The spin connection of twisted geometry
نویسندگان
چکیده
Twisted geometry is a piecewise-flat geometry less rigid than Regge geometry. In Loop Gravity, it provides the classical limit for each step of the truncation utilized in the definition of the quantum theory. We define the torsionless spin-connection of a twisted geometry. The difficulty given by the discontinuity of the triad is addressed by interpolating between triads. The curvature of the resulting spin connection reduces to the Regge curvature in the case of a Regge geometry.
منابع مشابه
Anti-de Sitter space from supersymmetric gauge theory
We construct a four dimensional Yang-Mills theory with N = 4 twisted supersymmetry whose classical vacua correspond to four dimensional anti-de Sitter space. The theory utilizes a complex gauge field whose real part is a spin connection which is used to enforce local Lorentz invariance. The imaginary part of the connection can then be interpreted as a vierbein. The topological construction ensu...
متن کاملSpin and Hyperelliptic Structures of Log Twisted Differentials
Using stable log maps, we introduce log twisted differentials extending the notion of abelian differentials to the Deligne-Mumford boundary of stable curves. The moduli stack of log twisted differentials provides a compactification of the strata of abelian differentials. The open strata can have up to three connected components, due to spin and hyperelliptic structures. We prove that the spin p...
متن کاملOn the noncommutative spin geometry of the standard Podleś sphere and index computations
The purpose of the paper is twofold: First, known results of the noncommutative spin geometry of the standard Podleś sphere are extended by discussing Poincaré duality and orientability. In the discussion of orientability, Hochschild homology is replaced by a twisted version which avoids the dimension drop. The twisted Hochschild cycle representing an orientation is related to the volume form o...
متن کاملConnections over Twisted Tensor Products of Algebras
Motivated from some results in classical differential geometry, we give a constructive procedure for building up a connection over a (twisted) tensor product of two algebras, starting from connections defined on the factors. The curvature for the product connection is explicitly calculated, and shown to be independent of the choice of the twisting map and the module twisting map used to define ...
متن کاملThe sl2 loop algebra symmetry of the twisted transfer matrix of the six vertex model at roots of unity
We discuss a family of operators which commute or anti-commute with the twisted transfer matrix of the six-vertex model at q being roots of unity: q = 1. The operators commute with the Hamiltonian of the XXZ spin chain under the twisted boundary conditions, and they are valid also for the inhomogeneous case. For the case of the anti-periodic boundary conditions, we show explicitly that the oper...
متن کامل