass squared for $K=4, 5, 6, 7, 8$; there is no differnce in behavior between bosonic and fermionic state.
• Figure 2: Mass squared of bosonic bound states for $K=5$ as a function of the average number of constituents; $M^2$ are measured in units of $g^2 N / \pi$
• Figure 3: Mass squared of $K=6$ bosonic bound states as a function of the average number of constituents; $M^2$ are measured in units of $g^2 N / \pi$
• Figure 4: Mass squared of $K=7$ bosonic bound states as a function of the average number of constituents; $M^2$ are measured in units of $g^2 N / \pi$
• Figure 5: Mass squared of bosonic bound states for $K=8$ as a function of the average number of constituents; $M^2$ are measured in units of ${g^2 N \over \pi}$.