Three-dimensional AdS gravity and extremal CFTs at<i>c</i>= 8<i>m</i>

Three dimensional Einstein gravity with negative cosmological constant −1/ℓ 2 deformed by a gravitational Chern-Simons action with coefficient 1/µ is studied in an asymptotically AdS 3 spacetime. It is argued to violate unitary or positivity for generic µ due to negativeenergy massive gravitons. However at the critical value µℓ = 1, the massive gravitons disappear and BTZ black holes all have mass and angular momentum related by ℓM = J. The corresponding chiral quantum theory of gravity is conjectured to exist and be dual to a purely right-moving boundary CFT with central charges (c L , c R ) = (0, 3ℓ/G).

show abstract

“…Using formula (13) for the central charges one readily finds that this agrees with the macroscopic result (56).…”

Section: Positivity Of Energy 41 Btz Black Holessupporting

confidence: 80%

Chiral gravity in three dimensions

Li¹,

Song²,

Strominger³

2008

J. High Energy Phys.

414

860

View full text Add to dashboard Cite

show abstract

“…The considerations in the previous paragraphs might be of interest for the Euclidean approach/CFT approach pursued in [42][43][44][45][46][47][48][49][50]. We conclude with three options, all of which are worthwhile pursuing:…”

Section: Discussionmentioning

confidence: 99%

Instability in cosmological topologically massive gravity at the chiral point

Grumiller

Johansson

2008

J. High Energy Phys.

236

448

View full text Add to dashboard Cite

We consider cosmological topologically massive gravity at the chiral point with positive sign of the Einstein-Hilbert term. We demonstrate the presence of a negative energy bulk mode that grows linearly in time. Unless there are physical reasons to discard this mode, this theory is unstable. To address this issue we prove that the mode is not pure gauge and that its negative energy is time-independent and finite. The isometry generators L 0 andL 0 have non-unitary matrix representations like in logarithmic CFT. While the new mode obeys boundary conditions that are slightly weaker than the ones by Brown and Henneaux, its fall-off behavior is compatible with spacetime being asymptotically AdS 3 . We employ holographic renormalization to show that the variational principle is well-defined. The corresponding Brown-York stress tensor is finite, traceless and conserved. Finally we address possibilities to eliminate the instability and prospects for chiral gravity.

show abstract

“…It is worth noting that for k = 3m for some m ≥ 1, these candidate partition functions are exactly the candidate torus path integral introduced in [19] . For k = 1 to k = 11, the chiral functions is obtained in [42]. Here are some examples: JHEP09(2020)083…”

Section: )mentioning

confidence: 99%

Three dimensional pure gravity and generalized Hecke operators

Ashrafi

2020

J. High Energ. Phys.

View full text Add to dashboard Cite

In this paper, we study mathematical functions of relevance to pure gravity in AdS3. Modular covariance places stringent constraints on the space of such functions; modular invariance places even stronger constraints on how they may be combined into physically viable candidate partition functions. We explicitly detail the list of holomorphic and anti-holomorphic functions that serve as candidates for chiral and anti-chiral partition functions and note that modular covariance is only consistent with such functions when the left (resp. right) central charge is an integer multiple of 8, c ∈ 8ℕ. We then find related constraints on the symmetry group of the corresponding topological, Chern-Simons, theory in the bulk of AdS. The symmetry group of the theory can be one of two choices: either SO(2; 1) × SO(2; 1) or its three-fold diagonal cover. We introduce the generalized Hecke operators which map the modular covariant functions to the modular covariant functions. With these mathematical results, we obtain conjectural partition functions for extremal CFT2s, and the corresponding microcanonical entropies, when the chiral central charges are multiples of eight. Finally, we compute subleading corrections to the Beckenstein-Hawking entropy in the bulk gravitational theory with these conjectural partition functions.

show abstract

Three-dimensional AdS gravity and extremal CFTs atc= 8m

Cited by 10 publications

References 40 publications

Chiral gravity in three dimensions

Chiral gravity in three dimensions

Instability in cosmological topologically massive gravity at the chiral point

Three dimensional pure gravity and generalized Hecke operators

Contact Info

Product

Resources

About