5 research outputs found
Index theorem for topological excitations on R^3 * S^1 and Chern-Simons theory
We derive an index theorem for the Dirac operator in the background of
various topological excitations on an R^3 \times S^1 geometry. The index
theorem provides more refined data than the APS index for an instanton on R^4
and reproduces it in decompactification limit. In the R^3 limit, it reduces to
the Callias index theorem. The index is expressed in terms of topological
charge and the eta-invariant associated with the boundary Dirac operator.
Neither topological charge nor eta-invariant is typically an integer, however,
the non-integer parts cancel to give an integer-valued index. Our derivation is
based on axial current non-conservation--an exact operator identity valid on
any four-manifold--and on the existence of a center symmetric, or approximately
center symmetric, boundary holonomy (Wilson line). We expect the index theorem
to usefully apply to many physical systems of interest, such as low temperature
(large S^1, confined) phases of gauge theories, center stabilized Yang-Mills
theories with vector-like or chiral matter (at S^1 of any size), and
supersymmetric gauge theories with supersymmetry-preserving boundary conditions
(also at any S^1). In QCD-like and chiral gauge theories, the index theorem
should shed light into the nature of topological excitations responsible for
chiral symmetry breaking and the generation of mass gap in the gauge sector. We
also show that imposing chirally-twisted boundary condition in gauge theories
with fermions induces a Chern-Simons term in the infrared. This suggests that
some QCD-like gauge theories should possess components with a topological
Chern-Simons phase in the small S^1 regime.Comment: 29 pages, refs added, published versio
The superstring Hagedorn temperature in a pp-wave background
The thermodynamics of type IIB superstring theory in the maximally
supersymmetric plane wave background is studied. We compute the thermodynamic
partition function for non-interacting strings exactly and the result differs
slightly from previous computations. We clarify some of the issues related to
the Hagedorn temperature in the limits of small and large constant RR 5-form.
We study the thermodynamic behavior of strings in the case of geometries in the presence of NS-NS and RR 3-form backgrounds. We
also comment on the relationship of string thermodynamics and the thermodynamic
behavior of the sector of Yang-Mills theory which is the holographic dual of
the string theory.Comment: 22 pages, JHEP style, minor misprints corrected, some comments adde
Photon mixing in universes with large extra-dimensions
In presence of a magnetic field, photons can mix with any particle having a
two-photon vertex. In theories with large compact extra-dimensions, there
exists a hierachy of massive Kaluza-Klein gravitons that couple to any photon
entering a magnetic field. We study this mixing and show that, in comparison
with the four dimensional situation where the photon couples only to the
massless graviton, the oscillation effect may be enhanced due to the existence
of a large number of Kaluza-Klein modes. We give the conditions for such an
enhancement and then investigate the cosmological and astrophysical
consequences of this phenomenon; we also discuss some laboratory experiments.
Axions also couple to photons in the same way; we discuss the effect of the
existence of bulk axions in universes with large extra-dimensions. The results
can also be applied to neutrino physics with extra-dimensions.Comment: 41 pages, LaTex, 6 figure