# The Geroch Group in One Dimension

@inproceedings{Penna2021TheGG, title={The Geroch Group in One Dimension}, author={Robert F. Penna}, year={2021} }

We study the dimensional reduction of general relativity to a single null spacetime dimension. The dimensionally reduced theory is a theory of six scalar fields governed by three constraints. It has an infinite dimensional symmetry which is an enhanced version of the Geroch group. To get a local action of the symmetry on solution space, we need to introduce an infinite tower of new fields and new constraints. The symmetry appears to be a hyperbolic Kac-Moody algebra, with the caveat that some…

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## References

SHOWING 1-10 OF 24 REFERENCES

### Vertex algebras

- Mathematics
- 1997

In this paper we try to define the higher dimensional analogues of vertex algebras. In other words we define algebras which we hope have the same relation to higher dimensional quantum field theories…

### Twistor Actions for Integrable Systems

- PhysicsJournal of High Energy Physics
- 2021

Abstract
Many integrable systems can be reformulated as holomorphic vector bundles on twistor space. This is a powerful organizing principle in the theory of integrable systems. One shortcoming is…

### The Geroch group and non-Hausdorff twistor spaces

- Mathematics
- 1988

By reducing the Ward correspondence, the authors show that there is a correspondence between stationary axisymmetric solutions of the vacuum Einstein equations and a class of holomorphic vector…

### Cosmological Billiards

- Physics, Mathematics
- 2002

It is shown in detail that the dynamics of the Einstein-dilaton-pform system in the vicinity of a spacelike singularity can be asymptotically described, at a generic spatial point, as a billiard…

### Duality and Hidden Symmetries in Gravitational Theories

- Physics
- 1999

Duality is presently considered the key to the Holy Grail of String Theory— it is supposed to provide links between the five known different superstring theories in ten dimensions, hoped to be just…

### On the Geroch Group

- Mathematics
- 1986

2014 The set of stationary, axially symmetric solutions of Einstein’s vacuum field equations is acted on by some infinite dimensional group (Geroch). A precise definition of this group is given as…

### Vertex algebras, Kac-Moody algebras, and the Monster.

- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1986

An integral form is constructed for the universal enveloping algebra of any Kac-Moody algebras that can be used to define Kac's groups over finite fields, some new irreducible integrable representations, and a sort of affinization of anyKac-moody algebra.

### A Lax Operator for $d=2$ $N=2$ Supergravity

- Physics
- 2021

General relativity and supergravity become integrable systems after dimensional reduction to two spacetime dimensions. This means the equations of motion can be encoded in the flatness condition for…

### Einstein–Rosen waves and the Geroch group

- Physics
- 2021

Under the action of the Geroch group, the Minkowski metric can be transformed into any vacuum metric with two commuting Killing vectors. In principle, this reduces the problem of deriving vacuum…