66,513 research outputs found
The Heat Kernel on AdS_3 and its Applications
We derive the heat kernel for arbitrary tensor fields on S^3 and (Euclidean)
AdS_3 using a group theoretic approach. We use these results to also obtain the
heat kernel on certain quotients of these spaces. In particular, we give a
simple, explicit expression for the one loop determinant for a field of
arbitrary spin s in thermal AdS_3. We apply this to the calculation of the one
loop partition function of N=1 supergravity on AdS_3. We find that the answer
factorizes into left- and right-moving super Virasoro characters built on the
SL(2, C) invariant vacuum, as argued by Maloney and Witten on general grounds.Comment: 46 pages, LaTeX, v2: Reference adde
Character Expansions for the Orthogonal and Symplectic Groups
Formulas for the expansion of arbitrary invariant group functions in terms of
the characters for the Sp(2N), SO(2N+1), and SO(2N) groups are derived using a
combinatorial method. The method is similar to one used by Balantekin to expand
group functions over the characters of the U(N) group. All three expansions
have been checked for all N by using them to calculate the known expansions of
the generating function of the homogeneous symmetric functions. An expansion of
the exponential of the traces of group elements, appearing in the finite-volume
gauge field partition functions, is worked out for the orthogonal and
symplectic groups.Comment: 20 pages, in REVTE
Generalized Kazakov-Migdal-Kontsevich Model: group theory aspects
The Kazakov-Migdal model, if considered as a functional of external fields,
can be always represented as an expansion over characters of group. The
integration over "matter fields" can be interpreted as going over the {\it
model} (the space of all highest weight representations) of . In the case
of compact unitary groups the integrals should be substituted by {\it discrete}
sums over weight lattice. The version of the model is the Generalized
Kontsevich integral, which in the above-mentioned unitary (discrete) situation
coincides with partition function of the Yang-Mills theory with the target
space of genus and holes. This particular quantity is always a
bilinear combination of characters and appears to be a Toda-lattice
-function. (This is generalization of the classical statement that
individual characters are always singular KP -functions.) The
corresponding element of the Universal Grassmannian is very simple and somewhat
similar to the one, arising in investigations of the string models.
However, under certain circumstances the formal sum over representations should
be evaluated by steepest descent method and this procedure leads to some more
complicated elements of Grassmannian. This "Kontsevich phase" as opposed to the
simple "character phase" deserves further investigation.Comment: 29 pages, UUITP-10/93, FIAN/TD-07/93, ITEP-M4/9
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