# Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models

@article{Mandal2017CoadjointOA, title={Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models}, author={Gautam Mandal and Pranjal Nayak and Spenta R. Wadia}, journal={Journal of High Energy Physics}, year={2017}, volume={2017}, pages={1-42} }

A bstractThe Nambu-Goldstone (NG) bosons of the SYK model are described by a coset space Diff/SL(2, ℝ), where Diff, or Virasoro group, is the group of diffeomorphisms of the time coordinate valued on the real line or a circle. It is known that the coadjoint orbit action of Diff naturally turns out to be the two-dimensional quantum gravity action of Polyakov without cosmological constant, in a certain gauge, in an asymptotically flat spacetime. Motivated by this observation, we explore Polyakov…

## 104 Citations

### A theory of reparameterizations for AdS3 gravity

- PhysicsJournal of High Energy Physics
- 2019

A bstractWe rewrite the Chern-Simons description of pure gravity on global AdS3 and on Euclidean BTZ black holes as a quantum field theory on the AdS boundary. The resulting theory is (two copies of)…

### Three dimensional view of arbitrary q SYK models

- Physics, Mathematics
- 2017

A bstractIn [15] it was shown that the spectrum and bilocal propagator of SYK model with four fermion interactions can be realized as a three dimensional model in AdS2 ×S1/Z2 with nontrivial boundary…

### Holographic dual to charged SYK from 3D gravity and Chern-Simons

- Physics
- 2020

In this paper, we obtain a bulk dual to the low energy sector of the SYK model, including SYK model with U(1) charge, by Kaluza-Klein (KK) reduction from three dimensions. We show that KK reduction…

### Coadjoint Orbits, Cocycles and Gravitational Wess–Zumino

- MathematicsReviews in Mathematical Physics
- 2018

About 30 years ago, in a joint work with L. Faddeev we introduced a geometric action on coadjoint orbits. This action, in particular, gives rise to a path integral formula for characters of the…

### Liouville theory and matrix models: a Wheeler DeWitt perspective

- Physics
- 2020

We analyse the connections between the Wheeler DeWitt approach for two dimensional quantum gravity and holography, focusing mainly in the case of Liouville theory coupled to $c=1$ matter. Our…

### Solving the Schwarzian via the conformal bootstrap

- Physics
- 2017

A bstractWe obtain exact expressions for a general class of correlation functions in the 1D quantum mechanical model described by the Schwarzian action, that arises as the low energy limit of the SYK…

### Three dimensional view of the SYK/AdS duality

- Mathematics
- 2017

A bstractWe show that the spectrum of the SYK model can be interpreted as that of a 3D scalar coupled to gravity. The scalar has a mass which is at the Breitenholer-Freedman bound of AdS2, and…

### Liouville quantum gravity — holography, JT and matrices

- Physics
- 2020

We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary…

### Defects in Jackiw-Teitelboim quantum gravity

- PhysicsJournal of High Energy Physics
- 2019

Abstract
We classify and study defects in 2d Jackiw-Teitelboim gravity. We show these are holographically described by a deformation of the Schwarzian theory where the reparametrization mode is…

### Nearly AdS2 holography in quantum CGHS model

- PhysicsJournal of High Energy Physics
- 2020

In light of recent developments in nearly AdS2 holography, we revisit the semiclassical version of two-dimensional dilaton gravity proposed by Callan, Giddings, Harvey, and Strominger (CGHS) [1] in…

## References

SHOWING 1-10 OF 70 REFERENCES

### From coadjoint orbits to scale invariant WZNW type actions and 2D quantum gravity action

- Mathematics
- 1990

### Fermions from half-BPS supergravity

- Physics
- 2005

We discuss collective coordinate quantization of the half-BPS geometries of Lin, Lunin and Maldacena [1]. The LLM geometries are parameterized by a single function u on a plane. We treat this…

### Path integral quantization of the coadjoint orbits of the virasoro group and 2-d gravity

- Physics, Geology
- 1989

### NON-RELATIVISTIC FERMIONS, COADJOINT ORBITS OF W∞ AND STRING FIELD THEORY AT c=1

- Physics, Mathematics
- 1992

We apply the method of coadjoint orbits of W∞-algebra to the problem of non-relativistic fermions in one dimension. This leads to a geometric formulation of the quantum theory in terms of the quantum…

### A Stress Tensor for Anti-de Sitter Gravity

- Physics
- 1999

Abstract:We propose a procedure for computing the boundary stress tensor associated with a gravitating system in asymptotically anti-de Sitter space. Our definition is free of ambiguities encountered…

### Quantum gravity partition functions in three dimensions

- Physics
- 2010

We consider pure three-dimensional quantum gravity with a negative cosmological constant. The sum of known contributions to the partition function from classical geometries can be computed exactly,…

### A generalization of Sachdev-Ye-Kitaev

- Mathematics
- 2016

A bstractThe SYK model: fermions with a q-body, Gaussian-random, all-to-all interaction, is the first of a fascinating new class of solvable large N models. We generalize SYK to include f flavors of…

### AdS2 holographic dictionary

- Physics
- 2016

A bstractWe construct the holographic dictionary for both running and constant dilaton solutions of the two dimensional Einstein-Maxwell-Dilaton theory that is obtained by a circle reduction from…

### Three-dimensional quantum geometry and black holes

- Physics
- 1998

We review some aspects of three-dimensional quantum gravity with emphasis in the ‘CFT → Geometry’ map that follows from the BrownHenneaux conformal algebra. The general solution to the classical…

### Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space

- Physics
- 2016

We study a two dimensional dilaton gravity system, recently examined by Almheiri and Polchinski, which describes near extremal black holes, or more generally, nearly $AdS_2$ spacetimes. The…