Related papers: Twisted reality condition for spectral triple on t…
We study the twisted reality condition of Math. Phys. Anal. Geom. 19 (2016),no. 3, Art. 16, for spectral triples, in particular with respect to the product and the commutant. Motivated by this we present the procedure, which allows one to…
Motivated by examples obtained from conformal deformations of spectral triples and a spectral triple construction on quantum cones we propose a new twisted reality condition for the Dirac operator.
We generalize the notion of spectral triple with reality structure to spectral triples with multitwisted real structure, the class of which is closed under the tensor product composition. In particular, we introduce a multitwisted order one…
We systematically investigate ways to twist a real spectral triple via an algebra automorphism and in particular, we naturally define a twisted partner for any real graded spectral triple. Among other things we investigate consequences of…
Twisted real structures are well-motivated as a way to implement the conformal transformation of a Dirac operator for a real spectral triple without needing to twist the noncommutative 1-forms. We study the coupling of spectral triples with…
We extend twisted inner fluctuations to twisted spectral triples that do not meet the twisted first-order condition, following what has been done in [6] for the non-twisted case. We find a similar non-linear term in the fluctuation, and…
We investigate the regularity condition for twisted spectral triples. This condition is equivalent to the existence of an appropriate pseudodifferential calculus compatible with the spectral triple. A natural approach to obtain such a…
After a brief review on the applications of twisted spectral triples to physics, we adapt to the twisted case the notion of real part of a spectral triple. In particular, when one twists a usual spectral triple by its grading, we show that…
We extend to twisted spectral triples the fluctuations of the metric, as well as their gauge transformations. The former are bounded perturbations of the Dirac operator that arise when a spectral triple is exported between Morita equivalent…
Nontrivial twisted boundary conditions associated with extra compact dimensions produce an ambiguity in the value of the four dimensional coupling constants of the renormalizable interactions of the twisted fields' zero modes. Resolving…
An interesting feature of the finite-dimensional real spectral triple (A,H,D,J) of the Standard Model is that it satisfies a ``second-order'' condition: conjugation by J maps the Clifford algebra Cl_D(A) into its commutant, which in fact is…
The junction condition across a singular surface in general relativity, formulated by Israel, has double covariance. In this paper, a general perturbation scheme of the junction condition around an arbitrary background is given in a doubly…
One-particle spectral properties in the normal phase of the two-dimensional attractive Hubbard model are investigated in the weak coupling regime using the non-selfconsistent T-matrix approximation. The corresponding equations are evaluated…
String compactifications with T-duality twists are revisited and the gauge algebra of the dimensionally reduced theories calculated. These reductions can be viewed as string theory on T-fold backgrounds, and can be formulated in a `doubled…
This is a review of the properties of spectral fluctations in disordered metals, their relation with Random Matrix Theory and semiclassical picture. We also review the physics of persistent currents in mesoscopic isolated rings, the…
The effects of three-dimensional perturbations in two-dimensional turbulence are investigated, through a conformal field theory approach. We compute scaling exponents for the energy spectra of enstrophy and energy cascades, in a strong…
Low lying scalar resonances emerge as a necessary part to adjust chiral perturbation theory to experimental data once unitarity constraint is taken into consideration. I review recent progress made in this direction in a model independent…
We study chiral algebra in the reduction of 3D $\mathcal{N} = 2 $ supersymmetric gauge theories on an interval with the $\mathcal{N}=(0,2)$ Dirichlet boundary conditions on both ends. By invoking the 3D ``twisted formalism'' and the 2D…
We consider the problem of variation of spectral subspaces for linear self-adjoint operators under off-diagonal perturbations. We prove a number of new optimal results on the shift of the spectrum and obtain (sharp) estimates on the norm of…
The perturbation of the symmetric orbifold of $\mathbb{T}^4$ under the triplet of exactly marginal operators from the $2$-cycle twisted sector is studied in perturbation theory. We show that the structure of the triplet perturbation is very…