The Relation between Polygonal Gravity and 3D Loop Quantum Gravity

Quantum Gravity;Discrete Gravity;Torus Universe;Loop quantum gravity;'t Hooft gravity

Tiede, Pauladvisor:Girelli, Florian ; affiliation1:Faculty of Mathematics ; Girelli, Florian ;

University of Waterloo

关键词: Loop quantum gravity;    Master Thesis;    Quantum Gravity;    Discrete Gravity;    t Hooft gravity;    '    Torus Universe;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/12372/3/Tiede_Paul.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

In this thesis, we explore the relation between ’t Hooft polygonal gravity and loopquantum gravity (LQG) - two models of discrete gravity in 2+1 dimensions. While therelation between the two theories has been studied in the past, the relation between LQGand polygonal gravity remains unclear. Indeed we argue that each approach does notimplement the same type of constraint at the kinematical level. Using a dual formulation ofLQG, we show that polygonal gravity is then recovered by a gauge fixing in this framework.However, whether these gauge choices are possible in general is unanswered in this work.Therefore, we analyze a specific example given by the torus universe in each approach,using one and two polygon decompositions. By using the map from dual LQG to polygonalgravity, we express the physical variables of discrete gravity, or observables, in terms ofpolygonal gravity quantities. Once the constraints in polygonal gravity are implemented wefind that physical observables are no longer independent, meaning that polygonal gravitycannot describe the torus universe using one and two polygon decompositions: the gaugefixing is actually over-constraining the theory. Faced with these results, we develop adual version of ’t Hooft gravity. The resulting theory is then proven to be equal to thekinematical phase space of LQG; therefore, dual ’t Hooft gravity is free of the issuesplaguing polygonal gravity.