nLab
hidden sector

Contents

Context

Algebraic Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Contents

Idea

In (perturbative) quantum field theory a hidden sector is a subspace of the space of fields whose only interaction with the remaining fields is via gravity.

If one interprets the remaining fields as constituting a model for phenomenology, then in the world this describes the fields in the subspace are literally hidden, they can only bee “seen” via their gravitational pull (or via gravitational waves).

Hidden sectors as a model for the real world remain hypothetical. They have been postulated notably as a means to explain supersymmetry breaking (see below). They appear generically in perturbative string theory vacua (further below) after KK-compactification.

Definition

Specifically in Lagrangian field theory this means that the field bundle EfbΣE \overset{fb}{\to} \Sigma over spacetime Σ\Sigma is a fiber product

E(p 1,P 2)E 1× ΣE 2 E \underoverset{\simeq}{(p_1,P_2)}{\longrightarrow} E_{1} \times_\Sigma E_2

such that the interaction Lagrangian density L int\mathbf{L}_{int} is of the form

L int=p 1 *L int,1+p 2 *L int,2+L grav \mathbf{L}_{int} = p_1^\ast \mathbf{L}_{int,1} + p_2^\ast \mathbf{L}_{int,2} + \mathbf{L}_{grav}

where the first two summands are pullbacks of interactions of the fields in E 1E_1 and E 2E_2 separately, while the last summand is the interaction term of gravity coupled to the respective fields jointly.

In this case E 2E_2 is a sector hidden from E 1E_1, and conversely.

Examples

In supersymmetry breaking

The concept of gravity-mediated supersymmetry breaking resulted from study of gaugino condensation in a hidden sector. (Nilles 01)

In string theory

In string theory hidden sectors appear naturally in various ways.

Hořava-Witten theory at finite interval length gives rise to a copy of heterotic supergravity at each of the “endpoints”, which, as gauge theories, interact with each others only via bulk gravity.

In models of M-theory on G2-manifolds such as the G2-MSSM, the 4d gauge-field content arises under KK-compactification from 3-cycles in the G2-manifold fiber, and if two such do not intersect, they give rise to hidden sectors in the 4d physics. (e.g. Kane 17, section 4.4)

References

Discussion in the context of supersymmetry breaking is in

Discussion specifically in the context of the G2-MSSM is in

Last revised on March 31, 2018 at 21:12:29. See the history of this page for a list of all contributions to it.