Photon defects in Noncommutative Photon defects in Noncommutative Standard Model CandidatesStandard Model Candidates

Joerg Jaeckel*Valentin V. Khoze†

Andreas Ringwald *

* DESY, †IPPP Durham

1. Introduction

Noncommutative Field TheoriesNoncommutative Field Theories

• Noncommutative field theories arise from

D-Branes and String theory• Noncommutative space-time means that

coordinates don’t commute

This violates Lorentz symmetry!• In noncommutative Field theory ordinary

multiplication is replaced by the Moyal product

Restrictions on Model BuildingRestrictions on Model Building

• NC gauge invariance is very restrictive:– Gauge groups are restricted to U(N)– Fields can only transform as (anti-)fundamental,

adjoint or bifundamentals– Charges of the fields are restricted to 0, §1

• UV/IR mixing in the trace-U(1) sector– Universality is lost; low energy behavior typically

depends on very massive modes– The running gauge coupling of the trace-U(1)

becomes asymptotically IR free– A new Lorentz Violating part appears in the

polarization tensor for this trace-U(1)

Where toWhere to

• U(A)£U(B)£! H. • We want a photon!

We need unbroken U(1)

(1) U(1) is traceless but there are additionalU(1)‘s with nonvanishing trace.

(2) U(1) has nonvanishing trace.

(3) U(1) has nonvanishing trace and there are additional U(1)‘s with nonvanishing trace

NC model building is in trouble!!

2. Additional U(1)‘s?

The polarization tensorThe polarization tensor

• Noncommutativity introduces a new vector

• This allows for a Lorentz violating contribution to the polarization tensor

• is very bad (see later), but absent when SUSY is unbroken.

Running couplingsRunning couplings

• The running couplings are defined by

U(1) is asymptotically free in the IR

ScatteringScattering

• In scattering the momentum scales k and are non-vanishing

• U(1) gauge coupling small but non vanishing

Additional massless U(1)‘s are ruled out by observations

3. A mass for Trace U(1)‘s

22 does not vanish anymore does not vanish anymore

• SUSY breaking leads to non-vanishing

A massive polarizationA massive polarization

• To find out about the mass, let us solve the equations of motion. With

and the boson flying in the 3-direction we find

for the two transverse polarizations

• One polarization has a mass

This cannot be the photon

Mixing Trace and traceless partsMixing Trace and traceless parts

• ... doesn‘t help.• Example U(2) broken by fundamental Higgs:

EOM for „bad“ direction

• The originally massless combination receives mass

Even a small admixture of a trace-U(1) is unacceptable

4. Conclusions

ConclusionsConclusions

• Trace-U(1) groups cannot be the photon• Even a small admixture is unacceptable• Additional trace-U(1) subgroups are observable

and cannot be massless• We cannot obtain a completely traceless U(1)

without having additional unbroken trace-U(1)‘s• This severly limits phenomenological prospects

if NC Standard Model building