Related papers: Localization principle in SUSY gauge theories
In the previous work, it was shown that, in supersymmetric (matrix) discretized quantum mechanics, inclusion of an external field twisting the boundary condition of fermions enables us to discuss spontaneous breaking of supersymmetry (SUSY)…
We describe applications of the gluing formalism discussed in the companion paper. When a $d$-dimensional local theory $\text{QFT}_d$ is supersymmetric, and if we can find a supersymmetric polarization for $\text{QFT}_d$ quantized on a…
We apply equivariant localization to supersymmetric quantum mechanics and show that the partition function localizes on the instantons of the theory. Our construction of equivariant cohomology for SUSY quantum mechanics is different than…
We construct Euclidean 5d supersymmetric gauge theories on the five-sphere with vector and hypermultiplets. The SUSY transformation and the action are explicitly determined from the standard Noether procedure as well as from off-shell…
We use localization to compute the partition function of a four dimensional, supersymmetric, abelian gauge theory on a hemisphere coupled to charged matter on the boundary. Our theory has eight real supercharges in the bulk of which four…
We review recent developments in two-dimensional $\mathcal{N}=(2,2)$ supersymmetric gauge theories focusing on the implementation and applications of localization techniques.
Recently there was a substantial progress in understanding of supersymmetric theories (in particular, their BPS spectrum) in space-times of different dimensions due to the exact computation of superconformal indices and partition functions…
Holomorphy of the superpotential and of the coefficient of the gauge kinetic terms in supersymmetric theories lead to powerful results. They are the underlying conceptual reason for the important non-renormalization theorems. They also…
We study localization of five-dimensional supersymmetric $U(1)$ gauge theory on $\mathbb{S}^3 \times \mathbb{R}_{\theta}^{2}$ where $\mathbb{R}_{\theta}^{2}$ is a noncommutative (NC) plane. The theory can be isomorphically mapped to…
The Batalin-Vilkovisky formalism provides a powerful technique to deal with gauge and global (super)symmetries that may only hold on shell. We argue that, since global (super)symmetries and gauge symmetries appear on an equal footing in the…
We use supersymmetric localization techniques to study the low-energy dynamics of BPS vortex-strings in four-dimensional N=2 theories. We focus on theories with SU(Nc)xU(1) gauge group and Nf hypermultiplets, all in the fundamental…
We study Euclidean 3D N=2 supersymmetric gauge theories on squashed three-spheres preserving isometries SU(2) x U(1) or U(1) x U(1). We show that, when a suitable background U(1) gauge field is turned on, these squashed spheres support…
We study 4D systems in which parameters of the theory have position dependence in one spatial direction. In the limit where these parameters jump, this can lead to 3D interfaces supporting localized degrees of freedom. A priori, this sort…
Using localization techniques, we compute the path integral of $N=2$ SUSY gauge theory coupled to matter on the hemisphere $HS^4$, with either Dirichlet or Neumann supersymmetric boundary conditions. The resulting quantities are…
We examine the relation between supersymmetric localization on $\mathbb{S}^4$ and standard QFT results for non-conformal theories in flat space. Specifically, we consider 1/2 BPS circular Wilson loops in four-dimensional SU($N$)…
Keeping N=1 supersymmetry in 4-dimension and in the leading order, we disuss the various orbifold compactifications of M-theory suggested by Horava and Witten on $T^6/Z_3$, $T^6/Z_6$, $T^6/Z_{12}$, and the compactification by keeping…
In the first part of the talk, I explain what empirical evidence points to the need for having an effective grand unification-like symmetry possessing the symmetry SU(4)-color in 4D. If one assumes the premises of a future predictive theory…
We consider $\mathcal{N}=2$ supersymmetric gauge theories on four manifolds admitting an isometry. Generalized Killing spinor equations are derived from the consistency of supersymmetry algebrae and solved in the case of four manifolds…
We apply the localization technique to topologically twisted N=(2,2) supersymmetric gauge theory on a discretized Riemann surface (the generalized Sugino model). We exactly evaluate the partition function and the vacuum expectation value…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…