ترغب بنشر مسار تعليمي؟ اضغط هنا

Canonical Analysis of the Jackiw-Teitelboim Model in the Temporal Gauge. I. The Classical Theory

475   0   0.0 ( 0 )
 نشر من قبل Olivier Piguet
 تاريخ النشر 2008
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

As a preparation for its quantization in the loop formalism, the 2-dimensional gravitation model of Jackiw and Teitelboim is analysed in the classical canonical formalism. The dynamics is of pure constraints as it is well-known. A partial gauge fixing of the temporal type being performed, the resulting second class constraints are sorted out and the corresponding Dirac bracket algebra is worked out. Dirac observables of this classical theory are then calculated.



قيم البحث

اقرأ أيضاً

In this note we study the $1+1$ dimensional Jackiw-Teitelboim gravity in Lorentzian signature, explicitly constructing the gauge-invariant classical phase space and the quantum Hilbert space and Hamiltonian. We also semiclassically compute the Hartle -Hawking wave function in two different bases of this Hilbert space. We then use these results to illustrate the gravitational version of the factorization problem of AdS/CFT: the Hilbert space of the two-boundary system tensor-factorizes on the CFT side, which appears to be in tension with the existence of gauge constraints in the bulk. In this model the tension is acute: we argue that JT gravity is a sensible quantum theory, based on a well-defined Lorentzian bulk path integral, which has no CFT dual. In bulk language, it has wormholes but it does not have black hole microstates. It does however give some hint as to what could be added to to rectify these issues, and we give an example of how this works using the SYK model. Finally we suggest that similar comments should apply to pure Einstein gravity in $2+1$ dimensions, which wed then conclude also cannot have a CFT dual, consistent with the results of Maloney and Witten.
137 - K.B. Alkalaev 2013
We formulate AdS_2 higher spin gravity as BF theory with fields taking values in sl(N,R) algebra treated as higher spin algebra. The theory is topological and naturally extends the Jackiw-Teitelboim gravity model so as to include higher spin fields. The BF equations linearized about AdS_2 background are interpreted as describing higher spin partially-massless fields of maximal depth along with dilaton fields. It is shown that there are dual metric-like formulations following from the original linearized BF higher spin theory. The duality establishes a dynamical equivalence of the metric-like field equations that can be given either as massive scalar field equations or as conservation conditions for higher spin currents.
50 - Davood Momeni 2020
An interesting deformation of the Jackiw-Teitelboim (JT) gravity has been proposed by Witten by adding a potential term $U(phi)$ as a self-coupling of the scalar dilaton field. During calculating the path integral over fields, a constraint comes from integration over $phi$ as $R(x)+2=2alpha delta(vec{x}-vec{x})$. The resulting Euclidean metric suffered from a conical singularity at $vec{x}=vec{x}$. A possible geometry modeled locally in polar coordinates $(r,varphi)$ by $ds^2=dr^2+r^2dvarphi^2,varphi cong varphi+2pi-alpha$. In this letter we showed that there exists another family of exact geometries for arbitrary values of the $alpha$. A pair of exact solutions are found for the case of $alpha=0$. One represents the static patch of the AdS and the other one is the non static patch of the AdS metric. These solutions were used to construct the Green function for the inhomogeneous model with $alpha eq 0$. We address a type of the phase transition between different patches of the AdS in theory because of the discontinuity in the first derivative of the metric at $x=x$. We extended the study to the exact space of metrics satisfying the constraint $R(x)+2=2sum_{i=1}^{k}alpha_idelta^{(2)}(x-x_i)$ as a modulo diffeomorphisms for an arbitrary set of the deficit parameters $(alpha_1,alpha_2,..,alpha_k)$. The space is the moduli space of Riemann surfaces of genus $g$ with $k$ conical singularities located at $x_k$ denoted by $mathcal{M}_{g,k}$.
The Jackiw-Teitelboim (JT) model arises from the dimensional reduction of charged black holes. Motivated by the holographic complexity conjecture, we calculate the late-time rate of change of action of a Wheeler-DeWitt patch in the JT theory. Surpris ingly, the rate vanishes. This is puzzling because it contradicts both holographic expectations for the rate of complexification and also action calculations for charged black holes. We trace the discrepancy to an improper treatment of boundary terms when naively doing the dimensional reduction. Once the boundary term is corrected, we find exact agreement with expectations. We comment on the general lessons that this might hold for holographic complexity and beyond.
We revisit a deformed Jackiw-Teitelboim model with a hyperbolic dilaton potential, constructed in the preceding work [arXiv:1701.06340]. Several solutions are discussed in a series of the subsequent papers, but all of them are pathological because of a naked singularity intrinsic to the deformation. In this paper, by employing a Weyl transformation to the original deformed model, we consider a Liouville-type potential with a cosmological constant term. Then regular solutions can be constructed with coupling to a conformal matter by using $SL(2)$ transformations. For a black hole solution, the Bekenstein-Hawking entropy is computed from the area law. It can also be reproduced by evaluating the boundary stress tensor with an appropriate local counter-term (which is essentially provided by a Liouville-type potential).
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا