MY WORKS AT COLUMBIA
 by Changhai Lu 
During the time in Columbia, I have been working with Professor Kimyeong Lee on
theoretical physics. My research has been focused in two directions:
1. ChernSimons Theory at Finite Temperature
Along this direction, I (in collaboration with Gerald Dunne and Kimyeong Lee)
studied the finite temperature ChernSimons coefficient problem. It is well
known that the coupling between a gauge field and a fermion field in an odd
dimensional spacetime will induce a ChernSimons term in the effective action
of the theory. Perturbative finite temperature calculations of the coefficient
of such term yield a continuous function of temperature. A serious problem
arises since gauge invariance requires the coefficient to be an integer. This
problem has been puzzling physicists for more than a decade. In our work
On
Finite Temperature ChernSimons Coefficient
(Physical Review Letters 78,
3434, 1997), we computed the exact finite temperature effective action in a
(0+1)dimensional field theory that shares all the significant features of the
(2+1)dimensional ChernSimon theories. This exact result explained the origin
and meaning of the temperature dependent coefficients found previously.
2. Topological Objects in Gauge Theories
Along this direction, I have studied three related topics on topological objects
in YangMillsHiggs Systems.
In Two
Massive and one Massless Sp(4) Monopoles
(Physical Review D 57,
5260, 1998), Kimyeong and I explored a BPS state made of two massive and one massless
monopole in an Sp(4) theory with the gauge symmetry broken to SU(2)×U(1). This
monopole system carries a purely Abelian total magnetic charge and is a highly
nontrivial system containing a nonAbelian cloud. One of the major topics in
monopole physics is to compute the moduli space metrics which not only determine
their low energy dynamics but also play an important role in the study of
nonperturbative effects of gauge theories. It turns out that computing moduli
space metrics is quite difficult and so far only a few exact results are known.
In this work, we computed the exact moduli space metric of this Sp(4) system by
employing the Nahm formalism. We also constructed field configurations with axial
symmetry and analyzed in detail the properties of various submanifolds of the
moduli space.
In SU(2)
Calorons and Magnetic Monopoles (Physical Review D 58, 025011, 1998),
Kimyeong and I investigated a single SU(2) caloron, or periodic instanton, with
nontrivial Higgs expectation value at spatial infinity. This work generalized
the previous results by considering gauge symmetry breaking. We constructed the
explicit field configuration of the caloron and studied various limits. From this
analysis we found a new picture of instantons in which an instanton is composed
of two selfdual monopoles of opposite magnetic charge. As an application of the
constituent monopole picture, we computed the moduli space metric of the caloron.
In TwoMonopole
Systems and the Formation of NonAbelian Clouds
(Physical Review D 58, 125010, 1998), I studied twomonopole systems in SU(3) and Sp(4) theories
with nonAbelian unbroken gauge symmetry. I computed the energy densities of both
systems and checked several special limits. As one of the major motivations of the
work, particular attention was paid on the massless limit of the two theories and
some insights were obtained concerning the formation of nonAbelian clouds. Another
major result of the work is that the coefficient of the internal part of the moduli
space metric of the Sp(4) system was computed from the analytic expression of energy
density. This result gives an attractive mechanical interpretation to the moduli
space metric.
3. Ph.D Thesis
My Ph.D thesis is entitled
Topological
Objects in Gauge Theories.
posted on May 1, 2000 http://www.changhai.org/
