  Previously we have indicated the relationship between quantum groups and
strings via WZWN models. In this note we discuss this relationship further and
point out its possible applications to cuprates and related materials. The
connection between quantum groups and strings is one way of seeing the validity
of our previous conjecture [i.e. that a theory for cuprates may be constructed
on the basis of quantum groups]. The cuprates seems to exhibit statistics,
dimensionality and phase transitions in novel ways. The nature of excitations
[i.e. quasiparticle or collective] must be understood. The Hubbard model
captures some of the behaviour of the phase transitions in these materials. On
the other hand the phases such as stripes in these materials bear relationship
to quantum group or string-like solutions. One thus expects that the relevant
solutions of Hubbard model may thus be written in terms of stringy solutions.
In short this approach may lead to the non-perturbative formualtion of Hubbard
and other condensed matter Hamiltonians. The question arises that how a 1-d
based symmetry such as quantum groups can be relevant in describing a 3-d
[spatial dimensions] system such as cuprates. The answer lies in the key
observation that strings which are 1-d objects can be used to describe physics
in $d$ dimensions. For example gravity [which is a 3-d [spatial] plus time]
phenomenon can be understood in terms of 1-d strings. Thus we expect that 1-d
quantum group object induces physics in 2-d and 3-d which may be relevant to
the cuprates.
