Exact symmetries and threshold states in two-dimensional models for QCD

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 $$ \mathfrak{osp} $$ 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.

Supersymmetry in QCD$_2$ coupled to fermions

“…that coincide with the action derived in [5]. It is convenient now to study this model in the light-cone gauge where we treat one of the light-cone coordinates, for instance, x − as time and the other, x + , as a spatial coordinate.…”

“…For this purpose, we consider a gauge field with gauge group G, that is assumed to be a simple Lie group, and couple it to a massive Majorana fermion field ψ i that belongs to an adjoint representation of the gauge group G. One of the remarkable properties that the spectrum of the model becomes supersymmetric at particular mass of the fermions m adj . It was shown first by Kutasov [3] and after that checked explicitly using some numerical methods [4,5,6]. Even though this property of two dimensional gauge theories was very well established, the physical intuition behind this result is still obscure and understood only in terms of light-cone quantization.…”

Four-fermion deformations of the massless Schwinger model and confinement

“…Indeed, by now it is common wisdom that 2d gauge theories with massless fermions do not confine, with both abelian examples like the charge-N Schwinger model and non-abelian examples such as 2d SU (N ) QCD with one Majorana fermion (see e.g. [8,[35][36][37][38][39][40][41][42][43][44][45]), among others [46].…”

Form Factors and Spectral Densities from Lightcone Conformal Truncation

“…While we only studied the case of the stress tensor and d = 2, the idea behind this construction was fairly general and should be applicable to any UV CFT operator in any theory to which LCT can be applied, regardless of spacetime dimension. 17 There are many other interesting CFTs to which these methods can be applied, and in particular another natural application where there has been significant lightcone Hamiltonian truncation work is QCD in two dimensions [27][28][29][30][31][32]. Moreover, we think it is likely that one could generalize this approach to equal-time truncation computations as well without much trouble.…”