SciPost Phys. 7, 056 (2019) ·
published 28 October 2019
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We use conformal embeddings involving exceptional affine Kac-Moody algebras
to derive new dualities of three-dimensional topological field theories. These
generalize the familiar level-rank duality of Chern-Simons theories based on
classical gauge groups to the setting of exceptional gauge groups. For
instance, one duality sequence we discuss is $(E_{N})_{1}\leftrightarrow
SU(9-N)_{-1}$. Others such as $SO(3)_{8}\leftrightarrow PSU(3)_{-6},$ are
dualities among theories with classical gauge groups that arise due to their
embedding into an exceptional chiral algebra. We apply these equivalences
between topological field theories to conjecture new boson-boson Chern-Simons
matter dualities. We also use them to determine candidate phase diagrams of
time-reversal invariant $G_{2}$ gauge theory coupled to either an adjoint
fermion, or two fundamental fermions.
SciPost Phys. 6, 017 (2019) ·
published 4 February 2019
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We study (1+1)-dimensional non-linear sigma models whose target space is the
flag manifold $U(N)\over U(N_1)\times U(N_2)\cdots U(N_m)$, with a specific
focus on the special case $U(N)/U(1)^{N}$. These generalize the well-known
$\mathbb{CP}^{N-1}$ model. The general flag model exhibits several new elements
that are not present in the special case of the $\mathbb{CP}^{N-1}$ model. It
depends on more parameters, its global symmetry can be larger, and its 't Hooft
anomalies can be more subtle. Our discussion based on symmetry and anomaly
suggests that for certain choices of the integers $N_I$ and for specific values
of the parameters the model is gapless in the IR and is described by an
$SU(N)_1$ WZW model. Some of the techniques we present can also be applied to
other cases.
