Abstract
We discuss aspects of generic 2-dimensional dilaton gravity theories. The 2-dim geometry is in general conformal to $AdS_2$ and has IR curvature singularities at zero temperature: this can be regulated by a black hole. The on-shell action is divergent: we discuss the holographic energy-momentum tensor by adding appropriate counterterms. For theories obtained by dimensional reduction of the gravitational sector of higher dimensional theories, for instance higher dimensional $AdS$ gravity as a concrete example, the 2-dimensional description dovetails with the higher dimensional one. We also discuss more general theories containing an extra scalar field which now drives nontrivial dynamics. Finally we discuss aspects of the 2-dimensional cosmological singularities discussed in earlier work. These studies suggest that generic 2-dim dilaton gravity theories are somewhat distinct from JT gravity and theories "near JT".
Highlights
Dilaton gravity in two-dimensions has been under active investigation in recent years, in part following discussions of nearly the two-dimensional anti–de Sitter(AdS2) holography [1,2,3,4,5] and more recently those of Jackiw-Teitelboim (JT) gravity [9,10] being dual to ensembles [11], with further development in [12,13,14,15,16,17,18,19,20,21]
1 ε4 divergence giving a finite term at this order; this is the term in the second line in (38). Note that this Oðε4Þ subleading term is at the same order as the term in (30) which gives the black hole excitation; in some ways this is in sync with the expectation of soft modes arising from the reduction of low lying hydrodynamic modes in the
The two-dimensional geometry is in general conformal to AdS2 and has IR curvature singularities at zero temperature, which are regulated by a black hole
Summary
Dilaton gravity in two-dimensions has been under active investigation in recent years, in part following discussions of nearly the two-dimensional anti–de Sitter(AdS2) holography [1,2,3,4,5] (reviewed in [6,7,8]) and more recently those of Jackiw-Teitelboim (JT) gravity [9,10] being dual to ensembles [11], with further development in [12,13,14,15,16,17,18,19,20,21]. Two-dimensional, (7) and more generally (1) is apparently encoding higher dimensional gravity intrinsically, this is quite different from the near extremal near horizon AdS2 × X throats in extremal objects, where the X-compactification leads to an intrinsically two-dimensional theory with a clear separation of scales To put this in perspective, we note that the gravity subsector, taken stand-alone, is universal to all string/M theories on AdSD × X10=11−D. From this point of view, it should not be surprising that these two-dimensional theories exhibit the divergences above; they are perhaps best regarded as UV incomplete low energy effective theories universal to all UV completions AdSD × X upstairs, so they are thermodynamic, akin to an ensemble These features appear generic to twodimensional dilaton gravity theories of the form (1), with general (nonlinear) potentials.
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