Metastable Vacua!

Yesterday I gave a talk on Supersymmetry(SUSY) breaking in a metastable vacua in the department. It was kind of discussion session which I started by giving a summary on this topic, specially the famous paper hep-th/0602239 (ISS) which has currently 345 citations. Metastable vacua is basically the ground state of a theory which has finite lifetime. Generally we encounter ground state which is perfectly stable and has infinite lifetime. But there are some theories where there can be multiple vacua which corresponds to different ground state energies. Suppose one minimum corresponds to ground state energy e and another corresponds to E. Now the tunneling between these two vacua will be negligible if

Thus although the vacuum with ground state energy E is not the true vacuum, yet it can be very stable and can have a life time same as the age of the Universe.

In the theories of dynamical SUSY breaking, SUSY is broken at the tree level, and it is restored non-perturbatively at high energy. Thus there are two vacua, one corresponds to the one with SUSY breaking and the other SUSY preserving. Since SUSY preserving vacua has ground state energy zero, this means our Universe (where SUSY is broken) is in a metastable state now. Just imagine what will happen if the Universe suddenly decays to the true vacuum tomorrow ;-). We will meet our superpartner friends then. Anyway the ISS paper which I mentioned above talks about these issues. They start with a SUSY QCD(Quantum Chromodynamics) based on a general gauge group

with flavors of quarks. This theory is asymptotically free (which means the couplings become strong at low energy and quarks become almost free at high energy) like our usual QCD. This theory is strongly coupled at low energy which makes the low energy computations go out of control. But the good thing is that this theory is dual to theory with singlets and chiral fields which transform as fundamental/anti-fundamental representation under this new gauge group. This is known as Seiberg's electromagnetic duality . The good thing is that for smaller than this theory is IR free which means that it is weakly coupled at low energy and strongly coupled at high energy. Thus we can do all the low energy computations with full control unlike in the gauge theory. This dual theory is found to break SUSY at tree level and preserve SUSY non-perturbatively after integrating out the massive chiral fields. These two vacua are however widely separated in field space and hence there is no danger of one going into another. The SUSY breaking vacuum is close to the origin whereas the SUSY preserving one is far away in field space. Since the SUSY preserving vacuum has zero vacuum energy, the SUSY breaking vacuum is not the true vacuum since it has non-zero vacuum energy. This means that the SUSY breaking vacuum is a metastable one whose life time can be parametrically made as long as the age of the Universe. This duality works for

and it is easy to see that this does not hold in case of minimal supersymmetric standard model (MSSM) for which . But no matter how close this framework is to the reality, it is very impressive from a theorist's point of view and that's the reason I guess why people all over the world is taking this model so seriously. It would be worth studying in fact, how this theoretical framework can be used to arrive at the MSSM with TeV scale SUSY breaking.