The low energy effective couplings of a four-dimensional $\mathcal{N}=2$ supersymmetric gauge theory to topological invariants of the background gravitational field are described by two functions $A$ and $B$. These two functions play an important role in the study of topologically twisted four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories and in the computation of central charges of $\mathcal{N}=2$ superconformal theories. In this paper, we compute $A$ and $B$ from the partition function in the $Ω$-background for $\mathrm{SU}(2)$ gauge theories. Our results not only confirm the predicted expressions of the effective gravitational couplings, but also give the previously undetermined overall multiplicative factors. We also analyze $A$ and $B$ for the $\mathrm{SU}(N)$ super-Yang-Mills theory, and confirm all the previous predictions.
The $\mathcal{N}{=}\,4$ supersymmetric $\mathrm{U}(2)$-spin hyperbolic Calogero-Sutherland model with odd matrix fields is examined. Explicit form of the $\mathcal{N}{=}\,4$ supersymmetry generators is derived. The Lax representation for the dynamics of the $\mathcal{N}{=}\,4$ hyperbolic $\mathrm{U}(2)$-spin Calogero-Sutherland system is found. The reduction to the $\mathcal{N}{=}\,4$ supersymmetric spinless hyperbolic Calogero-Sutherland system is established.
This paper studies supersymmetric ground states of 3d $\mathcal{N}=4$ supersymmetric gauge theories on a Riemann surface of genus $g$. There are two distinct spaces of supersymmetric ground states arising from the $A$ and $B$ type twists on the Riemann surface, which lead to effective supersymmetric quantum mechanics with four supercharges and supermultiplets of type $\mathcal{N}=(2,2)$ and $\mathcal{N}=(0,4)$ respectively. We compute the space of supersymmetric ground states in each case, graded by flavour and R-symmetries and in different chambers for real mass and FI parameters, for a large…
Mirror symmetry of 3d $\mathcal{N}=4$ gauge theories and supersymmetric indices
我们计算超对称指数来检验三维$\mathcal{N}=4$规范理论的镜像对称性和四维$\mathcal{N}=4$ Super Yang-Mills理论中半BPS富集边界条件和界面的对偶性。在IIB型弦论的S-对偶作用下，我们发现指数的匹配是Gaiotto和Witten提出的三维界面的各种对偶性的有力证据.
We define a manifestly supersymmetric version of the $T \overline{T}$ deformation appropriate for a class of $(0+1)$-dimensional theories with $\mathcal{N} = 1$ or $\mathcal{N} = 2$ supersymmetry, including one presentation of the super-Schwarzian theory which is dual to JT supergravity. These deformations are written in terms of Noether currents associated with translations in superspace, so we refer to them collectively as $f(\mathcal{Q})$ deformations. We provide evidence that the $f(\mathcal{Q})$ deformations of $\mathcal{N} = 1$ and $\mathcal{N} = 2$ theories are on-shell equivalent to th…
We consider soliton solutions in AdS$_{4}$ with a flat slicing and Wilson loops around one cycle. We study the phase structure and find the ground state and identify supersymmetric solutions as a function of the Wilson loops. We work in the context of a scalar field truncation of gauged $\mathcal{N}=8$ supergravity, where all the dilatons are equal and all the axions vanish in the STU model. In this theory, we construct new soliton solutions parameterized by two Wilson lines. We find that there is a degeneracy of supersymmetric solutions. We also show that, for alternate boundary conditions, t…
We apply the functional renormalization group approach to a $\mathcal{N}=1$ supersymmetric gauge model with one chiral superfield coupled to a vector $U(1)$ superfield. We find that the nonrenormalization theorem still works at leading order in the supercovariant derivative expansion of the fields. We also find the beta functions and we study the behavior of its fixed points in the local potential approximation. Regulators are also discussed.
