320 research outputs found
Duality from Topological Symmetry
We describe topological gauge theories for which duality properties are
encoded by construction. We study them for compact manifolds of dimensions
four, eight and two. The fields and their duals are treated symmetrically,
within the context of field--antifield unification. Dual formulations
correspond to different gauge-fixings of the topological symmetry. We also
describe novel features in eight-dimensional theories, and speculate about
their possible "Abelian" descriptions.Comment: 30 pages, harvmac file, references adde
Coadjoint Orbits, Cocycles and Gravitational Wess-Zumino
About 30 years ago, in a joint work with L. Faddeev we introduced a geometric
action on coadjoint orbits. This action, in particular, gives rise to a path
integral formula for characters of the corresponding group . In this paper,
we revisit this topic and observe that the geometric action is a 1-cocycle for
the loop group . In the case of being a central extension, we construct
Wess-Zumino (WZ) type terms and show that the cocycle property of the geometric
action gives rise to a Polyakov-Wiegmann (PW) formula. In particular, we obtain
a PW type formula for the Polyakov's gravitational WZ action. After
quantization, this formula leads to an interesting bulk-boundary decoupling
phenomenon previously observed in the WZW model. We explain that this
decoupling is a general feature of the Wess-Zumino terms obtained from
geometric actions, and that in this case the path integral is expressed in
terms of the 2-cocycle which defines the central extension. In memory of our
teacher Ludwig Faddeev.Comment: 15 pages, v2: references adde
Integrating Over Higgs Branches
We develop some useful techinques for integrating over Higgs branches in
supersymmetric theories with 4 and 8 supercharges. In particular, we define a
regularized volume for hyperkahler quotients. We evaluate this volume for
certain ALE and ALF spaces in terms of the hyperkahler periods. We also reduce
these volumes for a large class of hyperkahler quotients to simpler integrals.
These quotients include complex coadjoint orbits, instanton moduli spaces on
R^4 and ALE manifolds, Hitchin spaces, and moduli spaces of parabolic Higgs
bundles on Riemann surfaces. In the case of Hitchin spaces the evaluation of
the volume reduces to a summation over solutions of Bethe Ansatz equations for
the non-linear Schroedinger system. We discuss some applications of our
results.Comment: 32pp. harvmac big mode; v.2 34pp. typos fixed, sections 4.1, 5.2
substantially improve
Two-dimensional Conformal Field Theories on AdS_{2d+1} Backgrounds
Various exact two-dimensional conformal field theories with AdS_{2d+1} target
space are constructed. These models can be solved using bosonization
techniques. Some examples are presented that can be used in building
perturbative superstring theories with AdS backgrounds, including AdS_5.Comment: 36 pages, harvma
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