Elliptic genera of 2d \(\mathcal N = 2\) gauge theories. (English) Zbl 1321.81059
In a previous paper [F. Benini et al., Lett. Math. Phys. 104, No. 4, 465–493 (2014; Zbl 1312.58008)] the same authors computed the elliptic genera, i.e. the partition functions on \(\mathbb T^2\) with supersymmetric boundary conditions, for two-dimensional \(\mathcal N=2\) supersymmetric gauge theories with rank-one gauge groups. The paper reviewed here generalizes this computation to general \(\mathcal N=(2,2)\) and \(\mathcal N=(0,2)\) gauge theories. The result involves the sum of the Jeffrey-Kirwan residues [L. C. Jeffrey and F. C. Kirwan, Topology 34, No. 2, 291–327 (1995; Zbl 0833.55009)] of a meromorphic form that represents the one-loop determinant of the field theory and is defined on the moduli space of flat connections on \(\mathbb T^2\). Following the rather subtle derivation of their formula the authors apply it to several examples with both abelian and non-abelian gauge groups and discuss some dualities for \(\mathrm{U}(k)\) and \(\mathrm{SU}(k)\) theories.
Reviewer: Helmut Rumpf (Wien)
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 58J26 | Elliptic genera |
| 14D21 | Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |
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