| 1. |
- Dimofte, T., et al.
(author)
-
Exact results for perturbative Chern-Simons theory with complex gauge group
- 2009
-
In: Communications in Number Theory and Physics. - : International Press of Boston. - 1931-4523 .- 1931-4531. ; 3:2, s. 363-443
-
Journal article (peer-reviewed)abstract
- We develop several methods that allow us to compute all-loop partition functions in perturbative Chern-Simons theory with complex gauge group GC, sometimes in multiple ways. In the background of a non-abelian irreducible flat connection, perturbative GC invariants turn out to be interesting topological invariants, which are very different from the finite-type (Vassiliev) invariants usually studied in a theory with compact gauge group G and a trivial flat connection. We explore various aspects of these invariants and present an example where we compute them explicitly to high loop order. We also introduce a notion of "arithmetic topological quantum field theory" and conjecture (with supporting numerical evidence) that SL(2, C) Chern-Simons theory is an example of such a theory.
|
|
| 2. |
- Pioline, B., et al.
(author)
-
The automorphic NS5-brane
- 2009
-
In: Communications in Number Theory and Physics. - : International Press of Boston. - 1931-4531 .- 1931-4523. ; 3:4, s. 697-754
-
Journal article (other academic/artistic)abstract
- Understanding the implications of SL(2, Z) S-duality for the hyper-multiplet moduli space of type II string theories has led to much progress recently in uncovering D-instanton contributions. In this work, we suggest that the extended duality group SL(3, Z), which includes both S-duality and Ehlers symmetry, may determine the contributions of D5 and NS5-branes. We support this claim by automorphizing the perturbative corrections to the "extended universal hypermultiplet," a five-dimensional universal SO(3)\SL(3, R) subspace which includes the string coupling, overall volume, Ramond zero-form and six-form and NS axion. Using the non-Abelian Fourier expansion of the Eisenstein series attached to the principal series of SL(3, R), worked out many years ago by Vinogradov, Takhtajan and Bump, we extract the contributions of D(-1)-D5 and NS5-brane instantons, corresponding to the Abelian and non-Abelian coefficients, respectively. In particular, the contributions of k NS5-branes can be summarized into a vector of wave functions Psi(k,l), l = 0,..., k - 1, as expected on general grounds. We also point out that for more general models with a symmetric moduli space K\G, the minimal theta series of G generates an infinite series of exponential corrections of the form required for "small" D(-1)-D1-D3-D5-NS5 instanton bound states. As a mathematical spin-off, we make contact with earlier results in the literature about the spherical vectors for the principal series of SL(3, R) and for minimal representations.
|
|
