Infrared phases of 2d QCD

Abstract

We derive the necessary and sufficient conditions for a 2d QCD theory of massless gluons and left and right chiral quarks in arbitrary representations of a gauge group G to develop a mass gap. These results are obtained from spectral properties of the lightcone and temporal QCD Hamiltonians. The conditions can be explicitly solved, and we provide the complete list of all 2d QCD theories that have a quantum mechanical gap in the spectrum, while any other theory not in the list is gapless. The list of gapped theories includes QCD models with quarks in vector-like as well as chiral representations. The gapped theories consist of several infinite families of classical gauge groups with quarks in rank 1 and 2 representations, plus a finite number of isolated cases. We also put forward and analyze the effective infrared description of QCD — TQFTs for gapped theories and CFTs for gapless theories — and exhibit several interesting features in the infrared, such as the existence of non-trivial global ’t Hooft anomalies and emergent supersymmetry. We identify 2d QCD theories that flow in the infrared to celebrated CFTs such as minimal models, bosonic and supersymmetric, and Wess-Zumino-Witten and Kazama-Suzuki models.

Emergent Strings at an Infinite Distance with Broken Supersymmetry

“…and thus, one obtains a net contribution of 8×4 2 − 16 = 0 from the chiral fermions. However, the gravitational anomaly does not cancel on the worldvolume without an inflow mechanism, which suggests that the theories are, in general, gapless [84]. This is indeed what we find for the theories at stake.…”

“…This is expected, since they describe transverse fluctuations of a single D1-brane in spacetime. As we shall see shortly, the remaining degrees of freedom in the worldvolume theories ought to flow to WZW coset models [84,90], which can be constructed by means of non-Abelian bosonization.…”

Chiral limit of 2d QCD revisited with lightcone conformal truncation

“…Despite the focus here on one particular model, namely that of an SU(3) gauge group with a single Dirac fermion in the fundamental representation, perhaps the most interesting application of these methods is to the vast range of IR CFTs that can be obtained with vanishing quark masses by varying the gauge group and matter content. The IR has been conjectured [5,[9][10][11] to be described by gauged WZW coset models, where the specific coset is a quotient of the global symmetries of the UV free fermion theory divided by the gauge group. Gauged WZW coset models are extremely versatile and can be used to construct many well-known CFTs, including minimal models and much more.…”

“…Studying QCD in the light mass, or chiral limit, is desirable not only because of its closer resemblance to its 4d cousin, but also because the effective theory describing the low energy degrees of freedom of QCD like theories can be very rich in its own right. Indeed, recently, Delmastro, Gomis and Yu [9] have offered a full classification of the IR of QCD theories in the chiral limit, building on the earlier insights of [5,10,11]; examples include minimal models and WZW models. Hence, a method which can efficiently capture the chiral limit of QCD like theories, can also be used to study relevant deformations of a wide class of integrable CFTs.…”

Anomalies and symmetry fractionalization

“…The study of the infrared dynamics of 1 + 1d adjoint gauge theory goes back to [67,68] and there was progress on it recently, see [69][70][71][72][73][74][75] and references therein. This theory has a A 2 axial symmetry acting as…”