#### Alladi Ramakrishnan Hall

#### Two dimensional QCD with quarks in large gauge representations

#### Naveen S. Prabhakar

##### ICTS, Bangalore

*QCD in 1+1 dimensions is a great toy model for understanding the*

various intricate phenomena exhibited by gauge theories. In 1974,

SU(N) QCD in 1+1 dimensions coupled to quarks in the fundamental

representation was solved by 't Hooft in the large N limit: an elegant

integral equation was obtained for the meson spectrum by directly

summing the diagrams in the Bethe-Salpeter equation. The integral

equation was shown to have a discrete spectrum, thereby explicitly

demonstrating quark confinement.

The same integral equation was derived by Dhar et. al. in 1994 by

observing that the phase space of the quark can be described as a

particular coadjoint orbit of a $W_\infty$ algebra generated by the

gauge invariant meson operators. The large N limit was interpreted as

a semi-classical limit and the equation of motion for the fluctuations

along the coadjoint orbit was found to be 't Hooft's integral

equation. We work in a different, novel limit of QCD that exists only

in 1+1 dimensions where the representation of the quarks is taken to

be large. We treat the case of SU(2) QCD explicitly, with the quarks

being in the spin J representation of SU(2) with J taken to be

large. In this limit, we use $W_\infty$ algebra techniques and derive a

't Hooft-like integral equation for the meson spectrum.

Done