We define an index of the fermionic signature operator on even-dimensional globally hyperbolic spin manifolds of finite lifetime. The invariance of the index under homotopies is studied. The definition is generalized to causal fermion systems with a chiral grading. We give examples of space-times and Dirac operators thereon for which our index is non-trivial.

We couple a neutral scalar field and a Majorana fermion field to Einstein gravity represented by the Robertson-Walker metric and find a class of exact cosmological solutions.

We investigate the discrete chiral transformation of a Majorana fermion on a torus. Depending on the boundary conditions the integration measure can change sign. Taking this anomalous behavior into account we define a chiral order parameter as a ratio of partition functions with differing boundary conditions. Then the lattice realization of the Gross-Neveu model with Wilson fermions is simulate...

Lüscher’s local bosonic algorithm for Monte Carlo simulations of quantum field theories with fermions is applied to the simulation of a possibly supersymmetric Yang-Mills theory with a Majorana fermion in the adjoint representation. Combined with a correction step in a two-step polynomial approximation scheme, the obtained algorithm seems to be promising and could be competitive with more conve...

We briefly review the spin-bit formalism, describing the non-planar dynamics of the N = 4, d = 4 Super Yang-Mills SU(N) gauge theory. After considering its foundations, we apply such a formalism to the su(2) sector of purely scalar operators. In particular, we report an algorithmic formulation of a deplanarizing procedure for local operators in the planar gauge theory, used to obtain planarlyco...

We report an unprecedented quantum criticality crossover representing two different universal scaling behaviors in a Kitaev magnetic material $\alpha$-RuCl$_3$. $\alpha$-RuCl$_3$ presents both symmetry breaking antiferromagnetic order and long-range entangled topological of spin liquid, thus could be candidate system for new universality class involving deconfined fractionalized excitations the...

We study the effective field theory (including operators up to dimension five) of models in which dark matter is composite, consisting either an electroweak doublet Dirac fermion (`higgsino-like matter') or triplet Majorana (`wino-like matter'). Some dimension-five former case cause mass splittings between neutralino and chargino states, leading a depleted rate coannihilations viable thermal re...

We briefly review the spin-bit formalism, describing the non-planar dynamics of the N = 4, d = 4 Super Yang-Mills SU(N) gauge theory. After considering its foundations, we apply such a formalism to the su(2) sector of purely scalar operators. In particular, we report an algorithmic formulation of a deplanarizing procedure for local operators in the planar gauge theory, used to obtain planarlyco...

Fermions in (anti) de Sitter gravity theory in four dimensions are considered. Especially we propose new fermion actions to derive a Weyl or Majorana fermion action if we break the AdS (dS) group to the Lorentz group in curved spacetime. E-mail: [email protected], 2 E-mail: [email protected]