## 39 Citations

### Schrödinger algebra and non-relativistic holography

- Mathematics
- 2012

We give a group-theoretic interpretation of non-relativistic holography as equivalence between representations of the Schrödinger algebra describing bulk fields and boundary fields. The main result…

### Intertwining operators for non-self-adjoint Hamiltonians and bicoherent states

- Physics, Mathematics
- 2016

This paper is devoted to the construction of what we will call exactly solvable models, i.e., of quantum mechanical systems described by an Hamiltonian H whose eigenvalues and eigenvectors can be…

### Tenfold way for holography: AdS/CFT and beyond

- Mathematics
- 2020

The main purpose of the present paper is to lay the foundations of generalizing the AdS/CFT (holography) idea beyond the conformal setting. The main tool is to find suitable realizations of the bulk…

### Non-relativistic metrics with extremal limits

- Physics
- 2009

We present solutions of type IIB supergravity with z = 2 Schrodinger asymptotics that admit an extremal limit, i.e. the black hole horizon has a double zero. These solutions are obtained as TsT…

### On Casimir operators of conformal Galilei algebras

- MathematicsJournal of Mathematical Physics
- 2019

In a previous work (F. Alshammari, P. S. Isaac, and I. Marquette, J. Phys. A: Math. Theor. 51, 065206 (2018)), we introduced an algorithm that utilises differential operator realisations to find…

### Lowest weight representations of super Schrödinger algebras in low dimensional spacetime

- Mathematics
- 2010

We investigate the lowest weight representations of the super Schrödinger algebras introduced by Duval and Horváthy. This is done by the same procedure as the semisimple Lie algebras. Namely, all…

### Constructing Dualities from Quantum State Manifolds

- Physics
- 2015

The thesis develops a systematic procedure to construct semi-classical gravitational duals from quantum state manifolds. Though the systems investigated are simple quantum mechanical systems without…

### Generalized Heisenberg algebra and (non linear) pseudo-bosons

- Physics, Mathematics
- 2018

We propose a deformed version of the generalized Heisenberg algebra by using techniques borrowed from the theory of pseudo-bosons. In particular, this analysis is relevant when non self-adjoint…

### Non-self-adjoint Hamiltonians with complex eigenvalues

- Mathematics
- 2016

Motivated by what one observes dealing with PT-symmetric quantum mechanics, we discuss what happens if a physical system is driven by a diagonalizable Hamiltonian with not all real eigenvalues. In…

## References

SHOWING 1-10 OF 61 REFERENCES

### Non-relativistic holography

- Physics
- 2008

We consider holography for d-dimensional scale invariant but non-Lorentz invariant field theories, which do not admit the full Schrodinger symmetry group. We find new realizations of the…

### Correlation Functions in Non-Relativistic Holography

- Physics
- 2009

Recently constructed gravity solutions with Schrodinger symmetry provide a new example of AdS/CFT-type dualities for the type of non-relativistic field theories relevant to certain cold atom systems.…

### On the spectrum of nonrelativistic AdS/CFT

- Physics
- 2008

We develop a Hamiltonian picture for a family of models of nonrelativistic AdS/CFT duality. The Schrodinger group is realized via the conformal quantum mechanics of De Alfaro, Fubini and Furlan in…

### Gravity duals for nonrelativistic conformal field theories.

- PhysicsPhysical review letters
- 2008

This work attempts to generalize the anti-de Sitter/conformal field theory correspondence to nonrelativistic conformal field theories which are invariant under Galilean transformations, and constructs a family of metrics which realize these symmetries as isometries.

### Heating up Galilean holography

- Physics
- 2008

We embed a holographic description of a quantum field theory with Galilean conformal invariance in string theory. The key observation is that such field theories may be realized as conventional…

### Toward an AdS/cold atoms correspondence: A Geometric realization of the Schrodinger symmetry

- Physics
- 2008

We discuss a realization of the nonrelativistic conformal group (the Schr\"odinger group) as the symmetry of a spacetime. We write down a toy model in which this geometry is a solution to field…

### Galilean Conformal Algebras and AdS/CFT

- Mathematics, Physics
- 2009

Non-relativistic versions of the AdS/CFT conjecture have recently been investigated in some detail. These have primarily been in the context of the Schrodinger symmetry group. Here we initiate a…