Related papers: Localization for the norm-square of the moment map…
The role of a physical phase space structure in a classical and quantum dynamics of gauge theories is emphasized. In particular, the gauge orbit space of Yang-Mills theories on a cylindrical spacetime (space is compactified to a circle) is…
We consider the partition function of super Yang-Mills theories defined on $T^2 \times \Sigma_g$. This path integral can be computed by the localization. The one-loop determinant is evaluated by the elliptic genus. This elliptic genus gives…
By using supermanifold techniques we prove a generalization of the localization formula in equivariant cohomology which is suitable for studying supersymmetric Yang-Mills theories in terms of ADHM data. With these techniques one can compute…
The following is a master thesis centered around the concept of localisation and the Third Way Theory. This thesis discusses various aspects of supersymmetric localisation in one and three dimensions, and contains original results with…
We review localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low-dimensional gauge theories. These are the…
Path integral formulation based on the canonical method is discussed. Path integral for Yang-Mills theory is obtained by this procedure. It is shown that gauge fixing which is essential procedure to quantize singular systems by Faddeev's…
We review recent results on the derivation of a global path integral density for Yang-Mills theory. Based on a generalization of the stochastic quantization scheme and its geometrical interpretation we first recall how locally a modified…
The partition function of Euclidean Yang-Mills theory on two dimensional surfaces is given by the Migdal formula. It involves the area and topological characteristics of the surface. We consider this theory on a class of infinite genus…
Factorization of the (formal) path integral measure in a Wiener path integrals for Yang--Mills diffusion is studied. Using the nonlinear filtering stochastic differential equation, we perform the transformation of the path integral defined…
A new classical solution for the SU(2) Yang-Mills theory, in which the Euclidean energy plays a role of a parameter is found. A correspondence between this solution and the known selfdual multi-instanton configuration, which has the…
Based on a generalization of the stochastic quantization scheme recently a modified Faddeev-Popov path integral density for the quantization of Yang-Mills theory was derived, the modification consisting in the presence of specific finite…
We compute the exact all-orders perturbative expansion for the partition function of 2d $\mathrm{SU}(2)$ Yang-Mills theory on closed surfaces around higher critical points. We demonstrate that the expansion can be derived from the lattice…
We revisit Atiyah and Bott's study of Morse theory for the Yang-Mills functional over a Riemann surface, and establish new formulas for the minimum codimension of a (non-semi-stable) stratum. These results yield the exact connectivity of…
These are expository lectures reviewing (1) recent developments in two-dimensional Yang-Mills theory, and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of…
We show that a class of previously defined maps, called self-dual and causal morphisms, form classical symmetries of Yang-Mills fields in four complex dimensions. These maps generalize conformal transformations, and admit a nonlocal…
For the spinning superparticle we construct the pull-back of the world-line path integral to super moduli space in the Hamiltonian formulation. We describe the underlying geometric decomposition of super moduli space. Algebraically, this…
We describe discrete symmetries of two-dimensional Yang-Mills theory with gauge group $G$ associated to outer automorphisms of $G$, and their corresponding defects. We show that the gauge theory partition function with defects can be…
Based on a generalization of the stochastic quantization scheme we recently proposed a generalized, globally defined Faddeev-Popov path integral density for the quantization of Yang-Mills theory. In this talk first our approach on the whole…
Let $\mathfrak{g}$ be the Lie Algebra of a compact semi-simple gauge group. For a $\mathfrak{g}$-valued 1-form $A$, consider the Yang-Mills action \begin{equation} S_{{\rm YM}}(A) = \int_{\mathbb{R}^4} \left|dA + A \wedge A \right|^2\…
We show, by introducing purely auxiliary gluinos and scalars, that the quantum path integral for a class of 3D interacting non-supersymmetric gauge theories localises. The theories in this class all admit a `Manin gauge theory' formulation,…