Related papers: Graphical Representation of Supersymmetry and Comp…
A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if $(x,y)\in E$. A triangular grid graph is a subgraph of a tiling of the plane with…
A review is given of a recently developed technique for the analysis of SO(2N) invariant couplings which allows a full exhibition of the SU(N) invariant content of couplings involving the SO(2N) semi-spinors $|\Psi_{\pm}>$ with chiralilty…
We study d=2, N=(2,2) non-linear sigma-models in (2,2) superspace. By analyzing the most general constraints on a superfield, we show that through an appropriate choice of coordinates, there are no other superfields than chiral, twisted…
This paper treats some basic points in general relativity and in its perturbative analysis. Firstly a systematic classification of global SO(n) invariants, which appear in the weak-field expansion of n-dimensional gravitational theories, is…
The aim of this paper is to discuss a kinematical algebraic structure of a theory of gravity, that would be unitary, renormalizable and coupled in the same manner to both spinorial and tensorial matter fields. An analysis of the common…
A concrete representation of the Clifford algebra (for any hyperbolic quadratic space) is given using what are called Suslin matrices. This explicit construction is used to analyze the corresponding Spin groups and the involution and might…
Progress along the line of a previous article are reported. One main point is to include chiral operators with fractional quantum group spins (fourth or sixth of integers) which are needed to achieve modular invariance. We extend the study…
We consider high dimensional variants of the maximum flow and minimum cut problems in the setting of simplicial complexes and provide both algorithmic and hardness results. By viewing flows and cuts topologically in terms of the simplicial…
It is shown, that recently constructed PST Lagrangians for chiral supergravities follow directly from earlier Kavalov-Mkrtchyan Lagrangians by an Ansatz for the $\theta $ tensor by expressing this in terms of the PST scalar. The susy…
The spinorial geometry method of solving Killing spinor equations is reviewed as it applies to 6-dimensional (1,0) supergravity. In particular, it is explained how the method is used to identify both the fractions of supersymmetry preserved…
We construct the most general gaugings of the maximal D=6 supergravity. The theory is (2,2) supersymmetric, and possesses an on-shell SO(5,5) duality symmetry which plays a key role in determining its couplings. The field content includes…
We develop a new off-shell formulation for five-dimensional (5D) conformal supergravity obtained by gauging the 5D superconformal algebra in superspace. An important property of the conformal superspace introduced is that it reduces to the…
We conjecture infrared emergent $\mathcal{N}=4$ supersymmetry for a class of three-dimensional $\mathcal{N}=2$ $U(1)$ gauge theories coupled with a single chiral multiplet. One example is the case where $U(1)$ gauge group has the…
Supersymmetric nonlinear sigma models are obtained from linear sigma models by imposing supersymmetric constraints. If we introduce auxiliary chiral and vector superfields, these constraints can be expressed by D-terms and F-terms depending…
Using linear algebraic methods we show that every (possibly infinite-dimensional) representation of a quiver with underlying graph $A_{\infty, \infty}$ is Krull-Schmidt, as long as the arrows in the quiver eventually point outward.
Any N=2 superconformal field theory (SCFT) in four dimensions has a sector of operators related to a two-dimensional chiral algebra containing a Virasoro sub-algebra. Moreover, there are well-known examples of isolated SCFTs whose chiral…
We construct new classes of supersymmetric $AdS_2\times \Sigma$ solutions, where $\Sigma=\Sigma(n_N,n_S)$ is a spindle. Such solutions can arise as the near horizon limit of supersymmetric, accelerating black holes. The solutions are…
We obtain an explicit expression for the supersymmetric Wilson loop in terms of chiral superfields and supercurrents in superspace. The result turns out to be different from what one would expect from the simple replacement of Lie algebra…
We study the dynamics of chiral SU(N) gauge theories. These contain Weyl fermions in the symmetric or anti-symmetric representation of the gauge group, together with further fermions in the fundamental and anti-fundamental. We revisit an…
We study the minimal unitary representation (minrep) of SO(5,2), obtained by quantization of its geometric quasiconformal action, its deformations and supersymmetric extensions. The minrep of SO(5,2) describes a massless conformal scalar…