Gravity dual for very special conformal field theories in type IIB supergravity

Yu Nakayama

doi:10.1016/j.physletb.2018.09.051

Abstract

We study holographic dual descriptions of very special conformal field theories with the T(2) symmetry. After constructing solutions in effective five dimensional Einstein gravity coupled with massive two-form fields, we uplift them to the ten dimensional type IIB supergravity, via a consistent truncation ansatz, to derive new analytical solutions in string theory. From the Kaluza–Klein ansatz in terms of the internal Sasaki–Einstein space, we obtain their field theory interpretation with concrete realizations in a large class of holographic N=1 supersymmetric conformal field theories. Null compactification of these theories yields holographic dual descriptions of non-relativistic critical systems with translational invariance but without rotational invariance such as the ones induced from a constant electromagnetic field.

Highlights

In high energy physics, the Poincare symmetry is often regarded as a fundamental assumption, but it is theoretically possible that it is merely an accidental low energy symmetry
One way to break the Lorentz symmetry while preserving the translational symmetry is to choose a particular direction in space-time
There is a special “time direction” which emerges from the evolution of the universe, resulting in the breaking of the Lorentz symmetry down to a spatial rotation

Summary

Introduction

The Poincare symmetry is often regarded as a fundamental assumption, but it is theoretically possible that it is merely an accidental low energy symmetry. It is more interesting to choose a particular null direction to break the Lorentz symmetry, leading to more non-trivial residual symmetries than the mere spatial rotation. This was suggested by Cohen and Glashow sometime ago [1][2] and dubbed “very special relativity”. In [3], we have classified all the conformal extension of the very special relativity as possible candidates of the renormalization group fixed points that are consistent with the very special relativity Such theories were named “very special conformal field theories”.

Very Special Conformal Field Theories

Holographic realizations

Uplifting to type IIB supergravity

Field theory interpretation

Discussions