Related papers: Weak supersymmetry and superconformal indices
Hidden symmetries, described by higher order in momenta integrals of motion that generate nonlinear algebras, are explored at the level of classical and quantum mechanics in a variety of physical systems related to conformal and…
The polynomial deformations of the Witten extensions of the U(su(2)) and U(osp(1,2)) algebras are three generator algebras with normal ordering, admitting a two generator subalgebra. The modules and the representations of these algebras are…
We investigate a new class of dark matter: superweakly-interacting massive particles (superWIMPs). As with conventional WIMPs, superWIMPs appear in well-motivated particle theories with naturally the correct relic density. In contrast to…
Weak-scale supersymmetry is one of the most favoured theories beyond the Standard Model of particle physics that elegantly solves various theoretical and observational problems in both particle physics and cosmology. In this thesis, I…
For physicists: For supersymmetric quantum mechanics, there are cases when a mod-2 Witten index can be defined, even when a more ordinary $\mathbb{Z}$-valued Witten index vanishes. Similarly, for 2d supersymmetric quantum field theories,…
We classify possible supersymmetry-preserving relevant, marginal, and irrelevant deformations of unitary superconformal theories in $d \geq 3$ dimensions. Our method only relies on symmetries and unitarity. Hence, the results are model…
We apply the supersymmetry approach to one-dimensional quantum systems with spatially-dependent mass, by including their ordering ambiguities dependence. In this way we extend the results recently reported in the literature. Furthermore, we…
We investigate the unflavoured Schur indices of class $\mathcal S$ theories of modest rank, and in the case of $\mathcal{N}=4$ super Yang-Mills theory with special unitary gauge group of somewhat more general rank, with an eye towards their…
We consider quantum models corresponding to superymmetrizations of the two-dimensional harmonic oscillator based on worldline $d=1$ realizations of the supergroup SU$(\,{\cal N}/2\,|1)$, where the number of supersymmetries ${\cal N}$ is…
We construct supersymmetric conformal sigma models in three dimensions. Nonlinear sigma models in three dimensions are nonrenormalizable in perturbation theory. We use the Wilsonian renormalization group equation method, which is one of the…
For each pair of complex symmetric matrices $(A,B)$ we provide a normal form with a minimal number of independent parameters, to which all pairs of complex symmetric matrices $(\widetilde{A},\widetilde{B})$, close to $(A,B)$ can be reduced…
SuperWeakly-Interacting Massive Particles (superWIMPs) produced in the late decays of other particles are well-motivated dark matter candidates and may be favored over standard Weakly-Interacting Massive Particles (WIMPs) by small scale…
We study the superconformal indices of 4d theories coming from 6d N=(2,0) theory of type \Gamma on a Riemann surface, with the action of the outer-automorphism \sigma in the trace. We find that the indices are given by the partition…
A new, recursive method of calculating matrix elements of polynomial hamiltonians is proposed. It is particularly suitable for the recent algebraic studies of the supersymmetric Yang-Mills quantum mechanics in any dimensions. For the D=2…
We introduce the $L$-series of weakly holomorphic modular forms using Laplace transforms and give their functional equations. We then determine converse theorems for vector-valued harmonic weak Maass forms, Jacobi forms, and elliptic…
We analyze general structure of N-fold supersymmetry which provides a systematic framework to construct weakly quasi-solvable quantum mechanical systems. Main ingredients of our analysis are dimensional analysis and introduction of an…
The "superconformal index" is a character-valued invariant attached by theoretical physics to unitary representations of Lie superalgebras, such as $\mathfrak{su}(2,2\vert n)$, that govern certain quantum field theories. The index can be…
We systematically construct a class of two-dimensional $(2,2)$ supersymmetric gauged linear sigma models with phases in which a continuous subgroup of the gauge group is totally unbroken. We study some of their properties by employing a…
We propose two novel methods for computing the superconformal index of 5d superconformal field theories that cannot be described by conventional Lagrangian descriptions under mass deformations. The first approach involves the use of Higgs…
There are supersymmetric gauge theories which do not possess any parameters nor flat directions, and hence cannot be studied anywhere in the field space using holomorphy (``non-calculable''). Some of them are believed to break supersymmetry…