In this article, we extend the work of arXiv:0901.4744 to a Bethe/Gauge correspondence between 2d (or resp. 3d) SO/Sp gauge theories and open XXX (resp. XXZ) spin chains with diagonal boundary conditions. The case of linear quiver gauge theories is also considered.
The topological vertex formalism for 5d $mathcal{N}=1$ gauge theories is not only a convenient tool to compute the instanton partition function of these theories, but it is also accompanied by a nice algebraic structure that reveals various kinds of
nice properties such as dualities and integrability of the underlying theories. The usual refined topological vertex formalism is derived for gauge theories with $A$-type quiver structure (and $A$-type gauge groups). In this article, we propose a construction with a web of vertex operators for all $ABCDEFG$-type and affine quivers by introducing several new vertices into the formalism, based on the reproducing of known instanton partition functions and qq-characters for these theories.
We study non-perturbative aspects of QCD Kondo effect, which has been recently proposed for the finite density and strong magnetic field systems, using conformal field theory describing the low energy physics near the IR fixed point. We clarify the s
ymmetry class of QCD Kondo effect both for the finite density and magnetic field systems, and show how the IR fixed point is non-perturbatively characterized by the boundary condition, which incorporates the impurity effect in Kondo problem. We also obtain the low temperature behavior of several quantities of QCD Kondo effect in the vicinity of the IR fixed point based on the conformal field theory analysis.
We apply conformal field theory analysis to the $k$-channel SU($N$) Kondo system, and find a peculiar behavior in the cases $N > k > 1$, which we call Fermi/non-Fermi mixing: The low temperature scaling is described as the Fermi liquid, while the zer
o temperature IR fixed point exhibits the non-Fermi liquid signature. We also show that the Wilson ratio is no longer universal for the cases $N > k > 1$. The deviation from the universal value of the Wilson ratio could be used as an experimental signal of the Fermi/non-Fermi mixing.
We present a theoretical foundation for the Index theorem in naive and minimally doubled lattice fermions by studying the spectral flow of a Hermitean version of Dirac operators. We utilize the point splitting method to implement flavored mass terms,
which play an important role in constructing proper Hermitean operators. We show the spectral flow correctly detects the index of the would-be zero modes which is determined by gauge field topology. Using the flavored mass terms, we present new types of overlap fermions from the naive fermion kernels, with a number of flavors that depends on the choice of the mass terms. We succeed to obtain a single-flavor naive overlap fermion which maintains hypercubic symmetry.
