We study the equivariant instanton partition function in $\mathcal{N}=2$ supersymmetric theory on $\mathbb{C}^2$ with $SU(N)$ gauge group and find generalisation of Zamolodchikov recurrence relation. consider pure as well theories matter hypermultiplets adjoint fundamental representations.

A possible formulation of chiral gauge theories with an anomalous fermion content is re-examined in light of the lattice framework based on the Ginsparg-Wilson relation. It is shown that the fermion sector of a wide class of anomalous non-abelian theories cannot consistently be formulated within this lattice framework. In particular, in 4 dimension, all anomalous non-abelian theories are includ...

The mass differences between the lightest vector and pseudoscalar mesons containing one or two heavy quarks are persistently smaller in quenched lattice simulations than the experimental values[1–3]. Studies of the unquenched theory have found that the discrepancy persists[4]. Fewer lattice simulations have been performed for the mass differences between spin-3/2 and spin-1/2 baryons containing...

We employ a functional approach to investigate the confinement problem in quenched Landau gauge QCD. We demonstrate analytically that a linear rising potential between massive quarks is generated by infrared singularities in the dressed quark-gluon vertex. The selfconsistent mechanism that generates these singularities is driven by the scalar Dirac amplitudes of the full vertex and the quark pr...

The goal of this seminar is to understand the Nekrasov partition function introduced by Nekrasov in 2003 [Nek03]. This is a generating function for correlation functions in an N = 2 supersymmetric gauge theory, so my goal today is to explain what N = 2 gauge theory is and why we might find it interesting. We begin with the latter question, why is this interesting? There are two intertwined answ...

Certain quantum topological invariants of three manifolds can be written in the form of the Gaussian sum. It is shown that such topological invariants can be approximated efficiently by a quantum computer. The invariants discussed here are obtained as a partition function of the gauge theory on three manifolds with various gauge groups. Our algorithms are applicable to Abelian and finite gauge ...