Abstract
Two-dimensional SU(N) gauge theory coupled to a Majorana fermion in the adjoint representation is a nice toy model for higher-dimensional gauge dynamics. It possesses a multitude of “gluinoball” bound states whose spectrum has been studied using numerical diagonalizations of the light-cone Hamiltonian. We extend this model by coupling it to Nf flavors of fundamental Dirac fermions (quarks). The extended model also contains meson-like bound states, both bosonic and fermionic, which in the large-N limit decouple from the gluinoballs. We study the large-N meson spectrum using the Discretized Light-Cone Quantization (DLCQ). When all the fermions are massless, we exhibit an exact mathfrak{osp} (1|4) symmetry algebra that leads to an infinite number of degeneracies in the DLCQ approach. More generally, we show that many single-trace states in the theory are threshold bound states that are degenerate with multi-trace states. These exact degeneracies can be explained using the Kac-Moody algebra of the SU(N) current. We also present strong numerical evidence that additional threshold states appear in the continuum limit. Finally, we make the quarks massive while keeping the adjoint fermion massless. In this case too, we observe some exact degeneracies that show that the spectrum of mesons becomes continuous above a certain threshold. This demonstrates quantitatively that the fundamental string tension vanishes in the massless adjoint QCD2 without explicit four-fermion operators.
Highlights
Introduction and summarySoon after the emergence of Quantum Chromodynamics as the SU(3) Yang-Mills theory of strong interactions [1,2,3], ’t Hooft introduced its generalization to gauge group SU(N ) and the large N limit where gY2 MN is held fixed [4]
We will note that some of the Discretized Light-Cone Quantization (DLCQ) degeneracies between the single-trace and multi-trace states are not lifted and that the meson spectrum is continuous above a certain threshold
One implication of the vanishing fundamental string tension in massless adjoint QCD2 is that the spectrum of single-meson states at large N in theory T becomes continuous above a certain threshold [20]
Summary
Soon after the emergence of Quantum Chromodynamics as the SU(3) Yang-Mills theory of strong interactions [1,2,3], ’t Hooft introduced its generalization to gauge group SU(N ) and the large N limit where gY2 MN is held fixed [4]. For certain massive meson states does not change as the resolution parameter is increased and is the same as the sum of the values of P − for one or more fermionic gluinoball states We trace this exact result to the osp(1|4) symmetry of the DLCQ system with antiperiodic boundary conditions around the circle in x− direction. This symmetry helps us prove that in the continuum limit, there is a large amount of degeneracy in the spectrum of the meson states at the same value of masses as possessed by certain gluinoball states; the first of them occurs at.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have