Correlation functions and AdS/LCFT correspondence

Johansson

2008

J. High Energy Phys.

236

448

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.

Section: A Consistent Quantum Theory Of Euclidean Chiral Gravity Withmentioning

confidence: 86%

“…In the parlance of LCFT literature ψ new is the logarithmic partner of ψ L . (For reviews see [14,15]; for some applications to AdS/LCFT see [16][17][18][19][20]. 4 ) From the equations (3.5) we deduce…”

Section: Logarithmic Mode With Negative Energymentioning

confidence: 98%

Instability in cosmological topologically massive gravity at the chiral point

Johansson

2008

J. High Energy Phys.

236

448

“…To the best of our knowledge this would be the first explicit gravity dual of this type. Besides the AdS/LCFT literature [61][62][63][64][65] the only other context where gravity and LCFTs appear together so far seems to be twodimensional gravity coupled to matter [86]. It would be nice to find some condensed matter applications, like some strongly coupled systems described by a logarithmic CFT with c L = 0, c R > 0.…”

Section: Discussionmentioning

confidence: 99%

AdS3/LCFT2 — correlators in cosmological topologically massive gravity

Sachs²

2010

J. High Energ. Phys.

100

For cosmological topologically massive gravity at the chiral point we calculate momentum space 2-and 3-point correlators of operators in the postulated dual CFT on the cylinder. These operators are sourced by the bulk and boundary gravitons. Our correlators are fully consistent with the proposal that cosmological topologically massive gravity at the chiral point is dual to a logarithmic CFT. In the process we give a complete classification of normalizable and non-normalizeable left, right and logarithmic solutions to the linearized equations of motion in global AdS 3 .

“…(20). Thus, our first task is to find all solutions of the linearized equations of motion and to classify them into normalizable and non-normalizable ones, where "normalizable" refers to asymptotic (large ρ) behavior that is exponentially suppressed as compared to the AdS background (12).…”

Section: Growing Logsmentioning

confidence: 99%

Gravity duals for logarithmic conformal field theories

Johansson

2010

J. Phys.: Conf. Ser.

Logarithmic conformal field theories with vanishing central charge describe systems with quenched disorder, percolation or dilute self-avoiding polymers. In these theories the energy momentum tensor acquires a logarithmic partner. In this talk we address the construction of possible gravity duals for these logarithmic conformal field theories and present two viable candidates for such duals, namely theories of massive gravity in three dimensions at a chiral point. OutlineThis talk is organized as follows. In section 1 we recall salient features of 2-dimensional conformal field theories. In section 2 we review a specific class of logarithmic conformal field theories where the energy momentum tensor acquires a logarithmic partner. In section 3 we present a wish-list for gravity duals to logarithmic conformal field theories. In section 4 we discuss two examples of massive gravity theories that comply with all the items on that list. In section 5 we address possible applications of an Anti-deSitter/logarithmic conformal field theory correspondence in condensed matter physics.