Photon defects in Noncommutative Standard Model Candidates Joerg Jaeckel* Valentin V. Khoze † Andreas Ringwald * * DESY, † IPPP Durham

1. Introduction

Noncommutative 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 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 to? Additional massless U(1)‘s are ruled out The UV/IR mixing spoils U(1)‘s with nonvanishing trace as candidates for the photon The restrictions on the field content make it impossible to construct a model which has only one massless U(1) without an admixture of the trace-U(1) This rules out models fulfilling all those restrictions

Where to U(A)£U(B)£  ! H. We want a photon! We need unbroken U(1)  (1) U(1)  is traceless but there are additional U(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 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 couplings The running couplings are defined by U(1) is asymptotically free in the IR

Scattering 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

 2 does not vanish anymore SUSY breaking leads to non-vanishing

A 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 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. General Case

We learned so far... The trace-U(1) cannot be neglected But the trace-U(1) cannot be the photon Even a small admixture of a trace-U(1) to the photon is unacceptable The photon must be the only massless (unbroken) U(1) & It is constructed from a completely traceless generator

This is impossible One can prove: If the allowed fields break U(A)£U(B)£...! H. H nontrivial. Then one generator of H has nonvanishing trace and generates a U(1) subgroup. This rules out models fulfilling all mentioned restrictions

4. Conclusions

Conclusions 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